## Tuesday, January 14, 2014

### [ebvtnykc] Base 30

Base 30 has as many terminating "decimal" expansions of fractions as base 60 (sexagesimal), making me wonder why 60 was preferred in ancient mathematics. Maybe the compactness of one quarter.

```\$ bc obase=30 for(a=2;a<=30;a=a+1){1/a+1/10^29}```

 1/2 0.15 1/3 0.10 1/4 0.07 15 1/5 0.06 1/6 0.05 1/7 1/8 0.03 22 15 1/9 0.03 10 1/10 0.03 1/11 1/12 0.02 15 1/13 1/14 1/15 0.02 1/16 0.01 26 07 15 1/17 1/18 0.01 20 1/19 1/20 0.01 15 1/21 1/22 1/23 1/24 0.01 07 15 1/25 0.01 06 1/26 1/27 0.01 03 10 1/28 1/29 1/30 0.01

I could see 120 subdivisions of a circle, 4 quadrants of 30, as being reasonable for easy trigonometry.

pi/2 = 01.17 03 21 15
pi = 03.04 07 13 00
2*pi = 06.08 14 26 00
sqrt(2) = 01.12 12 23 23
sqrt(2)/2 = .21 06 11 26
sqrt(3) = 01.21 28 25 11
sqrt(3)/2 = .25 29 12 21
phi = 01.18 16 06 28
e = 02.21 16 13 18
log(30) = 03.12 01 02 10
sqrt(1/30) = .05 14 09 15 02 21 14 06 11 11 25 11 15 00 15 05 02 11 07 03 08 05 25 14 06 14 05 12 21 23 19 10 29 18 05 00 22 09 10 00 07 18 25 17 29 01 18 07 12 05 22 21 07 16 29 20 29 23 10 20 23 15 16 27 28 10 24 03 11 27 15 12 15 12 14 04 20 29 01 25 13 08 03 05 14 16 00 26 26 06 08 17 07 27 07 18 17 19 23 25 04 07 16 26 01 05 05 25 07 22 03 16 25 14 17 08 10 07 08 21 25 04 17 14 14 09 11 05 03 02 20 12 08 03 20 21 15 28 01 09 16 24 23 00 22 11 14 05 08 16 19 21 18 02 03 14 24 25 08 19 16 20 05 19 26 28 08 13 24 02 08 15 07 13 10 21 14 14 01 29 14 18 25 22 04 18 05 10 25 19 18 20 02 16 27 06 23 07 18 28 29 22 11 06 17 02 15 14 19 02 04 26 07 24 12 23 20 02 25 23 27 24 16 04 02 07 13 06 01 22 12 20 21 24 13 27 29 03 13 21 09 21 08 13 04 01 24 20 06 26 04 26 15 28 20 18 02 13 27 17 06 03 07 16 16 20 01 19 08 12 19 15 00 02 29 13 00 06 08 24 03 21 01 19 08 18 17 05 05 07 02 12 24 08 26 27 03 15 07 02 16 23 26 05 06 26 11 17 18 15 18 24 14 11 02 02 05 27 17 17 29 14 06 12 12 06 13 05 11 25 28 17 25 19 29 08 22 23 20 12 11 27 09 17 07 23 03 12 22 17 05 24 23 24 10 10 15 01 08 22 01 12 14 25 07 23 11 27 21 20 08 15 10 00 02 28 05 19 07 10 21 24 14 00 05 29 15 16 20 22 25 12 13 20 08 23 03 29 10 11 25 09 05 10 20 06 11 21 05 22 09 27 00 11 12 08 20 02 29 26 07 29 03 17 14 18 22 17 29 14 28 09 24 12 23 10 12 24 10 06 27 28 09 07 02 27 07 10 14 15 29 27 15 19 19 13 09 16 22 08 11 18 26 15 17 01 13 05 09 02 17 22 29 23 13 07 04 19 28 20 08 28 26 05 19 10 10 19 19 20 08 18 18 23 24 11 08 01 08 27 15 14 06 15 03 19 28 08 11 14 17 15 13 11 16 22 26 27 06 04 03 18 06 08 29 12 00 27 13 19 15 18 01 02 01 23 14 08 06 26 11 05 21 27 27 00 27 10 23 11 11 13 15 09 12 24 11 00 16 09 03 25 04 12 24 03 19 20 05 08 26 11 24 01 25 18 06 25 03 21 08 25 02 20 00 24 25 05 12 28 02 21 05 25 02 22 04 16 09 21 28 14 08 05 26 03 22 16 14 00 16 29 15 07 10 25 07 15 17 00 25 05 18 10 15 17 28 07 06 24 21 29 17 08 22 09 27 02 29 28 13 27 10 00 15 19 00 14 11 01 14 24 04 16 01 19 29 27 13 24 17 29 28 23 26 07 21 03 01 18 13 26 12 27 02 04 28 25 25 02 29 04 18 16 13 14 29 09 12 16 28 20 19 11 19 05 01 27 11 08 01 22 17 08 28 21 26 11 12 13 02 11 13 22 04 21 15 09 04 19 23 17 16 04 07 25 20 06 13 29 08 07 24 04 25 13 27 11 20 15 25 01 02 10 04 26 25 02 01 12 25 23 16 08 13 02 00 00 11 14 02 20 08 05 07 02 04 24 27 27 03 28 21 07 22 16 22 04 17 18 18 13 11 23 23 04 02 08 28 17 06 06 25 16 22 00 01 05 25 25 28 12 02 28 19 17 05 03 15 20 29 23 18 28 14 01 15 02 12 22 15 21 10 21 25 14 08 17 23 15 20 21 22 03 13 10 19 23 24 26 17 24 16 21 01 13 06 21 19 18 01 28 22 19 04 07 20 07 11 29 05 05 00 26 28 21 19 29 11 25 16 21 24 06 25 28 15 01 26 23 14 00 22 09 01 07 14 09 03 17 20 12 21 01 00 23 09 29 06 04