yopplwasupxxx 5665 Share Posted October 6, 2019 THE DULO-RUDRAN NUMERALS AND THE DUODECIMAL SYSTEM BY JAN RAWSZ Փ - Ւ - Բ - Գ - Դ - Ե - Զ - Է - Ը - Թ - Ժ - Ի In compilation with work of historians Tomasz Hidgor and Sofiya Kosselberg-Ladau and fellow mathematician Cetibor van Dhoon, together to create the first modern record of the ancient numerics of the highlander peoples. --- I dedicate this work to my sister, Yolanda, and her newborn, and a thousand curses upon the sout Vratemar, whose spine cracked upon the crux of fatherhood. Introduction Traditionally, compared to the southern heartlands, the numeric system of the highlander people was a barbaric trife. Called Bvt, or tally sticks, majority of records and numbers were maintained merely by sets of criss-crossed lines added together vertically. This archaic system was long-winded and not fit for calculations beyond simple addition and subtraction, and proved a burden and hinder upon progress in the north. Slowly, especially in the southern basin cities (Lahy, Mejen, Seventy), the Jrentic numerals and decimal system of the south came in use when trade flourished in the middle Migratory Period of the 700 AES. However, in the northern basin and beyond (Dules, Sorbzborg, and beyond) retained their primeval systems for many centuries. This changed come the Rhenyari Invasions of 500s AES, where the northern coasts of Waldenia and the northern (Waldorvian) basin were most hit, falling to both tribal and city-state infighting and the superior technology and logistics of the Akrito-Rudran forces. For the following century of on-and-off Rhenyari yolk, the incoming invaders introduced many of their social programs and reforms into the native Almanno-Raev societies, including a refinement of grammar, a recalculation of the calendar and time-systems, but most importantly, the introduction of proper integers. Dules and the lands of Dulonia (northern basin) first began use of a raevified numeral system by 570 AES, and first published in record in the Dulonian trade calculations by 566 AES. These numbers, known as the Dulo-Rudran numerals (simply called ‘Rudran’ by the native highlanders), spread rapidly in the Rhenyari-controlled areas, and for two centuries, were in common use, though soon fell out come the end of the migratory periods. When Karov the Great reunited the raev realms (including Dules and Lahy), he codified the common numbers over the Dulo-Rudran numbers in 423 AES as part of his economic reforms, and the northern hansetian kingdoms and tribes soon followed suit. Iconic to the Dulo-Rudran system is the duodecimal over the Jrentic decimal system, where twelve instead of ten is the base of units. Though the system is called ‘Rudran’, the duodecimal system is actually Akritian, with the modern Rudrans using the sexageismal system instead (60). --- The Dulo-Rudran Numbers Rudran Common Naumarian Trans. Rudran Common Naumarian Trans. Փ 0 Zur ՒՓ 12 Dwolv Ւ 1 Auwn ԲՓ 24 Trewolv Բ 2 Zwien ԳՓ 36 Merewolv Գ 3 Dres ԴՓ 48 Furwolv Դ 4 Vaur ԵՓ 60 Sarcelv Ե 5 Sieg ԶՓ 72 Gredelv Զ 6 Zeg ԷՓ 84 Zvelolv Է 7 Zelv ԸՓ 96 Bzorelv Ը 8 Aicht ԹՓ 104 Timorelv Թ 9 Nien ԺՓ 120 Yigrelv Ժ 10 Den ԻՓ 132 Iszirelv Ի 11 Arvin ՒՓՓ 144 Nzik --- The Dulo-Rudran Numbers – Base Powers Rudran Common Naumarian Trans. Rudran Naumarian Trans. Ւ 1 Auwn Փ.Ւ Aziy ՒՓ 12 Dwolv Փ.ՓՒ Dwoziy ՒՓՓ 144 Nzik Փ.ՓՓՒ Nzikoziy Ւ,ՓՓՓ 1,728 Muul Փ.ՓՓՓ,Ւ Muloziy ՒՓ,ՓՓՓ 20,736 Denmuul Փ.ՓՓՓ,ՓՒ Denmuloziy ՒՓՓ,ՓՓՓ 248,832 Nzikmuul Փ.ՓՓՓ,ՓՓՒ Nzikmuloziy Ւ,ՓՓՓ,ՓՓՓ 2,985,984 Karyg Փ.ՓՓՓ,ՓՓՓ,Ւ Krygziy --- The Dulo-Rudran Numbers – Conversion Table Rud. Com. Rud. Com. Rud. Com. Rud. Com. Rud. Com. Rud. Com. ՒՓ 12 ՒՓՓ 144 Ւ,ՓՓՓ 1,728 ՒՓ,ՓՓՓ 20,736 ՒՓՓ,ՓՓՓ 248,832 Ւ,ՓՓՓ,ՓՓՓ 2,985,984 ԲՓ 24 ԲՓՓ 288 Բ,ՓՓՓ 3,456 ԲՓ,ՓՓՓ 41,472 ԲՓՓ,ՓՓՓ 497,664 Բ,ՓՓՓ,ՓՓՓ 5,971,968 ԳՓ 36 ԳՓՓ 432 Գ,ՓՓՓ 5,184 ԳՓ,ՓՓՓ 62,208 ԳՓՓ,ՓՓՓ 746,496 Գ,ՓՓՓ,ՓՓՓ 8,957,952 ԴՓ 48 ԴՓՓ 576 Դ,ՓՓՓ 6,912 ԴՓ,ՓՓՓ 82,944 ԴՓՓ,ՓՓՓ 995,328 Դ,ՓՓՓ,ՓՓՓ 11,943,936 ԵՓ 60 ԵՓՓ 720 Ե,ՓՓՓ 8,640 ԵՓ,ՓՓՓ 103,680 ԵՓՓ,ՓՓՓ 1,244,160 Ե,ՓՓՓ,ՓՓՓ 14,929,920 ԶՓ 72 ԶՓՓ 864 Զ,ՓՓՓ 10,368 ԶՓ,ՓՓՓ 124,416 ԶՓՓ,ՓՓՓ 1,492,992 Զ,ՓՓՓ,ՓՓՓ 17,915,904 ԷՓ 84 ԷՓՓ 1,008 Է,ՓՓՓ 12,096 ԷՓ,ՓՓՓ 145,152 ԷՓՓ,ՓՓՓ 1,741,824 Է,ՓՓՓ,ՓՓՓ 20,901,888 ԸՓ 96 ԸՓՓ 1,152 Ը,ՓՓՓ 13,824 ԸՓ,ՓՓՓ 165,888 ԸՓՓ,ՓՓՓ 1,990,656 Ը,ՓՓՓ,ՓՓՓ 23,887,872 ԹՓ 108 ԹՓՓ 1,296 Թ,ՓՓՓ 15,552 ԹՓ,ՓՓՓ 186,624 ԹՓՓ,ՓՓՓ 2,239,488 Թ,ՓՓՓ,ՓՓՓ 26,873,856 ԺՓ 120 ԺՓՓ 1,440 Ժ,ՓՓՓ 17,280 ԺՓ,ՓՓՓ 207,360 ԺՓՓ,ՓՓՓ 2,488,320 Ժ,ՓՓՓ,ՓՓՓ 29,859,840 ԻՓ 132 ԻՓՓ 1,584 Ի,ՓՓՓ 19,008 ԻՓ,ՓՓՓ 228,096 ԻՓՓ,ՓՓՓ 2,737,152 Ի,ՓՓՓ,ՓՓՓ 32,845,824 --- The Dulo-Rudran Numbers – Multiplication Table C. / 1 2 3 4 5 6 7 8 9 10 11 12 / R. Ւ Բ Գ Դ Ե Զ Է Ը Թ Ժ Ի ՒՓ 1 Ւ Ւ Բ Գ Դ Ե Զ Է Ը Թ Ժ Ի ՒՓ 2 Բ Բ Դ Զ Ը Ժ ՒՓ ՒԲ ՒԴ ՒԶ ՒԸ ՒԺ ԲՓ 3 Գ Գ Զ Թ ՒՓ ՒԳ ՒԶ ՒԹ ԲՓ ԲԳ ԲԶ ԲԹ ԳՓ 4 Դ Դ Ը ՒՓ ՒԴ ՒԸ ԲՓ ԲԴ ԲԸ ԳՓ ԳԴ ԳԸ ԴՓ 5 Ե Ե Ժ ՒԳ ՒԸ ԲՒ ԲԶ ԲԻ ԳԴ ԳԹ ԴԲ ԴԷ ԵՓ 6 Զ Զ ՒՓ ՒԶ ԲՓ ԲԶ ԳՓ ԳԶ ԴՓ ԴԶ ԵՓ ԵԶ ԶՓ 7 Է Է ՒԲ ՒԹ ԲԴ ԲԻ ԳԶ ԴՒ ԴԸ ԵԳ ԵԺ ԶԵ ԷՓ 8 Ը Ը ՒԴ ԲՓ ԲԸ ԳԴ ԴՓ ԴԸ ԵԴ ԶՓ ԶԸ ԷԴ ԸՓ 9 Թ Թ ՒԶ ԲԳ ԳՓ ԳԹ ԴԶ ԵԳ ԶՓ ԶԹ ԷԶ ԸԳ ԹՓ 10 Ժ Ժ ՒԸ ԲԶ ԳԴ ԴԲ ԵՓ ԵԺ ԶԸ ԷԶ ԸԴ ԹԲ ԺՓ 11 Ի Ի ՒԺ ԲԹ ԳԸ ԴԷ ԵԶ ԶԵ ԷԴ ԸԳ ԹԲ ԺՒ ԻՓ 12 ՒՓ ՒՓ ԲՓ ԳՓ ԴՓ ԵՓ ԶՓ ԷՓ ԸՓ ԹՓ ԺՓ ԻՓ ՒՓՓ --- Divisibility Rules Because of the differences of the systems, I have included a list of easy-to-remember divisibility rules of these numbers. Ւ (1) All integers are divisible by Ւ (1). Բ (2) If an integer is divisible by Բ (2), then the unit digit of that number will be Փ (0), Բ (2), Դ (4), Զ (6), Ը (8), or Ժ (10). Գ (3) If an integer is divisible by Գ (3), then the unit digit of that number will be Փ (0), Գ (3), Զ (6), or Թ (9). Դ (4) If an integer is divisible by Դ (4), then the unit digit of that number will be Փ (0), Դ (4), or Ը (8). Ե (5) To test for divisibility by Ե (5), double the units digit and subtract the result from the number formed by the rest of the digits. If the result is divisible by Ե (5), then the number itself is divisible by Ե (5). Զ (6) If an integer is divisible by Զ (6), then the unit digit of that number will be Փ (0) or Զ (6). Է (7) To test for divisibility of Է (7), triple the units digit and add the result to the number formed by the rest of the digits. If the result is divisible by Է (7), then the number itself is divisible by Է (7). Ը (8) If the two-digit number formed by the last two digits of the given number is divisible by Ը (8), then the number itself is divisible by Ը (8). Թ (9) If the two-digit number formed by the last two digits of the given number is divisible by Թ (9), then the number itself is divisible by Թ (9). Ժ (10) If the integer is divisible by Բ (2) and Ե (5) then the number of divisible by Ժ (10). Ի (11) If the sum of the digits divisible by Ի (11), then the number itself is divisible by Ի (9). ՒՓ (12) If the integer is divisible by ՒՓ (10), then the unit digit of that number will be Փ (0). 5 Link to post Share on other sites More sharing options...
Lsuvsfar 255 Share Posted October 6, 2019 An ancient Elven astronomer would look over the published work, fascinated by the base 12 numbering system. However, he would look over the multiplication table, puzzled. Upon rechecking the numbers, he would pen a letter to the authors of this study, informing them of a miscalculation. (( @yopplwasupxxx 0 multiplied by any factor should still be 0, even under a base 12 system. You appear to have treated 0 as 1.)) Link to post Share on other sites More sharing options...
yopplwasupxxx 5665 Author Share Posted October 6, 2019 1 minute ago, Lsuvsfar said: An ancient Elven astronomer would look over the published work, fascinated by the base 12 numbering system. However, he would look over the multiplication table, puzzled. Upon rechecking the numbers, he would pen a letter to the authors of this study, informing them of a miscalculation. (( @yopplwasupxxx 0 multiplied by any factor should still be 0, even under a base 12 system. You appear to have treated 0 as 1.)) ((The chart is a tad confusing but the 0 ain’t being crossed with anything since I thought it kinda redundant to put it. I’ll try to make it more clear that 0 is more off to the side than actually looking like its being multiplied by anything.)) Link to post Share on other sites More sharing options...
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