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Dulo-Rudran Numbers


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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. 

 

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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).

 

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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

 

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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

 

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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

 

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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 

 

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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).

 

 

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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.))

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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.))

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