Volume 8 Number 1, 2023 Volume 8 Number 1, 2023 Faculty of Social Sciences, Enugu State University of Science And Technology EDITOR-IN-CHIEF Prof. Oby Omeje MANAGING EDITOR Prof. Barnabas Nwankwo PUBLISHED BY ENUGU STATE UNIVERSITY OF SCIENCE & TECHNOLOGY JOURNAL OF SOCIAL SCIENCES & HUMANITIES 1 Establishment of the Kifilideen, Lukmon and Fatimo Scales in the Determination of the Magnitude of Population of any Particular Entity and other Development Kifilideen L. Osanyinpeju1*, Lukmon A. Osanyinpeju 2, Fatimo F. Osanyinpeju 3 1Agricultural and Bio-Resources Engineering Department, College of Engineering, Federal University of Agriculture Abeokuta, Ogun State, Nigeria 2Mechanical Engineering Department, Faculty of Engineering, University of Lagos, Lagos State, Nigeria 3Mathematics Department, School of Education, Aderiran Ogunsanya College of Education, AOCDED, Ijanikin, Ojo, Lagos State in Affiliation to Ekiti State University, Nigeria * Corresponding author: amkifilideenosanyinpeju@gmail.com, prof_4us@yahoo.com Abstract: Overtime the parameters commonly used to measure the population of a location are number of population in figure, population density in ๐‘๐‘’๐‘œ๐‘๐‘™๐‘’/๐‘˜๐‘š2 and population growth in percentage. These parameters are not enough to quantify the intensity of the population of the entities of a place. The previous methods of measuring population which are number of population in figure and population density in ๐‘๐‘’๐‘œ๐‘๐‘™๐‘’/๐‘˜๐‘š2 have huge and large figure which is difficult to work with and interpret. Knowing the magnitude of the population of the entity of an area would help to figure the intensity and impact of such entity in that area. This study established the Kifilideen, Lukmon and Fatimo scales to determine the magnitude of the population of any particular entity of a state, nation or location. The research work also invented the Lukmon (Power of base 3) and AntiLumon (Antipower of base 3) with Fatimo (Power of base 8) and AntiFatimo (Antipower of base 8) tables in evaluating the magnitude of the population of an entity. The study provides formulas for the determination of the magnitude of both the population and population density of any particular entity such as human being, bacteria and plant which would help to decide the level of impact of that entity in such location. The magnitude of population provides a simplify form of representing the population of a place. Keywords Antikifilideen table, AntiFatimo table, AntiLukmon table, Entity, Fatimo table, Kifilideen table, Lukmon table, Kifilideen Scales, Population, Population Scales Introduction The population of an entity of a location is the number of the specify entity found in the location (Tarsi and Tuff, 2012). In micro level; entities of a population in a location can be atoms, molecules, ions or particles while in macro levels; the entities of a population can be plants, animals or human. In both classes of levels of the entities of the population: the increase in the entities of a location lead to the increase in the magnitude of interaction between individual members of the entities, members of other entities in contact and with the location. The elevation of the magnitude of the population of a particular entity; bring about higher tendency of change in the system which can be constructive or destructive change. For example, the population of plant presents in a farmland determines the loss of nutrient in such farmland per time (Sumithra et al., 2013). The increase in the magnitude of plants in the soil; lead to the increase in the loss of nutrient in that soil (Bashagaluke et al., 2018). Meanwhile, the higher the magnitude of residue of plants that exist in the soil the more the soil becomes more replenish with nutrients (Torma et al., 2017). mailto:prof_4us@yahoo.com 2 Overtime the parameters commonly used to measure the population of a location are number of population in figure, population density in ๐‘๐‘’๐‘œ๐‘๐‘™๐‘’/๐‘˜๐‘š2 and population growth in percentage (Stephan and David, 2017). These parameters are not enough to quantify the intensity of the population of the entities of a place. The previous methods of measuring population which are number of population in figure and population density in ๐‘๐‘’๐‘œ๐‘๐‘™๐‘’/๐‘˜๐‘š2 have huge and large figure which is difficult to work with and interpret. The conversion of these figures to magnitude form would easier calculation when determining the population of place over a given time in which when final answer is obtained the magnitude can be converted back to figure. It would also provide easy interpretation of population. The magnitude of the population of an entity is an easy and simplified form of representing the population of an entity. The magnitude of the population can be useful in the classification of the population of an entity into levels and sizes. The magnitude of a population of a particular entity such as human being, plant, animal, bacteria and virus presents in a state, nation or location determine the strength and weakness of such state, nation or location. Knowing the magnitude of the population of the entity in an area would help to figure the intensity and impact of such entity in that area. The population of a country is essential factor that serve as a weapon for social-economic, political and security development for such country (Mohammed et al., 2019). The establishment of procedure in measuring the magnitude of population of a location would supplement the conventional method in evaluating the population of a place. An insight in the magnitude of both population and population density of an entity of a location are essential and integral part of evaluating the level of impact and intensity of the entity can create in such location. The magnitude of both population and population density of different location of a place could be adopted in determining the sharing formula of the revenue allocation, demarcation of constituencies, creation of state and local government, allocation of representation in national and state assemblies among the different regions of the location (Domini et al., 2016). The magnitude of the population and population density is a crucial parameter that determines the economic strength and size of a nationโ€™s work force. The area or region with very high magnitude of population has very high election power during voting of people into post in a country. The larger magnitude of population density indicates higher human capital of a country. In case of the population of human being in a country, a large magnitude of the young who are the active participants of the economic activity of such country in the demographic composition is a blessing to that given country which lead to increasing the level of technology, production output, social amenities otherwise can lead to scarcity and increase in price of foods and service; lower per capital income as a result of increase in the magnitude of the population on natural resource and high magnitude of the population density; decrease capital accumulation and savings; impact poverty and unemployment; environmental complications such as rise in CO2, global warming, pollution (Agarwal, 2014). The rapid increase in rate of the magnitude of the population growth in Nigeria as a case study results to severe problem to national development, unemployment, poverty and insecurity issues. A very high magnitude of people in a small space will lead to various types of congestion in such space or location (Kozlak and Wach, 2018). The Kifilideen magnitude of population of entities of a location is established by determining the power the base of 11 is raised to claim the population of the entities. The power obtain can indicate the level of the population on the Kifiilideen scale. As the population of a location is increasing; so the magnitudes of the population is also increasing on the Kifilideen scale. The other scales 3 established in this paper in determining the magnitude of a population are Lukmon and Fatimo scales. The conversion of the magnitude on one scale to another was also established. The Lukmon and Fatimo scales are the scales of the magnitude of a population obtain by determining the power in which base of 3 and 8 are raised respectively to claim the population of the entities of a location. In order to evaluate the magnitude of the population of Lukmon and Fatimo scales the Lukmon (Power of base 3) and AntiLukmon (Antipower of base 3) tables with Fatimo (Power of base 8) and AntiFatimo (Anitpower of base 8) tables were inaugurated. The Kilifideen (Power of base 11) and AntiKifilideen (Anitpower of base 11) tables to evaluate the magnitude of the population on the Kifilideen scale had been established in 2019 (Osanyinpeju, 2019). The understanding of the utilization of the methods used in this paper in describing and measuring the population of location can be done by having full interaction with the procedure illustrated in the method. As the saying, you can only know more about something in different ways when you continue having interaction with that thing in different pattern (Osanyinpeju, 2020a; Osanyinpeju, 2020b). If you distance yourself from it you know less of it and some fact about that thing become hidden (Osanyinpeju, 2021). This study established the Kifilideen, Lukmon and Fatimo scales to determine the magnitude of the population of any particular entity of a location. The research work also invented the Lukmon (Power of base 3) and AntiLumon (Antipower of base 3) with Fatimo (Power of base 8) and AntiFatimo (Antipower of base 8) tables in evaluating the magnitude of the population of an entity. MATERIALS AND METHODS Definition of terms used in the methodology Kifilideen and AntiKifilideen tables Kifilideen table is the table which pinpoint the power in which base 11 has to be raised to signify a given number (Osanyinpeju, 2020c). AntiKifilideen table is the table that specifies the value that would be achieved when evaluating power of base 11 (Osanyinpeju, 2019). Osanyinpeju and AntiOsanyinpeju tables Osanyinpeju table is the table which offers the power in which base 2 has to be raised to express a given number (Osanyinpeju et al., 2019). AntiOsanyinpeju table is the table that stipulates the value that would be obtained for a given power of base 2. Lekan and AntiLekan Tables Lekan table is the table which point out the power in which base 5 has to be raised to proclaim a given number. The table is employed to transform ordinary number to power of base 5 (Osanyinpeju, 2020c). Antilekan table is the table that specifies the value that would be achieved when evaluating power of base 5. Lukmon and AntiLukmon tables 4 Lukmon table is a table which indicates the power in which base 3 has to be raised to stand for a given number. The table is used to transform ordinary number to power of base 3. The table was inaugurated in order to carry out computation related to power of base 3 without using calculator. AntiLukmon table is the table which is used to reverse the power of base 3 of a number back to ordinary number. The AntiLukmon table was originated to help in removing the power of base 3 of any number to ordinary number. Fatimo and AntiFatimo tables Fatimo table is the table which point out the power in which base 8 has to be raised to convey a given number. The table is used to change ordinary number to power of base 8. AntiFatimo table is the table that stipulates the value that would be obtained for a given power of base 8. Logarithm table Logarithm table is a table of logarithm of number in base 10 (Macrae et al., 2016) Kifilideen, Lukmon and Fatimo Scales Kifilideen Scale is a scale of the magnitude of a population achieves by authenticating the power in which base of 11 is raised to claim the population of the entities of a location using Kifilideen table. While Lukmon Scale is a scale of the magnitude of a population obtains by authenticating the power in which base of 3 is raised to claim the population of the entities of a location using Lukmon table. More so, Fatimo Scale is a scale of the magnitude of a population acquires by ascertaining the power in which base of 8 is raised to claim the population of the entities of a location using Fatimo table. Invention of Lukmon (Power of base 3) and AntiLumon (Antipower of base 3) with Fatimo (Power of base 8) and AntiFatimo (Antipower of base 8) tables in evaluating the magnitude of the population of an entity Tables 1 โ€“ 8 present the invention of Lukmon (Power of base 3) and AntiLumon (Antipower of base 3) with Fatimo (Power of base 8) and AntiFatimo (Antipower of base 8) tables in evaluating the magnitude of the population of an entity. The Lukmon (Power of base 3) and Fatimo (Power of base 8) tables with AntiLukmon (Antipower of base 3) and AntiFatimo (Antipower of base 8) tables were established based on manual method of computing and also with the assistance of calculator. However, the tables can be used to solve modern real life problem without the use of calculator (Osanyinpeju, 2022). The genesis of the manual method used to construct these tables mentioned above is demonstrated as follows: To convert 7 to the power of base 3, you start by looking for the value to be raised by 3 to give 7. 31 = 3 which is less than the 7 to be achieved. Then, the power of the base three is increased. So, we try 31.8 which gives 7.2247. The value obtained is greater than the value we needed that is 7. Then, the power is reduced to 1.7. Meanwhile, 31.7 = 6.4730. This value attained is getting closer to the required value. So, 31.77 is tried which gives 6.9904 but 31.78 gives 7.0677. The power is then given a 3 decimal places trial. For31.771 we have 6.9981 but 31.772 produces 7.0058. With this power 1.771 we are almost there. We go for power of 4 decimal places. Trying 31.7712 we obtained 6.9997. For 5 decimal places, 5 31.77124 gives 7.0000. Since the table was constructed base on power of 4 decimal places. So the power in which 3 must be raised to give 7 is 1.7712 indicating Luk (7) is 1.7712 or 7 = 3 ๐ฟ๐‘ข๐‘˜ (7) = 31.7712. 6 Table 1: Lukmon (Power of base 3) of Number ๐’™ โ†’ ๐‘ณ๐’–๐’Œ ๐’™ Difference (x) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 1 0.0000 0.0868 0.1660 0.2388 0.3063 0.3691 0.4278 0.4830 0.5350 0.5842 65 130 194 258 321 384 446 508 570 2 0.6309 0.6753 0.7177 0.7581 0.7969 0.8340 0.8697 0.9041 0.9372 0.9691 38 75 112 149 186 223 260 296 333 3 1.0000 1.0298 1.0587 1.0868 1.1139 1.1403 1.1660 1.1909 1.2152 1.2388 27 53 79 106 132 158 184 210 236 4 1.2619 1.2843 1.3063 1.3277 1.3486 1.3691 1.3891 1.4087 1.4278 1.4466 21 41 61 82 102 122 143 163 183 5 1.4650 1.4830 1.5007 1.5180 1.5350 1.5517 1.5681 1.5842 1.6001 1.6156 17 33 50 57 83 100 116 133 149 6 1.6309 1.6460 1.6608 1.6753 1.6897 1.7038 1.7177 1.7314 1.7449 1.7581 14 28 42 56 70 84 98 112 126 7 1.7712 1.7842 1.7969 1.8094 1.8218 1.8340 1.8461 1.8580 1.8697 1.8813 12 24 37 49 61 73 85 97 109 8 1.8928 1.9041 1.9153 1.9263 1.9372 1.9480 1.9586 1.9691 1.9795 1.9898 11 22 32 43 54 64 75 86 97 9 2.0000 2.0101 2.0200 2.0298 2.0396 2.0492 2.0587 2.0682 2.0775 2.0868 10 19 29 38 48 58 67 77 86 10 2.0959 2.1050 2.1139 2.1228 2.1316 2.1403 2.1489 2.1575 2.1660 2.1743 9 17 26 35 43 52 61 69 78 11 2.1827 2.1909 2.1991 2.2072 2.2152 2.2231 2.2310 2.2388 2.2466 2.2542 8 16 24 32 40 48 56 63 71 12 2.2619 2.2694 2.2769 2.2843 2.2917 2.2990 2.3063 2.3135 2.3206 2.3277 7 15 22 29 37 44 51 58 66 13 2.3347 2.3417 2.3486 2.3555 2.3623 2.3691 2.3758 2.3825 2.3891 2.3956 6 14 20 27 34 41 47 54 61 14 2.4022 2.4087 2.4151 2.4215 2.4278 2.4341 2.4404 2.4466 2.4528 2.4589 6 13 19 25 31 38 44 50 57 15 2.4650 2.4710 2.4770 2.4830 2.4889 2.4948 2.5007 2.5065 2.5123 2.5180 6 12 18 24 29 35 41 47 53 16 2.5237 2.5294 2.5350 2.5406 2.5462 2.5517 2.5572 2.5627 2.5681 2.5735 6 11 17 22 28 33 39 44 50 17 2.5789 2.5842 2.5895 2.5948 2.6001 2.6053 2.6105 2.6156 2.6208 2.6259 5 10 16 21 26 31 36 42 47 18 2.6309 2.6360 2.6410 2.6460 2.6509 2.6559 2.6608 2.6657 2.6705 2.6753 5 10 15 20 25 30 34 39 44 19 2.6801 2.6849 2.6897 2.6944 2.6991 2.7038 2.7084 2.7131 2.7177 2.7223 5 9 14 19 23 28 33 37 42 20 2.7268 2.7314 2.7359 2.7404 2.7449 2.7493 2.7537 2.7581 2.7625 2.7669 4 9 13 18 22 27 31 36 40 21 2.7712 2.7756 2.7799 2.7842 2.7884 2.7927 2.7969 2.8011 2.8053 2.8094 4 8 13 17 21 25 30 34 38 22 2.8136 2.8177 2.8218 2.8259 2.8300 2.8340 2.8381 2.8421 2.8461 2.8501 4 8 12 16 20 24 28 32 36 23 2.8540 2.8580 2.8619 2.8658 2.8697 2.8736 2.8775 2.8813 2.8852 2.8890 4 8 12 16 19 23 27 31 35 24 2.8928 2.8966 2.9003 2.9041 2.9078 2.9116 2.9153 2.9190 2.9226 2.9263 4 7 11 15 19 22 26 30 33 25 2.9299 2.9336 2.9372 2.9408 2.9444 2.9480 2.9515 2.9551 2.9586 2.9621 4 7 11 14 18 21 25 29 32 26 2.9656 2.9691 2.9726 2.9761 2.9795 2.9830 2.9864 2.9898 2.9932 2.9966 3 7 10 14 17 21 24 27 31 27 3.0000 3.0034 3.0067 3.0101 3.0134 3.0167 3.0200 3.0233 3.0266 3.0298 3 7 10 13 17 20 23 26 30 28 3.0331 3.0363 3.0396 3.0428 3.0460 3.0492 3.0524 3.0556 3.0587 3.0619 3 6 10 13 16 19 22 26 29 29 3.0650 3.0682 3.0713 3.0744 3.0775 3.0806 3.0837 3.0868 3.0898 3.0929 3 6 9 12 15 19 22 25 28 30 3.0959 3.0989 3.1020 3.1050 3.1080 3.1109 3.1139 3.1169 3.1199 3.1228 3 6 9 12 15 18 21 24 27 31 3.1257 3.1287 3.1316 3.1345 3.1374 3.1403 3.1432 3.1461 3.1489 3.1518 3 6 9 12 14 17 20 23 26 32 3.1546 3.1575 3.1603 3.1631 3.1660 3.1688 3.1716 3.1743 3.1771 3.1799 3 6 8 11 14 17 20 22 25 33 3.1827 3.1854 3.1882 3.1909 3.1936 3.1963 3.1991 3.2018 3.2045 3.2072 3 5 8 11 14 16 19 22 24 34 3.2098 3.2125 3.2152 3.2178 3.2205 3.2231 3.2258 3.2284 3.2310 3.2336 3 5 8 11 13 16 18 21 24 35 3.2362 3.2388 3.2414 3.2440 3.2466 3.2491 3.2517 3.2542 3.2568 3.2593 3 5 8 10 13 15 18 21 23 36 3.2619 3.2644 3.2669 3.2694 3.2719 3.2744 3.2769 3.2794 3.2819 3.2843 2 5 7 10 12 15 17 20 22 37 3.2868 3.2893 3.2917 3.2941 3.2966 3.2990 3.3014 3.3039 3.3063 3.3087 2 5 7 10 12 15 17 19 22 7 38 3.3111 3.3135 3.3159 3.3182 3.3206 3.3230 3.3253 3.3277 3.3300 3.3324 2 5 7 9 12 14 17 19 21 39 3.3347 3.3370 3.3394 3.3417 3.3440 3.3463 3.3486 3.3509 3.3532 3.3555 2 5 7 9 12 14 16 18 21 40 3.3578 3.3600 3.3623 3.3646 3.3668 3.3691 3.3713 3.3736 3.3758 3.3780 2 4 7 9 11 13 16 18 20 41 3.3802 3.3825 3.3847 3.3869 3.3891 3.3913 3.3935 3.3956 3.3978 3.4000 2 4 7 9 11 13 15 18 20 42 3.4022 3.4043 3.4065 3.4087 3.4108 3.4129 3.4151 3.4172 3.4193 3.4215 2 4 6 9 11 13 15 17 19 43 3.4236 3.4257 3.4278 3.4299 3.4320 3.4341 3.4362 3.4383 3.4404 3.4424 2 4 6 8 10 13 15 17 19 44 3.4445 3.4466 3.4486 3.4507 3.4528 3.4548 3.4568 3.4589 3.4609 3.4629 2 4 6 8 10 12 14 16 18 45 3.4650 3.4670 3.4690 3.4710 3.4730 3.4750 3.4770 3.4790 3.4810 3.4830 2 4 6 8 10 12 14 16 18 46 3.4850 3.4870 3.4889 3.4909 3.4929 3.4948 3.4968 3.4987 3.5007 3.5026 2 4 6 8 10 12 14 16 18 47 3.5046 3.5065 3.5084 3.5103 3.5123 3.5142 3.5161 3.5180 3.5199 3.5218 2 4 6 8 10 12 13 15 17 48 3.5237 3.5256 3.5275 3.5294 3.5313 3.5332 3.535 3.5369 3.5388 3.5406 2 4 6 8 9 11 13 15 17 49 3.5425 3.5443 3.5462 3.5480 3.5499 3.5517 3.5536 3.5554 3.5572 3.5591 2 4 6 7 9 11 13 15 17 50 3.5609 3.5627 3.5645 3.5663 3.5681 3.5699 3.5717 3.5735 3.5753 3.5771 2 4 5 7 9 11 13 14 16 51 3.5789 3.5807 3.5825 3.5842 3.5860 3.5878 3.5895 3.5913 3.5931 3.5948 2 4 5 7 9 11 12 14 16 52 3.5966 3.5983 3.6001 3.6018 3.6036 3.6053 3.607 3.6087 3.6105 3.6122 2 3 5 7 9 10 12 14 16 53 3.6139 3.6156 3.6173 3.6191 3.6208 3.6225 3.6242 3.6259 3.6276 3.6292 2 3 5 7 9 10 12 14 15 54 3.6309 3.6326 3.6343 3.6360 3.6376 3.6393 3.6410 3.6427 3.6443 3.646 2 3 5 7 8 10 12 13 15 55 3.6476 3.6493 3.6509 3.6526 3.6542 3.6559 3.6575 3.6591 3.6608 3.6624 2 3 5 7 8 10 11 13 15 56 3.6640 3.6657 3.6673 3.6689 3.6705 3.6721 3.6737 3.6753 3.6769 3.6785 2 3 5 6 8 10 11 13 15 57 3.6801 3.6817 3.6833 3.6849 3.6865 3.6881 3.6897 3.6913 3.6928 3.6944 2 3 5 6 8 10 11 13 14 58 3.6960 3.6975 3.6991 3.7007 3.7022 3.7038 3.7053 3.7069 3.7084 3.7100 2 3 5 6 8 9 11 12 14 59 3.7115 3.7131 3.7146 3.7162 3.7177 3.7192 3.7207 3.7223 3.7238 3.7253 2 3 5 6 8 9 11 12 14 60 3.7268 3.7283 3.7299 3.7314 3.7329 3.7344 3.7359 3.7374 3.7389 3.7404 2 3 5 6 8 9 11 12 14 61 3.7419 3.7434 3.7449 3.7463 3.7478 3.7493 3.7508 3.7523 3.7537 3.7552 1 3 4 6 7 9 10 12 13 62 3.7567 3.7581 3.7596 3.7611 3.7625 3.7640 3.7654 3.7669 3.7683 3.7698 1 3 4 6 7 9 10 12 13 63 3.7712 3.7727 3.7741 3.7756 3.7770 3.7784 3.7799 3.7813 3.7827 3.7842 1 3 4 6 7 9 10 11 13 64 3.7856 3.7870 3.7884 3.7898 3.7912 3.7927 3.7941 3.7955 3.7969 3.7983 1 3 4 6 7 8 10 11 13 65 3.7997 3.8011 3.8025 3.8039 3.8053 3.8067 3.8081 3.8094 3.8108 3.8122 1 3 4 6 7 8 10 11 13 66 3.8136 3.8150 3.8163 3.8177 3.8191 3.8205 3.8218 3.8232 3.8246 3.8259 1 3 4 5 7 8 10 11 12 67 3.8273 3.8286 3.8300 3.8313 3.8327 3.8340 3.8354 3.8367 3.8381 3.8394 1 3 4 5 7 8 9 11 12 68 3.8408 3.8421 3.8434 3.8448 3.8461 3.8474 3.8488 3.8501 3.8514 3.8527 1 3 4 5 7 8 9 11 12 69 3.8540 3.8554 3.8567 3.8580 3.8593 3.8606 3.8619 3.8632 3.8645 3.8658 1 3 4 5 7 8 9 10 12 70 3.8671 3.8684 3.8697 3.8710 3.8723 3.8736 3.8749 3.8762 3.8775 3.8788 1 3 4 5 6 8 9 10 12 71 3.8801 3.8813 3.8826 3.8839 3.8852 3.8864 3.8877 3.8890 3.8903 3.8915 1 3 4 5 6 8 9 10 11 72 3.8928 3.8941 3.8953 3.8966 3.8978 3.8991 3.9003 3.9016 3.9028 3.9041 1 3 4 5 6 8 9 10 11 73 3.9053 3.9066 3.9078 3.9091 3.9103 3.9116 3.9128 3.9140 3.9153 3.9165 1 2 4 5 6 7 9 10 11 74 3.9177 3.9190 3.9202 3.9214 3.9226 3.9239 3.9251 3.9263 3.9275 3.9287 1 2 4 5 6 7 9 10 11 75 3.9299 3.9312 3.9324 3.9336 3.9348 3.9360 3.9372 3.9384 3.9396 3.9408 1 2 4 5 6 7 8 10 11 76 3.9420 3.9432 3.9444 3.9456 3.9468 3.9480 3.9492 3.9503 3.9515 3.9527 1 2 4 5 6 7 8 10 11 77 3.9539 3.9551 3.9563 3.9574 3.9586 3.9598 3.961 3.9621 3.9633 3.9645 1 2 4 5 6 7 8 9 11 8 78 3.9656 3.9668 3.9680 3.9691 3.9703 3.9715 3.9726 3.9738 3.9749 3.9761 1 2 3 5 6 7 8 9 10 79 3.9772 3.9784 3.9795 3.9807 3.9818 3.9830 3.9841 3.9853 3.9864 3.9876 1 2 3 5 6 7 8 9 10 80 3.9887 3.9898 3.9910 3.9921 3.9932 3.9944 3.9955 3.9966 3.9977 3.9989 1 2 3 5 6 7 8 9 10 81 4.0000 4.0011 4.0022 4.0034 4.0045 4.0056 4.0067 4.0078 4.0089 4.0101 1 2 3 4 6 7 8 9 10 82 4.0112 4.0123 4.0134 4.0145 4.0156 4.0167 4.0178 4.0189 4.0200 4.0211 1 2 3 4 6 7 8 9 10 83 4.0222 4.0233 4.0244 4.0255 4.0266 4.0277 4.0288 4.0298 4.0309 4.0320 1 2 3 4 5 7 8 9 10 84 4.0331 4.0342 4.0353 4.0363 4.0374 4.0385 4.0396 4.0407 4.0417 4.0428 1 2 3 4 5 7 8 9 10 85 4.0439 4.0449 4.0460 4.0471 4.0481 4.0492 4.0503 4.0513 4.0524 4.0535 1 2 3 4 5 6 7 9 10 86 4.0545 4.0556 4.0566 4.0577 4.0587 4.0598 4.0609 4.0619 4.0629 4.0640 1 2 3 4 5 6 7 8 9 87 4.0650 4.0661 4.0671 4.0682 4.0692 4.0703 4.0713 4.0723 4.0734 4.0744 1 2 3 4 5 6 7 8 9 88 4.0754 4.0765 4.0775 4.0785 4.0796 4.0806 4.0816 4.0827 4.0837 4.0847 1 2 3 4 5 6 7 8 9 89 4.0857 4.0868 4.0878 4.0888 4.0898 4.0908 4.0918 4.0929 4.0939 4.0949 1 2 3 4 5 6 7 8 9 90 4.0959 4.0969 4.0979 4.0989 4.0999 4.1009 4.1020 4.1030 4.1040 4.1050 1 2 3 4 5 6 7 8 9 91 4.1060 4.1070 4.1080 4.1090 4.1100 4.1109 4.1119 4.1129 4.1139 4.1149 1 2 3 4 5 6 7 8 9 92 4.1159 4.1169 4.1179 4.1189 4.1199 4.1208 4.1218 4.1228 4.1238 4.1248 1 2 3 4 5 6 7 8 9 93 4.1257 4.1267 4.1277 4.1287 4.1297 4.1306 4.1316 4.1326 4.1335 4.1345 1 2 3 4 5 6 7 8 9 94 4.1355 4.1365 4.1374 4.1384 4.1394 4.1403 4.1413 4.1422 4.1432 4.1442 1 2 3 4 5 6 7 8 9 95 4.1451 4.1461 4.1470 4.1480 4.1489 4.1499 4.1508 4.1518 4.1528 4.1537 1 2 3 4 5 6 7 8 9 96 4.1546 4.1556 4.1565 4.1575 4.1584 4.1594 4.1603 4.1613 4.1622 4.1631 1 2 3 4 5 6 7 8 8 97 4.1641 4.1650 4.1660 4.1669 4.1678 4.1688 4.1697 4.1706 4.1716 4.1725 1 2 3 4 5 6 7 7 8 98 4.1734 4.1743 4.1753 4.1762 4.1771 4.1780 4.1790 4.1799 4.1808 4.1817 1 2 3 4 5 6 6 7 8 99 4.1827 4.1836 4.1845 4.1854 4.1863 4.1872 4.1882 4.1891 4.1900 4.1909 1 2 3 4 5 5 6 7 8 Table 2: Lukmon (Power of base 3) of ๐Ÿ๐ŸŽ ๐’ ๐‘ณ๐’–๐’Œ(๐Ÿ๐ŸŽ๐’) 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3 ๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ ๐ฟ๐‘ข๐‘˜(10๐‘›) ๐ฟ๐‘ข๐‘˜(10๐‘›) ๐ฟ๐‘ข๐‘˜(10๐‘›) ๐ฟ๐‘ข๐‘˜(10๐‘›) ๐ฟ๐‘ข๐‘˜(10๐‘›) ๐ฟ๐‘ข๐‘˜(10๐‘›) ๐ฟ๐‘ข๐‘˜(10๐‘›) n=1 y=2.0959 16 33.5345 31 64.9730 46 96.4116 61 127.8501 76 159.2887 91 190.7272 2 4.1918 17 35.6304 32 67.0689 47 98.5075 62 129.9460 77 161.3846 92 192.8231 3 6.2877 18 37.7263 33 69.1648 48 100.6034 63 132.0419 78 163.4805 93 194.9190 4 8.3836 19 39.8222 34 71.2607 49 102.6993 64 134.1378 79 165.5764 94 197.0149 5 10.4795 20 41.9181 35 73.3566 50 104.7952 65 136.2337 80 167.6723 95 199.1108 6 12.5754 21 44.0140 36 75.4525 51 106.8911 66 138.3296 81 169.7682 96 201.2067 7 14.6713 22 46.1099 37 77.5484 52 108.9870 67 140.4255 82 171.8641 97 203.3026 8 16.7672 23 48.2058 38 79.6443 53 111.0829 68 142.5214 83 173.9600 98 205.3985 9 18.8631 24 50.3017 39 81.7402 54 113.1788 69 144.6173 84 176.0559 99 207.4944 10 20.9590 25 52.3976 40 83.8361 55 115.2747 70 146.7132 85 178.1518 11 23.0549 26 54.4935 41 85.9320 56 117.3706 71 148.8091 86 180.2477 12 25.1508 27 56.5894 42 88.0279 57 119.4665 72 150.9050 87 182.3436 9 Table 3: ๐‘จ๐’๐’•๐’Š๐‘ณ๐’–๐’Œ๐’Ž๐’๐’ (๐‘จ๐’๐’•๐’Š๐‘ท๐’๐’˜๐’†๐’“ ๐’๐’‡ ๐’ƒ๐’‚๐’”๐’† ๐Ÿ‘) ๐’๐’‡ ๐‘ต๐’–๐’Ž๐’ƒ๐’†๐’“ ๐’™ โ†’ ๐‘จ๐’๐’•๐’Š๐‘ณ๐’–๐’Œ ๐’™ Difference (x) 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 1 2 3 4 5 6 7 8 9 0.00 1.0000 1.0011 1.0022 1.0033 1.0044 1.0055 1.0066 1.0077 1.0088 1.0099 1 2 3 4 6 7 8 9 10 0.01 1.0110 1.0122 1.0133 1.0144 1.0155 1.0166 1.0177 1.0189 1.0200 1.0211 1 2 3 4 6 7 8 9 10 0.02 1.0222 1.0233 1.0245 1.0256 1.0267 1.0278 1.0290 1.0301 1.0312 1.0324 1 2 3 5 6 7 8 9 10 0.03 1.0335 1.0346 1.0358 1.0369 1.0381 1.0392 1.0403 1.0415 1.0426 1.0438 1 2 3 5 6 7 8 9 10 0.04 1.0449 1.0461 1.0472 1.0484 1.0495 1.0507 1.0518 1.0530 1.0541 1.0553 1 2 3 5 6 7 8 9 10 0.05 1.0565 1.0576 1.0588 1.0600 1.0611 1.0623 1.0635 1.0646 1.0658 1.0670 1 2 3 5 6 7 8 9 11 0.06 1.0681 1.0693 1.0705 1.0717 1.0728 1.0740 1.0752 1.0764 1.0776 1.0788 1 2 4 5 6 7 8 9 11 0.07 1.0799 1.0811 1.0823 1.0835 1.0847 1.0859 1.0871 1.0883 1.0895 1.0907 1 2 4 5 6 7 8 10 11 0.08 1.0919 1.0931 1.0943 1.0955 1.0967 1.0979 1.0991 1.1003 1.1015 1.1027 1 2 4 5 6 7 8 10 11 0.09 1.1039 1.1051 1.1064 1.1076 1.1088 1.1100 1.1112 1.1125 1.1137 1.1149 1 2 4 5 6 7 9 10 11 0.10 1.1161 1.1174 1.1186 1.1198 1.1210 1.1223 1.1235 1.1247 1.1260 1.1272 1 2 4 5 6 7 9 10 11 0.11 1.1285 1.1297 1.1309 1.1322 1.1334 1.1347 1.1359 1.1372 1.1384 1.1397 1 2 4 5 6 7 9 10 11 0.12 1.1409 1.1422 1.1434 1.1447 1.1459 1.1472 1.1485 1.1497 1.1510 1.1523 1 3 4 5 6 8 9 10 11 0.13 1.1535 1.1548 1.1561 1.1573 1.1586 1.1599 1.1612 1.1624 1.1637 1.1650 1 3 4 5 6 8 9 10 11 0.14 1.1663 1.1675 1.1688 1.1701 1.1714 1.1727 1.1740 1.1753 1.1766 1.1779 1 3 4 5 6 8 9 10 12 0.15 1.1791 1.1804 1.1817 1.1830 1.1843 1.1856 1.1869 1.1883 1.1896 1.1909 1 3 4 5 7 8 9 10 12 0.16 1.1922 1.1935 1.1948 1.1961 1.1974 1.1987 1.2001 1.2014 1.2027 1.2040 1 3 4 5 7 8 9 11 12 0.17 1.2053 1.2067 1.2080 1.2093 1.2107 1.2120 1.2133 1.2146 1.2160 1.2173 1 3 4 5 7 8 9 11 12 0.18 1.2187 1.2200 1.2213 1.2227 1.2240 1.2254 1.2267 1.2281 1.2294 1.2308 1 3 4 5 7 8 9 11 12 0.19 1.2321 1.2335 1.2348 1.2362 1.2375 1.2389 1.2403 1.2416 1.2430 1.2444 1 3 4 5 7 8 10 11 12 0.20 1.2457 1.2471 1.2485 1.2498 1.2512 1.2526 1.2540 1.2553 1.2567 1.2581 1 3 4 6 7 8 10 11 12 0.21 1.2595 1.2609 1.2623 1.2637 1.2650 1.2664 1.2678 1.2692 1.2706 1.2720 1 3 4 6 7 8 10 11 13 0.22 1.2734 1.2748 1.2762 1.2776 1.2790 1.2804 1.2818 1.2832 1.2846 1.2861 1 3 4 6 7 8 10 11 13 0.23 1.2875 1.2889 1.2903 1.2917 1.2931 1.2946 1.2960 1.2974 1.2988 1.3003 1 3 4 6 7 9 10 11 13 0.24 1.3017 1.3031 1.3046 1.3060 1.3074 1.3089 1.3103 1.3117 1.3132 1.3146 1 3 4 6 7 9 10 12 13 0.25 1.3161 1.3175 1.3190 1.3204 1.3219 1.3233 1.3248 1.3262 1.3277 1.3292 1 3 4 6 7 9 10 12 13 0.26 1.3306 1.3321 1.3335 1.3350 1.3365 1.3379 1.3394 1.3409 1.3424 1.3438 1 3 4 6 7 9 10 12 13 0.27 1.3453 1.3468 1.3483 1.3498 1.3512 1.3527 1.3542 1.3557 1.3572 1.3587 1 3 4 6 7 9 10 12 13 0.28 1.3602 1.3617 1.3632 1.3647 1.3662 1.3677 1.3692 1.3707 1.3722 1.3737 2 3 5 6 8 9 11 12 14 0.29 1.3752 1.3767 1.3782 1.3797 1.3813 1.3828 1.3843 1.3858 1.3873 1.3889 2 3 5 6 8 9 11 12 14 0.30 1.3904 1.3919 1.3934 1.3950 1.3965 1.3980 1.3996 1.4011 1.4027 1.4042 2 3 5 6 8 9 11 12 14 0.31 1.4057 1.4073 1.4088 1.4104 1.4119 1.4135 1.4150 1.4166 1.4182 1.4197 2 3 5 6 8 9 11 12 14 0.32 1.4213 1.4228 1.4244 1.4260 1.4275 1.4291 1.4307 1.4322 1.4338 1.4354 2 3 5 6 8 9 11 13 14 0.33 1.4370 1.4386 1.4401 1.4417 1.4433 1.4449 1.4465 1.4481 1.4497 1.4513 2 3 5 6 8 10 11 13 14 13 27.2467 28 58.6853 43 90.1238 58 121.5624 73 153.0009 88 184.4395 14 29.3427 29 60.7812 44 92.2197 59 123.6583 74 155.0968 89 186.5354 15 31.4386 30 62.8771 45 94.3157 60 125.7542 75 157.1928 90 188.6313 10 0.34 1.4529 1.4544 1.4560 1.4576 1.4593 1.4609 1.4625 1.4641 1.4657 1.4673 2 3 5 6 8 10 11 13 14 0.35 1.4689 1.4705 1.4721 1.4737 1.4754 1.4770 1.4786 1.4802 1.4819 1.4835 2 3 5 6 8 10 11 13 15 0.36 1.4851 1.4868 1.4884 1.4900 1.4917 1.4933 1.4949 1.4966 1.4982 1.4999 2 3 5 7 8 10 11 13 15 0.37 1.5015 1.5032 1.5048 1.5065 1.5081 1.5098 1.5115 1.5131 1.5148 1.5165 2 3 5 7 8 10 12 13 15 0.38 1.5181 1.5198 1.5215 1.5231 1.5248 1.5265 1.5282 1.5298 1.5315 1.5332 2 3 5 7 8 10 12 13 15 0.39 1.5349 1.5366 1.5383 1.5400 1.5416 1.5433 1.5450 1.5467 1.5484 1.5501 2 3 5 7 8 10 12 14 15 0.40 1.5518 1.5536 1.5553 1.5570 1.5587 1.5604 1.5621 1.5638 1.5655 1.5673 2 3 5 7 9 10 12 14 15 0.41 1.5690 1.5707 1.5724 1.5742 1.5759 1.5776 1.5794 1.5811 1.5828 1.5846 2 3 5 7 9 10 12 14 16 0.42 1.5863 1.5881 1.5898 1.5916 1.5933 1.5951 1.5968 1.5986 1.6003 1.6021 2 4 5 7 9 11 12 14 16 0.43 1.6038 1.6056 1.6074 1.6091 1.6109 1.6127 1.6145 1.6162 1.6180 1.6198 2 4 5 7 9 11 12 14 16 0.44 1.6216 1.6233 1.6251 1.6269 1.6287 1.6305 1.6323 1.6341 1.6359 1.6377 2 4 5 7 9 11 13 14 16 0.45 1.6395 1.6413 1.6431 1.6449 1.6467 1.6485 1.6503 1.6521 1.6539 1.6558 2 4 5 7 9 11 13 14 16 0.46 1.6576 1.6594 1.6612 1.6631 1.6649 1.6667 1.6685 1.6704 1.6722 1.6741 2 4 5 7 9 11 13 15 16 0.47 1.6759 1.6777 1.6796 1.6814 1.6833 1.6851 1.6870 1.6888 1.6907 1.6925 2 4 6 7 9 11 13 15 17 0.48 1.6944 1.6963 1.6981 1.7000 1.7019 1.7037 1.7056 1.7075 1.7094 1.7112 2 4 6 7 9 11 13 15 17 0.49 1.7131 1.7150 1.7169 1.7188 1.7207 1.7226 1.7245 1.7264 1.7282 1.7301 2 4 6 8 9 11 13 15 17 0.50 1.7321 1.7340 1.7359 1.7378 1.7397 1.7416 1.7435 1.7454 1.7473 1.7493 2 4 6 8 10 11 13 15 17 0.51 1.7512 1.7531 1.7550 1.7570 1.7589 1.7608 1.7628 1.7647 1.7666 1.7686 2 4 6 8 10 12 14 15 17 0.52 1.7705 1.7725 1.7744 1.7764 1.7783 1.7803 1.7822 1.7842 1.7862 1.7881 2 4 6 8 10 12 14 16 18 0.53 1.7901 1.7921 1.7940 1.7960 1.7980 1.7999 1.8019 1.8039 1.8059 1.8079 2 4 6 8 10 12 14 16 18 0.54 1.8099 1.8119 1.8138 1.8158 1.8178 1.8198 1.8218 1.8238 1.8258 1.8278 2 4 6 8 10 12 14 16 18 0.55 1.8299 1.8319 1.8339 1.8359 1.8379 1.8399 1.8420 1.8440 1.8460 1.8480 2 4 6 8 10 12 14 16 18 0.56 1.8501 1.8521 1.8541 1.8562 1.8582 1.8603 1.8623 1.8644 1.8664 1.8685 2 4 6 8 10 12 14 16 18 0.57 1.8705 1.8726 1.8746 1.8767 1.8787 1.8808 1.8829 1.8849 1.8870 1.8891 2 4 6 8 10 12 14 17 19 0.58 1.8912 1.8932 1.8953 1.8974 1.8995 1.9016 1.9037 1.9058 1.9079 1.9100 2 4 6 8 10 13 15 17 19 0.59 1.9121 1.9142 1.9163 1.9184 1.9205 1.9226 1.9247 1.9268 1.9289 1.9311 2 4 6 8 11 13 15 17 19 0.60 1.9332 1.9353 1.9374 1.9396 1.9417 1.9438 1.9460 1.9481 1.9502 1.9524 2 4 6 9 11 13 15 17 19 0.61 1.9545 1.9567 1.9588 1.9610 1.9631 1.9653 1.9675 1.9696 1.9718 1.9740 2 4 6 9 11 13 15 17 19 0.62 1.9761 1.9783 1.9805 1.9827 1.9848 1.9870 1.9892 1.9914 1.9936 1.9958 2 4 7 9 11 13 15 17 20 0.63 1.9980 2.0002 2.0024 2.0046 2.0068 2.0090 2.0112 2.0134 2.0156 2.0178 2 4 7 9 11 13 15 18 20 0.64 2.0200 2.0222 2.0245 2.0267 2.0289 2.0312 2.0334 2.0356 2.0379 2.0401 2 4 7 9 11 13 16 18 20 0.65 2.0423 2.0446 2.0468 2.0491 2.0513 2.0536 2.0559 2.0581 2.0604 2.0626 2 5 7 9 11 14 16 18 20 0.66 2.0649 2.0672 2.0694 2.0717 2.0740 2.0763 2.0786 2.0808 2.0831 2.0854 2 5 7 9 11 14 16 18 21 0.67 2.0877 2.0900 2.0923 2.0946 2.0969 2.0992 2.1015 2.1038 2.1061 2.1085 2 5 7 9 12 14 16 18 21 0.68 2.1108 2.1131 2.1154 2.1177 2.1201 2.1224 2.1247 2.1271 2.1294 2.1318 2 5 7 9 12 14 16 19 21 0.69 2.1341 2.1364 2.1388 2.1411 2.1435 2.1458 2.1482 2.1506 2.1529 2.1553 2 5 7 9 12 14 16 19 21 0.70 2.1577 2.1600 2.1624 2.1648 2.1672 2.1696 2.1719 2.1743 2.1767 2.1791 2 5 7 10 12 14 17 19 21 0.71 2.1815 2.1839 2.1863 2.1887 2.1911 2.1935 2.1959 2.1983 2.2008 2.2032 2 5 7 10 12 14 17 19 22 0.72 2.2056 2.2080 2.2105 2.2129 2.2153 2.2178 2.2202 2.2226 2.2251 2.2275 2 5 7 10 12 15 17 19 22 0.73 2.2300 2.2324 2.2349 2.2373 2.2398 2.2423 2.2447 2.2472 2.2497 2.2521 2 5 7 10 12 15 17 20 22 0.74 2.2546 2.2571 2.2596 2.2620 2.2645 2.2670 2.2695 2.2720 2.2745 2.2770 2 5 7 10 12 15 17 20 22 0.75 2.2795 2.2820 2.2845 2.2870 2.2895 2.2921 2.2946 2.2971 2.2996 2.3022 3 5 8 10 13 15 18 20 23 0.76 2.3047 2.3072 2.3098 2.3123 2.3148 2.3174 2.3199 2.3225 2.3250 2.3276 3 5 8 10 13 15 18 20 23 11 0.77 2.3301 2.3327 2.3353 2.3378 2.3404 2.3430 2.3456 2.3481 2.3507 2.3533 3 5 8 10 13 15 18 21 23 0.78 2.3559 2.3585 2.3611 2.3637 2.3663 2.3689 2.3715 2.3741 2.3767 2.3793 3 5 8 10 13 16 18 21 23 0.79 2.3819 2.3845 2.3872 2.3898 2.3924 2.3950 2.3977 2.4003 2.4029 2.4056 3 5 8 11 13 16 18 21 24 0.80 2.4082 2.4109 2.4135 2.4162 2.4188 2.4215 2.4242 2.4268 2.4295 2.4322 3 5 8 11 13 16 19 21 24 0.81 2.4348 2.4375 2.4402 2.4429 2.4456 2.4482 2.4509 2.4536 2.4563 2.4590 3 5 8 11 13 16 19 22 24 0.82 2.4617 2.4644 2.4671 2.4699 2.4726 2.4753 2.4780 2.4807 2.4835 2.4862 3 5 8 11 14 16 19 22 24 0.83 2.4889 2.4917 2.4944 2.4971 2.4999 2.5026 2.5054 2.5081 2.5109 2.5136 3 5 8 11 14 16 19 22 25 0.84 2.5164 2.5192 2.5219 2.5247 2.5275 2.5303 2.5331 2.5358 2.5386 2.5414 3 6 8 11 14 17 19 22 25 0.85 2.5442 2.5470 2.5498 2.5526 2.5554 2.5582 2.5610 2.5639 2.5667 2.5695 3 6 8 11 14 17 20 22 25 0.86 2.5723 2.5751 2.5780 2.5808 2.5836 2.5865 2.5893 2.5922 2.5950 2.5979 3 6 9 11 14 17 20 23 26 0.87 2.6007 2.6036 2.6065 2.6093 2.6122 2.6151 2.6179 2.6208 2.6237 2.6266 3 6 9 11 14 17 20 23 26 0.88 2.6295 2.6324 2.6352 2.6381 2.6410 2.6439 2.6469 2.6498 2.6527 2.6556 3 6 9 12 15 17 20 23 26 0.89 2.6585 2.6614 2.6644 2.6673 2.6702 2.6732 2.6761 2.6790 2.6820 2.6849 3 6 9 12 15 18 21 23 26 0.90 2.6879 2.6908 2.6938 2.6967 2.6997 2.7027 2.7057 2.7086 2.7116 2.7146 3 6 9 12 15 18 21 24 27 0.91 2.7176 2.7206 2.7235 2.7265 2.7295 2.7325 2.7355 2.7385 2.7416 2.7446 3 6 9 12 15 18 21 24 27 0.92 2.7476 2.7506 2.7536 2.7567 2.7597 2.7627 2.7658 2.7688 2.7718 2.7749 3 6 9 12 15 18 21 24 27 0.93 2.7779 2.7810 2.7840 2.7871 2.7902 2.7932 2.7963 2.7994 2.8025 2.8055 3 6 9 12 15 18 21 25 28 0.94 2.8086 2.8117 2.8148 2.8179 2.8210 2.8241 2.8272 2.8303 2.8334 2.8365 3 6 9 12 16 19 22 25 28 0.95 2.8397 2.8428 2.8459 2.8490 2.8522 2.8553 2.8584 2.8616 2.8647 2.8679 3 6 9 13 16 19 22 25 28 0.96 2.8710 2.8742 2.8773 2.8805 2.8837 2.8868 2.8900 2.8932 2.8964 2.8995 3 6 10 13 16 19 22 25 29 0.97 2.9027 2.9059 2.9091 2.9123 2.9155 2.9187 2.9219 2.9251 2.9284 2.9316 3 6 10 13 16 19 22 26 29 0.98 2.9348 2.9380 2.9413 2.9445 2.9477 2.9510 2.9542 2.9575 2.9607 2.9640 3 6 10 13 16 19 23 26 29 0.99 2.9672 2.9705 2.9737 2.9770 2.9803 2.9836 2.9868 2.9901 2.9934 2.9967 3 7 10 13 16 20 23 26 29 Table 4: Conversion of ๐Ÿ‘๐’š to ๐Ÿ๐ŸŽ๐’ ๐Ÿ‘๐’š โ†’ ๐Ÿ๐ŸŽ๐’ 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 3๐‘ฆ 10๐‘› 1 0.4771 16 7.6339 31 14.7908 46 21.9476 61 29.1044 76 36.2612 91 43.4180 2 0.9542 17 8.1111 32 15.2679 47 22.4247 62 29.5815 77 36.7383 92 43.8952 3 1.4314 18 8.5882 33 15.7450 48 22.9018 63 30.0586 78 37.2155 93 44.3723 4 1.9085 19 9.0653 34 16.2221 49 23.3789 64 30.5358 79 37.6926 94 44.8494 5 2.3856 20 9.5424 35 16.6992 50 23.8561 65 31.0129 80 38.1697 95 45.3265 6 2.8627 21 10.0196 36 17.1764 51 24.3332 66 31.4900 81 38.6468 96 45.8036 7 3.3399 22 10.4967 37 17.6535 52 24.8103 67 31.9671 82 39.1239 97 46.2808 8 3.8170 23 10.9738 38 18.1306 53 25.2874 68 32.4443 83 39.6011 98 46.7579 9 4.2941 24 11.4509 39 18.6077 54 25.7646 69 32.9214 84 40.0782 99 47.2350 10 4.7712 25 11.9280 40 19.0849 55 26.2417 70 33.3985 85 40.5553 11 5.2483 26 12.4052 41 19.5620 56 26.7188 71 33.8756 86 41.0324 12 5.7255 27 12.8823 42 20.0391 57 27.1959 72 34.3527 87 41.5096 13 6.2026 28 13.3594 43 20.5162 58 27.6730 73 34.8299 88 41.9867 14 6.6797 29 13.8365 44 20.9933 59 28.1502 74 35.3070 89 42.4638 15 7.1568 30 14.3136 45 21.4705 60 28.6273 75 35.7841 90 42.9409 12 Table 5: Fatimo (Power of base 8) of Number x โ†’ ๐‘ญ๐’‚๐’• ๐’™ Difference (x) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 1 0.0000 0.0458 0.0877 0.1262 0.1618 0.1950 0.2260 0.2552 0.2827 0.3087 34 69 103 136 170 203 236 269 301 2 0.3333 0.3568 0.3792 0.4005 0.4210 0.4406 0.4595 0.4777 0.4951 0.5120 20 40 59 79 98 118 137 157 176 3 0.5283 0.5441 0.5594 0.5742 0.5885 0.6025 0.6160 0.6292 0.6420 0.6545 14 28 42 56 70 83 97 111 125 4 0.6667 0.6785 0.6901 0.7014 0.7125 0.7233 0.7339 0.7442 0.7543 0.7643 11 22 32 43 54 65 75 86 97 5 0.7740 0.7835 0.7928 0.8020 0.8110 0.8198 0.8285 0.8370 0.8454 0.8536 9 18 26 35 44 53 62 70 79 6 0.8617 0.8696 0.8774 0.8851 0.8927 0.9001 0.9075 0.9147 0.9218 0.9289 7 15 22 30 37 45 52 59 67 7 0.9358 0.9426 0.9493 0.9560 0.9625 0.9690 0.9753 0.9816 0.9878 0.9940 6 13 19 26 32 39 45 51 58 8 1.0000 1.0060 1.0119 1.0177 1.0235 1.0292 1.0348 1.0403 1.0458 1.0513 6 11 17 23 28 34 40 45 51 9 1.0566 1.0620 1.0672 1.0724 1.0776 1.0826 1.0877 1.0927 1.0976 1.1025 5 10 15 20 25 30 36 41 46 10 1.1073 1.1121 1.1168 1.1215 1.1262 1.1308 1.1353 1.1398 1.1443 1.1488 5 9 14 18 23 28 32 37 41 11 1.1531 1.1575 1.1618 1.1661 1.1703 1.1745 1.1787 1.1828 1.1869 1.1910 4 8 13 17 21 25 29 34 38 12 1.1950 1.1990 1.2029 1.2069 1.2108 1.2146 1.2185 1.2223 1.2260 1.2298 4 8 12 15 19 23 27 31 35 13 1.2335 1.2372 1.2408 1.2445 1.2481 1.2516 1.2552 1.2587 1.2622 1.2657 4 7 11 14 18 21 25 29 32 14 1.2691 1.2725 1.2759 1.2793 1.2827 1.2860 1.2893 1.2926 1.2958 1.2991 3 7 10 13 17 20 23 27 30 15 1.3023 1.3055 1.3087 1.3118 1.3150 1.3181 1.3212 1.3242 1.3273 1.3303 3 6 9 12 16 19 22 25 28 16 1.3333 1.3363 1.3393 1.3423 1.3452 1.3481 1.3510 1.3539 1.3568 1.3597 3 6 9 12 15 18 20 23 26 17 1.3625 1.3653 1.3681 1.3709 1.3737 1.3764 1.3792 1.3819 1.3846 1.3873 3 6 8 11 14 17 19 22 25 18 1.3900 1.3926 1.3953 1.3979 1.4005 1.4032 1.4057 1.4083 1.4109 1.4134 3 5 8 10 13 16 18 21 23 19 1.4160 1.4185 1.4210 1.4235 1.4260 1.4285 1.4309 1.4334 1.4358 1.4382 2 5 7 10 12 15 17 20 22 20 1.4406 1.4430 1.4454 1.4478 1.4502 1.4525 1.4549 1.4572 1.4595 1.4618 2 5 7 9 12 14 16 19 21 21 1.4641 1.4664 1.4687 1.4709 1.4732 1.4754 1.4777 1.4799 1.4821 1.4843 2 4 7 9 11 13 16 18 20 22 1.4865 1.4887 1.4908 1.4930 1.4951 1.4973 1.4994 1.5015 1.5037 1.5058 2 4 6 9 11 13 15 17 19 23 1.5079 1.5099 1.5120 1.5141 1.5161 1.5182 1.5202 1.5223 1.5243 1.5263 2 4 6 8 10 12 14 16 18 24 1.5283 1.5303 1.5323 1.5343 1.5363 1.5382 1.5402 1.5421 1.5441 1.5460 2 4 6 8 10 12 14 16 18 25 1.5480 1.5499 1.5518 1.5537 1.5556 1.5575 1.5594 1.5612 1.5631 1.5650 2 4 6 8 9 11 13 15 17 26 1.5668 1.5687 1.5705 1.5723 1.5742 1.5760 1.5778 1.5796 1.5814 1.5832 2 4 5 7 9 11 13 15 16 27 1.5850 1.5867 1.5885 1.5903 1.5920 1.5938 1.5955 1.5973 1.5990 1.6007 2 4 5 7 9 11 12 14 16 28 1.6025 1.6042 1.6059 1.6076 1.6093 1.6110 1.6126 1.6143 1.6160 1.6177 2 3 5 7 8 10 12 14 15 29 1.6193 1.6210 1.6226 1.6243 1.6259 1.6275 1.6292 1.6308 1.6324 1.6340 2 3 5 7 8 10 11 13 15 30 1.6356 1.6372 1.6388 1.6404 1.6420 1.6436 1.6452 1.6467 1.6483 1.6498 2 3 5 6 8 9 11 13 14 31 1.6514 1.6529 1.6545 1.6560 1.6576 1.6591 1.6606 1.6621 1.6637 1.6652 2 3 5 6 8 9 11 12 14 32 1.6667 1.6682 1.6697 1.6712 1.6726 1.6741 1.6756 1.6771 1.6785 1.6800 1 3 4 6 7 9 10 12 13 33 1.6815 1.6829 1.6844 1.6858 1.6873 1.6887 1.6901 1.6916 1.6930 1.6944 1 3 4 6 7 9 10 11 13 34 1.6958 1.6972 1.6986 1.7000 1.7014 1.7028 1.7042 1.7056 1.7070 1.7084 1 3 4 6 7 8 10 11 13 35 1.7098 1.7111 1.7125 1.7139 1.7152 1.7166 1.7179 1.7193 1.7206 1.7220 1 3 4 5 7 8 9 11 12 36 1.7233 1.7246 1.726 1.7273 1.7286 1.7299 1.7313 1.7326 1.7339 1.7352 1 3 4 5 7 8 9 11 12 37 1.7365 1.7378 1.7391 1.7404 1.7417 1.7429 1.7442 1.7455 1.7468 1.7480 1 3 4 5 6 8 9 10 12 38 1.7493 1.7506 1.7518 1.7531 1.7543 1.7556 1.7568 1.7581 1.7593 1.7606 1 3 4 5 6 7 9 10 11 39 1.7618 1.7630 1.7643 1.7655 1.7667 1.7679 1.7691 1.7704 1.7716 1.7728 1 2 4 5 6 7 9 10 11 40 1.7740 1.7752 1.7764 1.7776 1.7788 1.7800 1.7811 1.7823 1.7835 1.7847 1 2 4 5 6 7 8 10 11 13 41 1.7859 1.7870 1.7882 1.7894 1.7905 1.7917 1.7928 1.7940 1.7951 1.7963 1 2 3 5 6 7 8 9 10 42 1.7974 1.7986 1.7997 1.8009 1.8020 1.8031 1.8043 1.8054 1.8065 1.8076 1 2 3 5 6 7 8 9 10 43 1.8088 1.8099 1.8110 1.8121 1.8132 1.8143 1.8154 1.8165 1.8176 1.8187 1 2 3 4 6 7 8 9 10 44 1.8198 1.8209 1.8220 1.8231 1.8242 1.8252 1.8263 1.8274 1.8285 1.8295 1 2 3 4 5 6 8 9 10 45 1.8306 1.8317 1.8328 1.8338 1.8349 1.8359 1.8370 1.8380 1.8391 1.8401 1 2 3 4 5 6 7 8 10 46 1.8412 1.8422 1.8433 1.8443 1.8454 1.8464 1.8474 1.8485 1.8495 1.8505 1 2 3 4 5 6 7 8 9 47 1.8515 1.8526 1.8536 1.8546 1.8556 1.8566 1.8576 1.8586 1.8596 1.8607 1 2 3 4 5 6 7 8 9 48 1.8617 1.8627 1.8637 1.8647 1.8656 1.8666 1.8676 1.8686 1.8696 1.8706 1 2 3 4 5 6 7 8 9 49 1.8716 1.8726 1.8735 1.8745 1.8755 1.8765 1.8774 1.8784 1.8794 1.8803 1 2 3 4 5 6 7 8 9 50 1.8813 1.8822 1.8832 1.8842 1.8851 1.8861 1.8870 1.8880 1.8889 1.8899 1 2 3 4 5 6 7 8 9 51 1.8908 1.8918 1.8927 1.8936 1.8946 1.8955 1.8964 1.8974 1.8983 1.8992 1 2 3 4 5 6 7 7 8 52 1.9001 1.9011 1.9020 1.9029 1.9038 1.9047 1.9057 1.9066 1.9075 1.9084 1 2 3 4 5 5 6 7 8 53 1.9093 1.9102 1.9111 1.9120 1.9129 1.9138 1.9147 1.9156 1.9165 1.9174 1 2 3 4 4 5 6 7 8 54 1.9183 1.9192 1.9201 1.9210 1.9218 1.9227 1.9236 1.9245 1.9254 1.9262 1 2 3 4 4 5 6 7 8 55 1.9271 1.9280 1.9289 1.9297 1.9306 1.9315 1.9323 1.9332 1.9341 1.9349 1 2 3 3 4 5 6 7 8 56 1.9358 1.9366 1.9375 1.9384 1.9392 1.9401 1.9409 1.9418 1.9426 1.9435 1 2 3 3 4 5 6 7 8 57 1.9443 1.9451 1.9460 1.9468 1.9477 1.9485 1.9493 1.9502 1.9510 1.9518 1 2 3 3 4 5 6 7 8 58 1.9527 1.9535 1.9543 1.9551 1.9560 1.9568 1.9576 1.9584 1.9592 1.9601 1 2 2 3 4 5 6 7 7 59 1.9609 1.9617 1.9625 1.9633 1.9641 1.9649 1.9657 1.9666 1.9674 1.9682 1 2 2 3 4 5 6 6 7 60 1.9690 1.9698 1.9706 1.9714 1.9722 1.9730 1.9737 1.9745 1.9753 1.9761 1 2 2 3 4 5 6 6 7 61 1.9769 1.9777 1.9785 1.9793 1.9801 1.9808 1.9816 1.9824 1.9832 1.9840 1 2 2 3 4 5 5 6 7 62 1.9847 1.9855 1.9863 1.9871 1.9878 1.9886 1.9894 1.9901 1.9909 1.9917 1 2 2 3 4 5 5 6 7 63 1.9924 1.9932 1.9940 1.9947 1.9955 1.9962 1.9970 1.9977 1.9985 1.9992 1 2 2 3 4 5 5 6 7 64 2.0000 2.0008 2.0015 2.0022 2.0030 2.0037 2.0045 2.0052 2.0060 2.0067 1 1 2 3 4 4 5 6 7 65 2.0075 2.0082 2.0089 2.0097 2.0104 2.0111 2.0119 2.0126 2.0133 2.0141 1 1 2 3 4 4 5 6 7 66 2.0148 2.0155 2.0163 2.0170 2.0177 2.0184 2.0192 2.0199 2.0206 2.0213 1 1 2 3 4 4 5 6 7 67 2.0220 2.0227 2.0235 2.0242 2.0249 2.0256 2.0263 2.0270 2.0277 2.0284 1 1 2 3 4 4 5 6 6 68 2.0292 2.0299 2.0306 2.0313 2.0320 2.0327 2.0334 2.0341 2.0348 2.0355 1 1 2 3 4 4 5 6 6 69 2.0362 2.0369 2.0376 2.0383 2.0390 2.0396 2.0403 2.0410 2.0417 2.0424 1 1 2 3 3 4 5 6 6 70 2.0431 2.0438 2.0445 2.0452 2.0458 2.0465 2.0472 2.0479 2.0486 2.0492 1 1 2 3 3 4 5 5 6 71 2.0499 2.0506 2.0513 2.0519 2.0526 2.0533 2.0540 2.0546 2.0553 2.0560 1 1 2 3 3 4 5 5 6 72 2.0566 2.0573 2.0580 2.0586 2.0593 2.0600 2.0606 2.0613 2.0620 2.0626 1 1 2 3 3 4 5 5 6 73 2.0633 2.0639 2.0646 2.0652 2.0659 2.0666 2.0672 2.0679 2.0685 2.0692 1 1 2 3 3 4 5 5 6 74 2.0698 2.0705 2.0711 2.0718 2.0724 2.0731 2.0737 2.0743 2.0750 2.0756 1 1 2 3 3 4 5 5 6 75 2.0763 2.0769 2.0776 2.0782 2.0788 2.0795 2.0801 2.0807 2.0814 2.0820 1 1 2 3 3 4 4 5 6 76 2.0826 2.0833 2.0839 2.0845 2.0852 2.0858 2.0864 2.0871 2.0877 2.0883 1 1 2 3 3 4 4 5 6 77 2.0889 2.0896 2.0902 2.0908 2.0914 2.0920 2.0927 2.0933 2.0939 2.0945 1 1 2 2 3 4 4 5 6 78 2.0951 2.0958 2.0964 2.0970 2.0976 2.0982 2.0988 2.0994 2.1000 2.1007 1 1 2 2 3 4 4 5 6 79 2.1013 2.1019 2.1025 2.1031 2.1037 2.1043 2.1049 2.1055 2.1061 2.1067 1 1 2 2 3 4 4 5 5 80 2.1073 2.1079 2.1085 2.1091 2.1097 2.1103 2.1109 2.1115 2.1121 2.1127 1 1 2 2 3 4 4 5 5 81 2.1133 2.1139 2.1145 2.1151 2.1157 2.1162 2.1168 2.1174 2.1180 2.1186 1 1 2 2 3 4 4 5 5 82 2.1192 2.1198 2.1204 2.1209 2.1215 2.1221 2.1227 2.1233 2.1239 2.1244 1 1 2 2 3 3 4 5 5 83 2.1250 2.1256 2.1262 2.1267 2.1273 2.1279 2.1285 2.1291 2.1296 2.1302 1 1 2 2 3 3 4 5 5 14 84 2.1308 2.1313 2.1319 2.1325 2.1331 2.1336 2.1342 2.1348 2.1353 2.1359 1 1 2 2 3 3 4 5 5 85 2.1365 2.1370 2.1376 2.1382 2.1387 2.1393 2.1398 2.1404 2.1410 2.1415 1 1 2 2 3 3 4 5 5 86 2.1421 2.1426 2.1432 2.1438 2.1443 2.1449 2.1454 2.1460 2.1465 2.1471 1 1 2 2 3 3 4 4 5 87 2.1476 2.1482 2.1488 2.1493 2.1499 2.1504 2.1510 2.1515 2.1520 2.1526 1 1 2 2 3 3 4 4 5 88 2.1531 2.1537 2.1542 2.1548 2.1553 2.1559 2.1564 2.1570 2.1575 2.1580 1 1 2 2 3 3 4 4 5 89 2.1586 2.1591 2.1597 2.1602 2.1607 2.1613 2.1618 2.1623 2.1629 2.1634 1 1 2 2 3 3 4 4 5 90 2.1640 2.1645 2.1650 2.1656 2.1661 2.1666 2.1671 2.1677 2.1682 2.1687 1 1 2 2 3 3 4 4 5 91 2.1693 2.1698 2.1703 2.1708 2.1714 2.1719 2.1724 2.1729 2.1735 2.1740 1 1 2 2 3 3 4 4 5 92 2.1745 2.1750 2.1756 2.1761 2.1766 2.1771 2.1776 2.1782 2.1787 2.1792 1 1 2 2 3 3 4 4 5 93 2.1797 2.1802 2.1808 2.1813 2.1818 2.1823 2.1828 2.1833 2.1838 2.1844 1 1 2 2 3 3 4 4 5 94 2.1849 2.1854 2.1859 2.1864 2.1869 2.1874 2.1879 2.1884 2.1889 2.1894 1 1 2 2 3 3 4 4 5 95 2.1900 2.1905 2.1910 2.1915 2.1920 2.1925 2.1930 2.1935 2.1940 2.1945 1 1 2 2 3 3 4 4 5 96 2.1950 2.1955 2.1960 2.1965 2.1970 2.1975 2.1980 2.1985 2.1990 2.1995 1 1 1 2 2 3 3 4 4 97 2.2000 2.2005 2.2010 2.2015 2.2019 2.2024 2.2029 2.2034 2.2039 2.2044 1 1 1 2 2 3 3 4 4 98 2.2049 2.2054 2.2059 2.2064 2.2069 2.2074 2.2078 2.2083 2.2088 2.2093 1 1 1 2 2 3 3 4 4 99 2.2098 2.2103 2.2108 2.2112 2.2117 2.2122 2.2127 2.2132 2.2137 2.2141 1 1 1 2 2 3 3 4 4 Table 6: Fatimo (Power of base 8) of ๐Ÿ๐ŸŽ ๐’ ๐Ÿ๐ŸŽ ๐’ โ†’ ๐Ÿ–๐’š 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8 ๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) 10๐‘› ๐น๐‘Ž๐‘ก(10๐‘›) n=1 y=1.1073 16 17.7170 31 34.3266 46 50.9362 61 67.5459 76 84.1555 91 100.7652 2 2.2146 17 18.8243 32 35.4339 47 52.0435 62 68.6532 77 85.2628 92 101.8725 3 3.3219 18 19.9316 33 36.5412 48 53.1509 63 69.7605 78 86.3701 93 102.9798 4 4.4292 19 21.0389 34 37.6485 49 54.2582 64 70.8678 79 87.4774 94 104.0871 5 5.5366 20 22.1462 35 38.7558 50 55.3655 65 71.9751 80 88.5848 95 105.1944 6 6.6439 21 23.2535 36 39.8631 51 56.4728 66 73.0824 81 89.6921 96 106.3017 7 7.7512 22 24.3608 37 40.9705 52 57.5801 67 74.1897 82 90.7990 97 107.4090 8 8.8585 23 25.4681 38 42.0778 53 58.6874 68 75.2970 83 91.9067 98 108.5163 9 9.9658 24 26.5754 39 43.1851 54 59.7947 69 76.4044 84 93.0140 99 109.6236 10 11.0731 25 27.6827 40 44.2924 55 60.9020 70 77.5117 85 94.1213 11 12.1804 26 28.7900 41 45.3997 56 62.0093 71 78.6190 86 95.2286 12 13.2877 27 29.8974 42 46.5070 57 63.1166 72 79.7263 87 96.3359 13 14.3950 28 31.0047 43 47.6143 58 64.2239 73 80.8336 88 97.4432 14 15.5023 29 32.1200 44 48.7216 59 65.3313 74 81.9409 89 98.5505 15 16.6096 30 33.2193 45 49.8289 60 66.4386 75 83.0482 90 99.6578 15 Table 7: AntiFatimo (AntiPower of base 8) of Number x โ†’ AntiFat x Difference (x) 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 1 2 3 4 5 6 7 8 9 0.00 1.0000 1.0021 1.0042 1.0063 1.0084 1.0105 1.0126 1.0147 1.0168 1.0189 2 4 6 8 11 13 15 17 19 0.01 1.0210 1.0231 1.0253 1.0274 1.0295 1.0317 1.0338 1.0360 1.0381 1.0403 2 4 6 9 11 13 15 17 19 0.02 1.0425 1.0446 1.0468 1.0490 1.0512 1.0534 1.0556 1.0578 1.0600 1.0622 2 4 7 9 11 13 15 18 20 0.03 1.0644 1.0666 1.0688 1.0710 1.0733 1.0755 1.0777 1.0800 1.0822 1.0845 2 4 7 9 11 13 16 18 20 0.04 1.0867 1.0890 1.0913 1.0935 1.0958 1.0981 1.1004 1.1027 1.1050 1.1073 2 5 7 9 11 14 16 18 21 0.05 1.1096 1.1119 1.1142 1.1165 1.1188 1.1212 1.1235 1.1258 1.1282 1.1305 2 5 7 9 12 14 16 19 21 0.06 1.1329 1.1352 1.1376 1.1400 1.1423 1.1447 1.1471 1.1495 1.1519 1.1543 2 5 7 10 12 14 17 19 21 0.07 1.1567 1.1591 1.1615 1.1639 1.1663 1.1688 1.1712 1.1736 1.1761 1.1785 2 5 7 10 12 15 17 19 22 0.08 1.1810 1.1835 1.1859 1.1884 1.1909 1.1933 1.1958 1.1983 1.2008 1.2033 2 5 7 10 12 15 17 20 22 0.09 1.2058 1.2083 1.2108 1.2134 1.2159 1.2184 1.2209 1.2235 1.2260 1.2286 3 5 8 10 13 15 18 20 23 0.10 1.2311 1.2337 1.2363 1.2388 1.2414 1.2440 1.2466 1.2492 1.2518 1.2544 3 5 8 10 13 16 18 21 23 0.11 1.2570 1.2596 1.2623 1.2649 1.2675 1.2702 1.2728 1.2754 1.2781 1.2808 3 5 8 11 13 16 18 21 24 0.12 1.2834 1.2861 1.2888 1.2915 1.2941 1.2968 1.2995 1.3022 1.3050 1.3077 3 5 8 11 13 16 19 22 24 0.13 1.3104 1.3131 1.3159 1.3186 1.3213 1.3241 1.3268 1.3296 1.3324 1.3351 3 6 8 11 14 17 19 22 25 0.14 1.3379 1.3407 1.3435 1.3463 1.3491 1.3519 1.3547 1.3575 1.3604 1.3632 3 6 8 11 14 17 20 22 25 0.15 1.3660 1.3689 1.3717 1.3746 1.3775 1.3803 1.3832 1.3861 1.3890 1.3918 3 6 9 11 14 17 20 23 26 0.16 1.3947 1.3976 1.4006 1.4035 1.4064 1.4093 1.4123 1.4152 1.4181 1.4211 3 6 9 12 15 18 21 23 26 0.17 1.4241 1.4270 1.4300 1.4330 1.4359 1.4389 1.4419 1.4449 1.4479 1.4510 3 6 9 12 15 18 21 24 27 0.18 1.4540 1.4570 1.4600 1.4631 1.4661 1.4692 1.4722 1.4753 1.4784 1.4814 3 6 9 12 15 18 21 24 27 0.19 1.4845 1.4876 1.4907 1.4938 1.4969 1.5000 1.5032 1.5063 1.5094 1.5126 3 6 9 12 16 19 22 25 28 0.20 1.5157 1.5189 1.5220 1.5252 1.5284 1.5316 1.5347 1.5379 1.5411 1.5444 3 6 10 13 16 19 22 25 29 0.21 1.5476 1.5508 1.5540 1.5572 1.5605 1.5637 1.5670 1.5703 1.5735 1.5768 3 6 10 13 16 20 23 26 29 0.22 1.5801 1.5834 1.5867 1.5900 1.5933 1.5966 1.5999 1.6033 1.6066 1.6099 3 7 10 13 17 20 23 27 30 0.23 1.6133 1.6166 1.6200 1.6234 1.6268 1.6301 1.6335 1.6369 1.6403 1.6438 3 7 10 14 17 20 24 27 31 0.24 1.6472 1.6506 1.6540 1.6575 1.6609 1.6644 1.6679 1.6713 1.6748 1.6783 3 7 10 14 17 21 24 28 31 0.25 1.6818 1.6853 1.6888 1.6923 1.6958 1.6994 1.7029 1.7065 1.7100 1.7136 4 7 11 14 18 21 25 28 32 0.26 1.7171 1.7207 1.7243 1.7279 1.7315 1.7351 1.7387 1.7423 1.7459 1.7496 4 7 11 14 18 22 25 29 32 0.27 1.7532 1.7569 1.7605 1.7642 1.7679 1.7715 1.7752 1.7789 1.7826 1.7863 4 7 11 15 18 22 26 29 33 0.28 1.7901 1.7938 1.7975 1.8013 1.8050 1.8088 1.8125 1.8163 1.8201 1.8239 4 8 11 15 19 23 26 30 34 0.29 1.8277 1.8315 1.8353 1.8391 1.8429 1.8468 1.8506 1.8545 1.8583 1.8622 4 8 12 15 19 23 27 31 35 0.30 1.8661 1.8700 1.8738 1.8777 1.8817 1.8856 1.8895 1.8934 1.8974 1.9013 4 8 12 16 20 24 27 31 35 0.31 1.9053 1.9092 1.9132 1.9172 1.9212 1.9252 1.9292 1.9332 1.9372 1.9413 4 8 12 16 20 24 28 32 36 0.32 1.9453 1.9494 1.9534 1.9575 1.9616 1.9656 1.9697 1.9738 1.9779 1.9821 4 8 12 16 20 25 29 33 37 0.33 1.9862 1.9903 1.9945 1.9986 2.0028 2.0069 2.0111 2.0153 2.0195 2.0237 4 8 13 17 21 25 29 33 38 0.34 2.0279 2.0321 2.0364 2.0406 2.0449 2.0491 2.0534 2.0577 2.0619 2.0662 4 9 13 17 21 26 30 34 38 0.35 2.0705 2.0748 2.0792 2.0835 2.0878 2.0922 2.0965 2.1009 2.1053 2.1096 4 9 13 17 22 26 30 35 39 0.36 2.1140 2.1184 2.1228 2.1273 2.1317 2.1361 2.1406 2.1450 2.1495 2.1540 4 9 13 18 22 27 31 36 40 0.37 2.1585 2.1629 2.1675 2.1720 2.1765 2.1810 2.1856 2.1901 2.1947 2.1992 5 9 14 18 23 27 32 36 41 0.38 2.2038 2.2084 2.2130 2.2176 2.2222 2.2268 2.2315 2.2361 2.2408 2.2454 5 9 14 19 23 28 32 37 42 0.39 2.2501 2.2548 2.2595 2.2642 2.2689 2.2736 2.2784 2.2831 2.2879 2.2926 5 9 14 19 24 28 33 38 43 16 0.40 2.2974 2.3022 2.3070 2.3118 2.3166 2.3214 2.3262 2.3311 2.3359 2.3408 5 10 14 19 24 29 34 39 43 0.41 2.3457 2.3506 2.3554 2.3603 2.3653 2.3702 2.3751 2.3801 2.3850 2.3900 5 10 15 20 25 30 34 39 44 0.42 2.3950 2.3999 2.4049 2.4099 2.4150 2.4200 2.4250 2.4301 2.4351 2.4402 5 10 15 20 25 30 35 40 45 0.43 2.4453 2.4504 2.4555 2.4606 2.4657 2.4708 2.4760 2.4811 2.4863 2.4915 5 10 15 21 26 31 36 41 46 0.44 2.4967 2.5019 2.5071 2.5123 2.5175 2.5228 2.5280 2.5333 2.5385 2.5438 5 10 16 21 26 31 37 42 47 0.45 2.5491 2.5544 2.5597 2.5651 2.5704 2.5758 2.5811 2.5865 2.5919 2.5973 5 11 16 21 27 32 37 43 48 0.46 2.6027 2.6081 2.6135 2.6190 2.6244 2.6299 2.6354 2.6408 2.6463 2.6519 5 11 16 22 27 33 38 44 49 0.47 2.6574 2.6629 2.6684 2.6740 2.6796 2.6851 2.6907 2.6963 2.7019 2.7076 6 11 17 22 28 33 39 45 50 0.48 2.7132 2.7189 2.7245 2.7302 2.7359 2.7416 2.7473 2.7530 2.7587 2.7645 6 11 17 23 28 34 40 46 51 0.49 2.7702 2.7760 2.7818 2.7876 2.7934 2.7992 2.8050 2.8108 2.8167 2.8226 6 12 17 23 29 35 41 47 52 0.50 2.8284 2.8343 2.8402 2.8461 2.8521 2.8580 2.8639 2.8699 2.8759 2.8819 6 12 18 24 30 36 42 48 53 0.51 2.8879 2.8939 2.8999 2.9059 2.9120 2.9180 2.9241 2.9302 2.9363 2.9424 6 12 18 24 30 36 42 49 55 0.52 2.9485 2.9547 2.9608 2.9670 2.9732 2.9794 2.9856 2.9918 2.9980 3.0042 6 12 19 25 31 37 43 50 56 0.53 3.0105 3.0168 3.0230 3.0293 3.0356 3.0420 3.0483 3.0546 3.0610 3.0674 6 13 19 25 32 38 44 51 57 0.54 3.0738 3.0801 3.0866 3.0930 3.0994 3.1059 3.1123 3.1188 3.1253 3.1318 6 13 19 26 32 39 45 52 58 0.55 3.1383 3.1449 3.1514 3.1580 3.1645 3.1711 3.1777 3.1844 3.1910 3.1976 7 13 20 26 33 40 46 53 59 0.56 3.2043 3.2109 3.2176 3.2243 3.2310 3.2378 3.2445 3.2513 3.2580 3.2648 7 13 20 27 34 40 47 54 61 0.57 3.2716 3.2784 3.2852 3.2921 3.2989 3.3058 3.3127 3.3196 3.3265 3.3334 7 14 21 27 34 41 48 55 62 0.58 3.3404 3.3473 3.3543 3.3613 3.3683 3.3753 3.3823 3.3893 3.3964 3.4035 7 14 21 28 35 42 49 56 63 0.59 3.4105 3.4176 3.4248 3.4319 3.4390 3.4462 3.4534 3.4605 3.4678 3.4750 7 14 21 29 36 43 50 57 64 0.60 3.4822 3.4895 3.4967 3.5040 3.5113 3.5186 3.5259 3.5333 3.5406 3.5480 7 15 22 29 37 44 51 59 66 0.61 3.5554 3.5628 3.5702 3.5776 3.5851 3.5925 3.6000 3.6075 3.6150 3.6225 7 15 22 30 37 45 52 60 67 0.62 3.6301 3.6376 3.6452 3.6528 3.6604 3.6680 3.6757 3.6833 3.6910 3.6987 8 15 23 30 38 46 53 61 69 0.63 3.7064 3.7141 3.7218 3.7295 3.7373 3.7451 3.7529 3.7607 3.7685 3.7764 8 16 23 31 39 47 54 62 70 0.64 3.7842 3.7921 3.8000 3.8079 3.8158 3.8238 3.8317 3.8397 3.8477 3.8557 8 16 24 32 40 48 56 64 72 0.65 3.8637 3.8718 3.8798 3.8879 3.8960 3.9041 3.9123 3.9204 3.9286 3.9367 8 16 24 32 41 49 57 65 73 0.66 3.9449 3.9531 3.9614 3.9696 3.9779 3.9862 3.9945 4.0028 4.0111 4.0195 8 17 25 33 41 50 58 66 75 0.67 4.0278 4.0362 4.0446 4.0530 4.0615 4.0699 4.0784 4.0869 4.0954 4.1039 8 17 25 34 42 51 59 68 76 0.68 4.1125 4.1210 4.1296 4.1382 4.1468 4.1554 4.1641 4.1728 4.1814 4.1901 9 17 26 35 43 52 60 69 78 0.69 4.1989 4.2076 4.2164 4.2251 4.2339 4.2428 4.2516 4.2604 4.2693 4.2782 9 18 26 35 44 53 62 71 79 0.70 4.2871 4.2960 4.3050 4.3139 4.3229 4.3319 4.3409 4.3500 4.3590 4.3681 9 18 27 36 45 54 63 72 81 0.71 4.3772 4.3863 4.3954 4.4046 4.4137 4.4229 4.4321 4.4414 4.4506 4.4599 9 18 28 37 46 55 64 74 83 0.72 4.4691 4.4785 4.4878 4.4971 4.5065 4.5159 4.5253 4.5347 4.5441 4.5536 9 19 28 38 47 56 66 75 85 0.73 4.5631 4.5726 4.5821 4.5916 4.6012 4.6107 4.6203 4.6300 4.6396 4.6493 10 19 29 38 48 58 67 77 86 0.74 4.6589 4.6686 4.6784 4.6881 4.6978 4.7076 4.7174 4.7272 4.7371 4.7469 10 20 29 39 49 59 69 78 88 0.75 4.7568 4.7667 4.7767 4.7866 4.7966 4.8065 4.8165 4.8266 4.8366 4.8467 10 20 30 40 50 60 70 80 90 0.76 4.8568 4.8669 4.8770 4.8872 4.8973 4.9075 4.9178 4.9280 4.9383 4.9485 10 20 31 41 51 61 71 82 92 0.77 4.9588 4.9692 4.9795 4.9899 5.0002 5.0107 5.0211 5.0315 5.0420 5.0525 10 21 31 42 52 62 73 83 94 0.78 5.063 5.0736 5.0841 5.0947 5.1053 5.1159 5.1266 5.1373 5.1480 5.1587 11 21 32 43 53 64 74 85 96 0.79 5.1694 5.1802 5.1910 5.2018 5.2126 5.2234 5.2343 5.2452 5.2561 5.2671 11 22 33 43 54 65 76 87 98 0.80 5.2780 5.2890 5.3000 5.3111 5.3221 5.3332 5.3443 5.3554 5.3666 5.3777 11 22 33 44 55 67 78 89 100 0.81 5.3889 5.4002 5.4114 5.4227 5.4339 5.4453 5.4566 5.4679 5.4793 5.4907 11 23 34 45 57 68 79 91 102 0.82 5.5022 5.5136 5.5251 5.5366 5.5481 5.5597 5.5712 5.5828 5.5945 5.6061 12 23 35 46 58 69 81 92 104 17 0.83 5.6178 5.6295 5.6412 5.6529 5.6647 5.6765 5.6883 5.7002 5.7120 5.7239 12 24 35 47 59 71 83 94 106 0.84 5.7358 5.7478 5.7597 5.7717 5.7837 5.7958 5.8078 5.8199 5.8320 5.8442 12 24 36 48 60 72 84 96 108 0.85 5.8563 5.8685 5.8807 5.8930 5.9053 5.9176 5.9299 5.9422 5.9546 5.967 12 25 37 49 61 74 86 98 111 0.86 5.9794 5.9918 6.0043 6.0168 6.0293 6.0419 6.0545 6.0671 6.0797 6.0924 13 25 38 50 63 75 88 100 113 0.87 6.1050 6.1177 6.1305 6.1432 6.1560 6.1688 6.1817 6.1946 6.2074 6.2204 13 26 38 51 64 77 90 103 115 0.88 6.2333 6.2463 6.2593 6.2723 6.2854 6.2985 6.3116 6.3247 6.3379 6.3511 13 26 39 52 65 79 92 105 118 0.89 6.3643 6.3775 6.3908 6.4041 6.4174 6.4308 6.4442 6.4576 6.4711 6.4845 13 27 40 53 67 80 94 107 120 0.90 6.4980 6.5115 6.5251 6.5387 6.5523 6.5659 6.5796 6.5933 6.6070 6.6208 14 27 41 55 68 82 96 109 123 0.91 6.6346 6.6484 6.6622 6.6761 6.6900 6.7039 6.7179 6.7318 6.7458 6.7599 14 28 42 56 70 84 98 112 125 0.92 6.7740 6.7881 6.8022 6.8164 6.8305 6.8448 6.8590 6.8733 6.8876 6.9019 14 28 43 57 71 85 100 114 128 0.93 6.9163 6.9307 6.9451 6.9596 6.9741 6.9886 7.0031 7.0177 7.0323 7.0470 15 29 44 58 73 87 102 116 131 0.94 7.0616 7.0763 7.0911 7.1058 7.1206 7.1354 7.1503 7.1652 7.1801 7.1950 15 30 44 59 74 89 104 119 134 0.95 7.2100 7.2250 7.2401 7.2551 7.2702 7.2854 7.3005 7.3157 7.3309 7.3462 15 30 45 61 76 91 106 121 136 0.96 7.3615 7.3768 7.3922 7.4076 7.4230 7.4384 7.4539 7.4694 7.4850 7.5006 15 31 46 62 77 93 108 124 139 0.97 7.5162 7.5318 7.5475 7.5632 7.5790 7.5947 7.6105 7.6264 7.6423 7.6582 16 32 47 63 79 95 111 126 142 0.98 7.6741 7.6901 7.7061 7.7221 7.7382 7.7543 7.7705 7.7866 7.8028 7.8191 16 32 48 64 81 97 113 129 145 0.99 7.8354 7.8517 7.8680 7.8844 7.9008 7.9173 7.9337 7.9502 7.9668 7.9834 16 33 49 66 82 99 115 132 148 Table 8: Conversion of ๐Ÿ–๐’š to ๐Ÿ๐ŸŽ๐’ ๐Ÿ–๐’š โ†’ ๐Ÿ๐ŸŽ๐’ 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 8๐‘ฆ 10๐‘› 1 0.9031 16 14.4494 31 27.9958 46 41.5421 61 55.0885 76 68.6348 91 82.1812 2 1.8062 17 15.3525 32 28.8989 47 42.4452 62 55.9916 77 69.5379 92 83.0843 3 2.7093 18 16.2556 33 29.8020 48 43.3483 63 56.8947 78 70.4410 93 83.9874 4 3.6124 19 17.1587 34 30.7051 49 44.2514 64 57.7978 79 71.3441 94 84.8905 5 4.5155 20 18.0618 35 31.6082 50 45.1545 65 58.7009 80 72.2472 95 85.7936 6 5.4185 21 18.9649 36 32.5112 51 46.0576 66 59.6039 81 73.1503 96 86.6966 7 6.3216 22 19.8680 37 33.4143 52 46.9607 67 60.5070 82 74.0534 97 87.5997 8 7.2247 23 20.7711 38 34.3174 53 47.8638 68 61.4101 83 74.9565 98 88.5028 9 8.1278 24 21.6742 39 35.2205 54 48.7669 69 62.3132 84 75.8596 99 89.4059 10 9.0309 25 22.5773 40 36.1236 55 49.6700 70 63.2163 85 76.7627 11 9.9340 26 23.4803 41 37.0267 56 50.5730 71 64.1194 86 77.6657 12 10.8371 27 24.3834 42 37.9298 57 51.4761 72 65.0225 87 78.5688 13 11.7402 28 25.2865 43 38.8329 58 52.3792 73 65.9256 88 79.4719 14 12.6433 29 26.1896 44 39.7360 59 53.2823 74 66.8287 89 80.3750 15 13.5464 30 27.0927 45 40.6391 60 54.1854 75 67.7318 90 81.2781 18 Establishment of the magnitude of the population of any particular entity The establishment of the magnitude of the population of a state, nation or location using Kifilideen population scale is given as: ๐‘€ = ๐พ๐‘–๐‘“ ๐‘ƒ (1) Where ๐‘€ is the magnitude of the population of a state, nation or location of any particular entity, ๐พ๐‘–๐‘“ is the Logarithm of base 11 and ๐‘ƒ is the population of the particular entity of a state, nation or location. The establishment of the magnitude of the population of a state, nation or location using Lukmon population scale is given as: ๐‘€ = ๐ฟ๐‘ข๐‘˜ ๐‘ƒ (2) Where ๐‘€ is the magnitude of the population of a state, nation or location of any particular entity, ๐ฟ๐‘ข๐‘˜ is the Logarithm of base 3 and ๐‘ƒ is the population of the particular entity of a state, nation or location. The establishment of the magnitude of the population of a state, nation or location using Fatimo population scale is given as: ๐‘€ = ๐น๐‘Ž๐‘ก ๐‘ƒ (3) Where ๐‘€ is the magnitude of the population of a state, nation or location of any particular entity, ๐น๐‘Ž๐‘ก is the Logarithm of base 8 and ๐‘ƒ is the population of the particular entity of a state, nation or location. Kifildeen conversion of magnitude of the population on one scale to another If the magnitude of population, ๐‘ƒ on the Kifilideen, Lukmon and Fatimo scales are ๐‘€๐‘˜, ๐‘€๐‘™ and ๐‘€๐‘“ then: ๐‘€๐‘˜ = ๐พ๐‘–๐‘“ ๐‘ƒ, ๐‘ƒ = 11๐‘€๐‘˜ , ๐‘€๐‘™ = ๐ฟ๐‘ข๐‘˜ ๐‘ƒ (4), (5), (6) Put (5) in (6) ๐‘€๐‘™ = ๐ฟ๐‘ข๐‘˜ 11๐‘€๐‘˜ , ๐‘€๐‘™ = ๐‘€๐‘˜ ๐ฟ๐‘ข๐‘˜ 11, ๐‘€๐‘™ = 2.1827๐‘€๐‘˜ (7), (8), (9) Similarly, ๐‘€๐‘˜ = ๐‘€๐‘™ ๐พ๐‘–๐‘“ 3 , ๐‘€๐‘˜ = 0.4582๐‘€๐‘™ (10), (11) To convert Fatimo to Kifilideen scale vice versa ๐‘€๐‘“ = ๐‘€๐‘˜ ๐น๐‘Ž๐‘ก 11, ๐‘€๐‘“ = 1.153๐‘€๐‘˜ (12), (13) Similarly, ๐‘€๐‘˜ = ๐‘€๐‘“ ๐พ๐‘–๐‘“ 8, ๐‘€๐‘˜ = 0.8672๐‘€๐‘“ (14), (15) To convert Lukmon to Fatimo scale vice versa ๐‘€๐‘“ = ๐‘€๐‘™ ๐น๐‘Ž๐‘ก 3, ๐‘€๐‘“ = 0.5283๐‘€๐‘™ (16), (17) Similarly, ๐‘€๐‘™ = ๐‘€๐‘“ ๐ฟ๐‘ข๐‘˜ 8, ๐‘€๐‘™ = 1.8928๐‘€๐‘“ (18), (19) Inauguration of Kifilideen conversion scale method If the population of an entity is ๐‘ƒ while the magnitude of the population ๐‘ƒ in the Kifilideen, Lukmon and Fatimo scales are ๐‘€๐‘˜, ๐‘€๐‘™ and ๐‘€๐‘“; then From the Kifilideen population scale; ๐‘€๐‘˜ = ๐พ๐‘–๐‘“ ๐‘ƒ , ๐‘ƒ = 11๐‘€๐‘˜ (20) From the Lukmon population scale; ๐‘€๐‘™ = ๐ฟ๐‘ข๐‘˜ ๐‘ƒ , ๐‘ƒ = 3๐‘€๐‘™ (21) From the Fatimo population scale; ๐‘€๐‘“ = ๐น๐‘Ž๐‘ก ๐‘ƒ , ๐‘ƒ = 8๐‘€๐‘“ (22) Therefore, ๐‘ƒ = 11๐‘€๐‘˜ = 3๐‘€๐‘™ = 8๐‘€๐‘“ (23) For ๐‘€๐‘˜ = 0, (24) ๐‘€๐‘™ = 2.1827๐‘€๐‘˜ = 2.1827 ร— 0 = 0 (25) ๐‘€๐‘“ = 1.153๐‘€๐‘˜ = 1.153 ร— 0 = 0 (26) For ๐‘€๐‘˜ = 10, (27) ๐‘€๐‘™ = 2.1827๐‘€๐‘˜ = 2.1827 ร— 10 = 21.827 โ‰ˆ 21.83 (28) ๐‘€๐‘“ = 1.1530๐‘€๐‘˜ = 1.1530 ร— 10 = 11.530 โ‰ˆ 11.53 (29) For ๐‘€๐‘˜ = ๐‘ฅ, ๐‘€๐‘™ = ๐‘ฆ and ๐‘€๐‘“ = ๐‘ง (30) 19 So, Kifilideen magnitude population conversion method is given as: Kifilideen scale Lukmon scale Fatimo scale Osanyinpeju scale Lekan scale 10 21.83 11.53 34.59 14.90 ๐’™ ๐‘€๐‘˜ ๐’š ๐‘€๐‘™ ๐‘ง ๐‘€๐‘“ ๐‘  ๐‘€๐‘œ ๐‘› ๐‘€๐‘™๐‘’ 0 0 0 0 0 Establishment of Kifilideen formula in determining the difference between the magnitudes of population in two different locations using Kifilideen, Lukmon and Fatimo scales If the magnitude of the first population, ๐‘ƒ1 is ๐‘€1 and the magnitude of the second population, ๐‘ƒ2 is ๐‘€2; then the difference, ๐ท in the magnitude of the population of ๐‘ƒ1 and ๐‘ƒ2 in two differences location using Kifilideen population scale is given as: If the magnitude of the first population ๐‘ƒ1 is ๐‘€1 in location 1; using the Kifilideen population scale, then ๐‘€1 = ๐พ๐‘–๐‘“ ๐‘ƒ1 (31) If the magnitude of the second population ๐‘ƒ2 is ๐‘€2 in location 2; using the Kifilideen population scale, then ๐‘€2 = ๐พ๐‘–๐‘“ ๐‘ƒ2 (32) The difference in the magnitude of the population, ๐ท for the two locations 1 and 2 is given as; ๐ท = ๐‘€2 โˆ’ ๐‘€1 = ๐พ๐‘–๐‘“ ๐‘ƒ2 ๐‘ƒ1 (33) On Lukmon scale, The difference in the magnitude of the population, ๐ท for the two locations 1 and 2 using the Lukmon scale is; ๐ท = ๐‘€2 โˆ’ ๐‘€1 = ๐ฟ๐‘ข๐‘˜ ๐‘ƒ2 ๐‘ƒ1 (34) On Fatimo scale, The difference in the magnitude of the population, ๐ท for the two locations 1 and 2 using the Fatimo scale is given as; ๐ท = ๐‘€2 โˆ’ ๐‘€1 = ๐น๐‘Ž๐‘ก ๐‘ƒ2 ๐‘ƒ1 (35) Inauguration of Kifildeen rate of change in the magnitude of the population formula using Kifilideen, Lukmon and Fatimo population scales If the magnitude of the initial population ๐‘ƒ๐‘œ is ๐‘€๐‘œ; using the Kifilideen population scale, then ๐‘€๐‘œ = ๐พ๐‘–๐‘“ ๐‘ƒ๐‘œ (36) In ๐‘› years, the magnitude of the population ๐‘ƒ๐‘› is ๐‘€๐‘›; using the Kifilideen population scale, then ๐‘€๐‘› = ๐พ๐‘–๐‘“ ๐‘ƒ๐‘› (37) The change in the magnitude of the population for the ๐‘› years is given as; ๐‘‘๐‘€ = ๐‘€๐‘› โˆ’ ๐‘€๐‘œ = ๐พ๐‘–๐‘“ ๐‘ƒ๐‘› ๐‘ƒ๐‘œ (38) The Kifilideen rate of change in the magnitude of the population for the ๐‘› years using Kifilideen population scale is given as; ๐‘‘๐‘€ ๐‘‘๐‘ก = ๐‘€๐‘›โˆ’๐‘€๐‘œ ๐‘› = ๐ท ๐‘› = 1 ๐‘› ๐พ๐‘–๐‘“ ๐‘ƒ๐‘› ๐‘ƒ๐‘œ (39) Where ๐‘‘๐‘€ ๐‘‘๐‘ก is the rate of change of magnitude of the population, ๐‘‘๐‘€ or ๐ท is the change in population, ๐‘€๐‘› is the magnitude of the population ๐‘ƒ๐‘›, ๐‘€๐‘œ is the magnitude of the initial population ๐‘ƒ๐‘œ, ๐‘› is the number of years, ๐‘ƒ๐‘œ is the initial population of entity and ๐‘ƒ๐‘› is the population after ๐‘› years. โˆซ ๐‘‘๐‘€ = โˆซ ๐ท ๐‘› ๐‘‘๐‘ก (40) ๐‘€ = ๐ท ๐‘› ๐‘ก + ๐ถ (41) When ๐‘ก = 0, ๐‘€ = ๐‘€๐‘œ (42) 20 ๐‘€๐‘œ = ๐ท ๐‘› ร— 0 + ๐ถ (43) ๐ถ = ๐‘€๐‘œ (44) ๐‘€๐‘ = ๐ท ๐‘› ๐‘ก + ๐‘€๐‘œ (45) Where ๐ท is the difference between the magnitude of the population at ๐‘ก = ๐‘› and ๐‘ก = 0; ๐‘› is the number of years considered; ๐‘ก is the ๐‘›๐‘กโ„Ž years; ๐‘€๐‘› is the magnitude of the population of the ๐‘›๐‘กโ„Ž year and ๐‘€๐‘œ is the magnitude of the population of the 0๐‘กโ„Ž year For Lukmon population scale, The Kifilideen rate of change in the magnitude of the population for the ๐‘› years using Kifilideen population scale is given as; ๐‘‘๐‘€ ๐‘‘๐‘ก = ๐‘€๐‘›โˆ’๐‘€๐‘œ ๐‘› = 1 ๐‘› ๐ฟ๐‘ข๐‘˜ ๐‘ƒ๐‘› ๐‘ƒ๐‘œ (46) Where ๐‘‘๐‘€ ๐‘‘๐‘ก is the rate of change of magnitude of the population, ๐‘‘๐‘€ is the change in population ๐‘€๐‘› is the magnitude of the population ๐‘ƒ๐‘›, ๐‘€๐‘œ is the magnitude of the initial population ๐‘ƒ๐‘œ, ๐‘› is the number of years, ๐‘ƒ๐‘œ is the initial population of entity and ๐‘ƒ๐‘› is the population after ๐‘› years. For Fatimo population scale, The Kifilideen rate of change in the magnitude of the population for the ๐‘› years using Kifilideen population scale is given as; ๐‘‘๐‘€ ๐‘‘๐‘ก = ๐‘€๐‘›โˆ’๐‘€๐‘œ ๐‘› = 1 ๐‘› ๐น๐‘Ž๐‘ก ๐‘ƒ๐‘› ๐‘ƒ๐‘œ (47) Where ๐‘‘๐‘€ ๐‘‘๐‘ก is the rate of change of magnitude of the population, ๐‘‘๐‘€ is the change in population ๐‘€๐‘› is the magnitude of the population ๐‘ƒ๐‘›, ๐‘€๐‘œ is the magnitude of the initial population ๐‘ƒ๐‘œ, ๐‘› is the number of years, ๐‘ƒ๐‘œ is the initial population of entity and ๐‘ƒ๐‘› is the population after ๐‘› years. The Kifilideen population growth/decline rate equation in term of magnitude The Kifilideen population growth/decline equation in term of magnitude using Kifilideen scale is given as: ๐‘€๐‘“ = ๐‘…๐‘š๐‘ก + ๐‘€๐‘– (48) Where ๐‘€๐‘– is the initial magnitude of the population, ๐‘€๐‘“ is the final magnitude of the population, ๐‘…๐‘š is the Kifilideen population growth/decline rate using the Kifilideen scale and the ๐‘ก is the time interval between the initial and final. Results and Discussion Demonstration of the determination of the magnitude of the population of any entity of a state, nation or location using the Kifilideen Scale [a] Three candidates X, Y and Z are to contest for president where states A, B and C are to determine the next president from these candidates where candidate X has his strength in states A; candidates Y in state B and candidates Z in state C respectively. The population of the three states A, B and C are 1.456 million, 60.32 thousand and 9.689 million respectively. Determine [i] the magnitude of population of the states A, B and C in determining the next president using the Kifilideen scale. [ii] the state that would have the highest impact in determining the outcome of the election. [iii] which candidates is likely to win Solution [i] Using Kifilideen population scale, ๐‘€๐ด = Magnitude of population of state A = ๐พ๐‘–๐‘“ ๐‘ƒ๐ด = ๐พ๐‘–๐‘“[14.56 ร— 105] = ๐พ๐‘–๐‘“[14.56] + ๐พ๐‘–๐‘“[105] (49) = 1.11694 + 4.80126 = 5.9182 (50) ๐‘€๐ต = Magnitude of population of state B = ๐พ๐‘–๐‘“ ๐‘ƒ๐ต = ๐พ๐‘–๐‘“[60.32 ร— 103 ] = ๐พ๐‘–๐‘“[60.32] + ๐พ๐‘–๐‘“ [103] (51) = 1.70969 + 2.88076 = 4.59045 (52) ๐‘€๐ถ = Magnitude of population of state C = ๐พ๐‘–๐‘“ ๐‘ƒ๐ถ = ๐พ๐‘–๐‘“ [96.89 ร— 105] = ๐พ๐‘–๐‘“[96.89] + ๐พ๐‘–๐‘“[105] (53) = 1.90733 + 4.80126 = 6.70859 (54) [i] Since the state C has the highest of magnitude of population with value 6.70859, so state C would have the highest impact in determining the outcome of the election 21 [iii] Candidate Z has his strength in state C with the highest magnitude of population. So, candidate Z is likely to win the election Utilization of the Kifilideen conversion method of one population scale to another [b] Convert the magnitude of population 9.5 in Kifilideen scale to [i] Lukmon scale [ii] Fatimo scale Solution Kifilideen scale Lukmon scale Fatimo scale 3 10 21.83 11.53 2 9.5 ๐‘€๐‘™ y ๐‘€๐‘“ z 1 0 0 0 [i] ๐พ2โˆ’๐พ1 ๐พ3โˆ’๐พ1 = ๐ฟ2โˆ’๐ฟ1 ๐ฟ3โˆ’๐ฟ1 (55) 9.5โˆ’0 10โˆ’0 = ๐‘€๐‘™โˆ’0 21.83โˆ’0 (56) ๐‘€๐‘™ = 9.5ร—21.83 10 = 20.7385 โ‰ˆ 20.74 (57) [ii] ๐พ2โˆ’๐พ1 ๐พ3โˆ’๐พ1 = ๐น2โˆ’๐น1 ๐น3โˆ’๐น1 (59) 9.5โˆ’0 10โˆ’0 = ๐‘€๐‘“โˆ’0 11.53 โˆ’0 (60) ๐‘€๐‘“ = 9.5ร—11.53 10 = 10.9535 โ‰ˆ 10.95 (61) Illustration on the Kifilideen conversion of magnitude of the population on one scale to another scale [c] If the magnitude of the population of Town V is 6.53 using the Kilfideen scale. [i] Determine the population of Town V [ii] Obtain the magnitude of the population of town V on the Lukmon scale [iii] Obtain the magnitude of the population of Town on the Fatimo scale ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง [๐‘–] From Kifilideen population scale, ๐‘€๐‘ฃ = ๐พ๐‘–๐‘“ ๐‘ƒ๐‘ฃ , 4.56 = ๐พ๐‘–๐‘“ ๐‘ƒ๐‘ฃ (62), (63) ๐‘ƒ๐‘ฃ = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ (6.53) = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“[0.76848 + 5.76152] (64) Population of town V = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“[0.76848] ร— ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“[5.76152] = 6.314 ร— 106 (65) [ii] From Lukmon population scale, ๐‘€๐‘ฃ = ๐ฟ๐‘ข๐‘˜ [6.314 ร— 106] = ๐ฟ๐‘ข๐‘˜[63.14 ร— 105] = ๐ฟ๐‘ข๐‘˜[63.14] + ๐ฟ๐‘ข๐‘˜[105] (66) Magnitude of population of town V = ๐‘€๐‘ฃ = 3.7733 + 10.4795 = 14.2528 โ‰ˆ 14.25 (67) [ii] ๐น๐‘Ÿ๐‘œ๐‘š ๐น๐‘Ž๐‘ก๐‘–๐‘š๐‘œ ๐‘๐‘œ๐‘๐‘ข๐‘™๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘ ๐‘๐‘Ž๐‘™๐‘’, ๐‘€๐‘ฃ = ๐น๐‘Ž๐‘ก[6.314 ร— 106] = ๐น๐‘Ž๐‘ก[63.14 ร— 105] = ๐น๐‘Ž๐‘ก [63.14] + ๐ฟ๐‘ข๐‘˜[105] (68) Magnitude of population of town V = ๐‘€๐‘ฃ = 1.9935 + 5.5366 = 7.5301 โ‰ˆ 7.53 (69) The population and magnitude of the population using Kifilideen, Lukmon and Fatimo scales Table 9 indicates the population and magnitude of the population using Kifilideen, Lukmon and Fatimo scales. 22 Table 9 The population and magnitude of the population using Kifilideen, Lukmon and Fatimo scales Magnitude of Population Population Kifilideen population Scale Lukmon population scale Fatimo population scale 100 0.00 0.00 0.00 101 0.96 2.10 1.11 102 1.92 4.19 2.21 103 2.88 6.29 3.32 104 3.84 8.38 4.43 105 4.80 10.48 5.54 106 5.76 12.58 6.64 107 6.72 14.67 7.75 108 7.68 16.77 8.86 109 8.64 18.86 9.97 1010 9.60 20.96 11.07 1011 10.56 23.05 12.18 1012 11.52 25.15 13.29 1013 12.48 27.25 14.40 1014 13.44 29.34 15.50 1015 14.40 31.44 16.61 1016 15.36 33.53 17.72 1017 16.32 35.63 18.82 1018 17.28 17.28 19.93 1019 18.24 37.73 21.04 1020 19.21 41.92 22.15 Utilization of Kifilideen formula in determining the difference between the magnitudes of population in two different locations using Kifilideen, Lukmon and Fatimo scales [d] If the difference between the magnitude of population of two towns A and B is 0.87 using the Kifilideen scale and the population of A is larger than population B. If the population of B is 2.71 million, determine the [i] the magnitudes of population A and B [ii] the population of A Solution [i] ๐‘ƒ๐ต = 27.1 ร— 105 (70) Using the Kifilideen formula of difference in magnitude of population, ๐ท = ๐‘€๐ด โˆ’ ๐‘€๐ต (71) ๐‘€๐ต = ๐พ๐‘–๐‘“ ๐‘ƒ๐ต = ๐พ๐‘–๐‘“[27.1 ร— 105] = ๐พ๐‘–๐‘“[27.1] + ๐พ๐‘–๐‘“[105] = 1.37601 + 4.80126 (72) Magnitude of population B = ๐‘€๐ต = 6.17727 โ‰ˆ 6.18 (73) Magnitude of population A = ๐‘€๐ด = ๐ท + ๐‘€๐ต = 0.87 + 6.17727 = 7.04727 โ‰ˆ 7.05 (74) [ii] ๐‘€๐ด = ๐พ๐‘–๐‘“ ๐‘ƒ๐ด (75) ๐‘ƒ๐ด = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“๐‘€๐ด = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [7.04727] = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [0.3255 + 6.72177] (76) Population of A = ๐‘ƒ๐ด = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“[0.32550] ร— ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [6.72177] = 2.18259 ร— 107 (77) Population of A โ‰ˆ 21.8 ๐‘š๐‘–๐‘™๐‘™๐‘–๐‘œ๐‘› Implementation of Population Growth formula using Kifilideen, Lukmon and Fatimo Population Scales [e] The initial population of town B is 500. In five yearsโ€™ time the population of town B is 15, 000. Determine [i] the initial and final magnitude of the population of town B [ii] the change in magnitude of population of town B after the five years [iii] the rate of change of magnitude of population of towns B [iv] the population and the magnitude of the population for the 1st to fifth years and after 10 years using the Kiflideen population scales 23 Solution [i] Using Kifilideen population scale, Initial magnitude of population of town B = [๐‘€๐‘œ]๐ต = ๐พ๐‘–๐‘“ [๐‘ƒ๐‘œ]๐ต = ๐พ๐‘–๐‘“ [5 ร— 102] = ๐พ๐‘–๐‘“ 5 + ๐พ๐‘–๐‘“ [102] (78) Initial magnitude of population of town B = [๐‘€๐‘œ]๐ต = 0.67119 + 1.92051 = 2.59170 โ‰ˆ 2.59 (79) Final magnitude of population of town B after 5 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘  = ๐พ๐‘–๐‘“ [๐‘ƒ5]๐ต = ๐พ๐‘–๐‘“ [15 ร— 103] = ๐พ๐‘–๐‘“ [15] + ๐พ๐‘–๐‘“ [103] Final magnitude of population of town B after 5 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘  = [๐‘€5]๐ต = 1.12934 + 2.88076 = 4.0101 โ‰ˆ 4.01 (80) [ii] Using the Kifilideen formula of difference in magnitude of population, Change in magnitude of population of B = ๐ท๐ด = [๐‘€5]๐ต โˆ’ [๐‘€๐‘œ]๐ต = ๐พ๐‘–๐‘“ [๐‘ƒ5]๐ต [๐‘ƒ๐‘œ]๐ต = ๐พ๐‘–๐‘“ [ 15000 500 ] = ๐พ๐‘–๐‘“ 30 (81) Change in magnitude of population of B after 5 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘  = ๐ท๐ต = [๐‘‘๐‘€]๐ต = 1.41841 โ‰ˆ 1.42 (82) [iii] Using the Kifilideen formula of rate of change of magnitude of population of any entity, The rate of change in the magnitude of the population of town B = [๐‘‘๐‘€]๐ต ๐‘‘๐‘ก = ๐ท๐ต [๐‘›]๐ต = [๐‘€5]๐ตโˆ’[๐‘€๐‘œ]๐ต [๐‘›]๐ต = 1 [๐‘›]๐ต ๐พ๐‘–๐‘“ [๐‘ƒ5]๐ต [๐‘ƒ๐‘œ]๐ต The rate of change in the magnitude of the population of town B = ๐ท๐ต [๐‘›]๐ต = 1.41841 5 = 0.28368/๐‘ฆ๐‘’๐‘Ž๐‘Ÿ (83) [iv] Using Kifilideen population scale To determine the magnitude of the population of B for 1๐‘ ๐‘ก to 5๐‘กโ„Ž year and after 20 years, [๐‘‘๐‘€]๐ต ๐‘‘๐‘ก = 0.28368/๐‘ฆ๐‘’๐‘Ž๐‘Ÿ (84) โˆซ[๐‘‘๐‘€]๐ต = โˆซ 0.28368 ๐‘‘๐‘ก (85) ๐‘€๐ต = 0.28368 ๐‘ก + ๐ถ (86) When ๐‘ก = 0 (87) [๐‘€๐‘œ]๐ต = 0.28368 ร— 0 + ๐ถ = ๐ถ (88) ๐‘€๐ต = 0.28368 ๐‘ก + [๐‘€๐‘œ]๐ต (89) From (3.34), [๐‘€๐‘œ]๐ต = 2.59170 (90) ๐‘€๐ต = 0.28368 ๐‘ก + 2.59170 (91) ๐‘ก = 0 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ, [๐‘€๐‘œ]๐ต = 0.28368 ร— 0 + 2.59170 = 2.59170 (92) ๐‘ก = 1 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ, [๐‘€1]๐ต = 0.28368 ร— 1 + 2.59170 = 2.87538 (93) ๐‘ก = 2 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘€2]๐ต = 0.28368 ร— 2 + 2.59170 = 3.15906 (94) ๐‘ก = 3 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘€3]๐ต = 0.28368 ร— 3 + 2.59170 = 3.44274 (95) ๐‘ก = 4 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘€4]๐ต = 0.28368 ร— 4 + 2.59170 = 3.72642 (96) ๐‘ก = 5 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘€5]๐ต = 0.28368 ร— 5 + 2.59170 = 4.01010 (97) ๐‘ก = 10 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘€10]๐ต = 0.28368 ร— 10 + 2.59170 = 5.4285 (98) To determine the population of B for 1๐‘ ๐‘ก to 5๐‘กโ„Ž year and after 10 years, [๐‘ƒ๐‘ก]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€๐‘ก]๐ต (99) ๐‘ก = 0 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ, [๐‘ƒ๐‘œ]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€๐‘œ]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 2.59170 = 500 (100) ๐‘ก = 1 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ, [๐‘ƒ1]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€1]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 2.87538 = 987 (101) ๐‘ก = 2 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘ƒ2]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€2]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 3.15906 = 1, 949 (102) ๐‘ก = 3๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘ƒ3]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€3]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 3.44274 = 3, 848 (103) ๐‘ก = 4 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ, [๐‘ƒ4]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€4]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 3.72642 = 7, 597 (104) ๐‘ก = 5 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘ƒ5]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€5]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 4.01010 = 15, 000 (105) ๐‘ก = 10 ๐‘ฆ๐‘’๐‘Ž๐‘Ÿ๐‘ , [๐‘ƒ10]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ [๐‘€10]๐ต = ๐ด๐‘›๐‘ก๐‘–๐พ๐‘–๐‘“ 5.4285 = 449, 987 (106) So the population of B after 10 years is 449, 987 4 Conclusion This study established the Kifilideen, Lukmon and Fatimo scales to determine the magnitude of the population of any particular entity of a state, nation or location. The research work also invented the Lukmon (Power of base 3) and AntiLumon (Antipower of base 3) with Fatimo (Power of base 8) and AntiFatimo (Antipower of base 8) tables in evaluating the magnitude of the population of an entity. The paper illustrates on how to convert from one population scale to another. The study provides formulas for the determination of the magnitude of both the population and population density of any particular entities such as human being, bacteria and plant which would be useful to decide the level of impact of that entity in the location. The magnitude of the population of an entity is an easy and simplified form of representing the population of an entity. The magnitude of the population can be useful in the classification of the population of an entity into levels and sizes. 24 References Agarwal, S. (2014). Impact of Indiaโ€™s Population Growth on Economic Development. 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