newmath
Tools for NewBase60, NewBase64 and NewDateTime numbering systems.
NewBase60
NewBase60 is a base 60 (sexagesimal) numbering system that uses only ASCII numbers and letters that are print, prose and code safe. Lowercase l and uppercase I are aliased to the number 1. Capital O is aliased to the number 0.
0123456789ABCDEFGHJKLMNPQRSTUVWXYZ_abcdefghijkmnopqrstuvwxyz
NewBase60 encoded numbers sort properly in the typical case.
NewBase64
NewBase64 is a base 64 numbering system that extends NewBase60 for use in shortly encoding square grids. The four characters added are -, +, * and $.
0 1 2 3 4 5 6 7 ---------------- 0| 0 1 2 3 4 5 6 7 8| 8 9 A B C D E F 16| G H J K L M N P 24| Q R S T U V W X 32| Y Z _ a b c d e 40| f g h i j k m n 48| o p q r s t u v 56| w x y z - + * $
latitude: -90 to 90 (pole to pole) longitude: -180 to 180 (meridian back to meridian)
Earth is split into 32 quadrants:
0 1 2 3 4 5 6 7 8 9 A B C D E F G H J K L M N P Q R S T U V W X
Each quadrant can be further scoped by 1/64ths. e.g. the 0th quadrant:
0 1 2 3 4 5 6 7 8 9 A B C D E F G H J K L M N P Q R S T U V W X Y Z _ a b c d e f g h i j k m n o p q r s t u v w x y z - + * $
The initial quadrant is divided into 64 subquadrants with dimensions 5.625 degrees square. Second and third subquadrants are 0.703125 and 0.087890625 degrees square respectively.
1 degree latitude = between 110.567 (at equator) and 111.699 km (at poles) 1 degree longitude = between 111.321 (at equator) and 0 (at poles)
precision scope
1 4.950 Mm
2 618.75 km 3 77.34375 km 4 9.66796875 km 5 1.20849609375 km
6 151.06201171 m 7 18.8827514648 m 8 2.36034393311 m
9 295.04299163 mm 10 36.88037395 mm 11 4.61004674 mm
12 576.25584 μm 13 72.0319803804 μm 14 9.00399754755 μm 15 1.12549969344 μm
NewDateTime
Four sundays (0th day of the week) mark solar equinoxes and solstices. Monday through Saturday are days 1-6. Friday and Saturday are weekends resulting in a "4 day work week".
5 days 52 weeks = 260 work days in existing calendar 5 days 50 weeks = 250 work days accounting for two weeks vacation 4 days * 60 weeks = 240 work days in NewDateTime
Four 90 day, 15 week quarters. Each quarter is split into three months.
52 days * 4 quarters = 184 work days accounting for mid-quarter vacation
Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar
0123456789ABCDEFGHJKLMNPQRSTUVWXYZ_abcdefghijkmnopqrstuvwxyz Su @--------------@--------------@--------------@-------------- 0 Mo X X X X 1 Tu X X X X 2 We X X X X X X X X X X X X 3 Th X X X X X X X X X X X X 4 Fr XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 5 Sa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 6
@ - sunday X - non-work
0 year 1
000 new epoch
000 Sunday
000 northern tilt - new first sunday (old Mar 20, equinox) 0F0 northern sun - new second sunday (old Jun 21, northern solstice) 0W0 southern tilt - new third sunday (old Sep 23, equinox) 0k0 southern sun - new fourth sunday (old Dec 21, southern solstice)
001 Monday 002 Tuesday 003 Wednesday 004 Thursday 005 Friday 006 Saturday
0z6 last day of first year
100 second new new year
1 year 2 1R 26th week of the 2nd year 1R0 Monday of the 26th week of the 2nd year
Based upon @[Tantek Çelik][1]'s [NewBase60][2], [NewBase64][3] and [NewCalendar][4] specifications.