Dustin Jon Scott Ancient Borea
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Palæoboreanic Mathematics

Copyright © 2002-2020 C.E. by Dustin Jon Scott

Early Borean Base-5

The western Boreans tended to use base-5 numeral systems.

Base 5 00I0II0IIIIV
Base 10 0001020304
Base 5 VVIVIIVIIIVIV
Base 10 0506070809
Base 5 VVVVIVVIIVVIIIVVIV
Base 10 1011121314
Base 5 VVVVVVIVVVIIVVVIIIIVX
Base 10 1516171819
Base 5 VXVXIVXIIVXIIIIX
Base 10 2021222324
Base 5 X
Base 10 25

Late Borean Base-5

The western Boreans tended to use base-5 numeral systems.

Base 5 0001020304
Base 10 0001020304
Base 5 1011121314
Base 10 0506070809
Base 5 2021222324
Base 10 1011121314
Base 5 3031323334
Base 10 1516171819
Base 5 4041424344
Base 10 2021222324
Base 5 50
Base 10 25

Borean Base-13

The eastern Boreans tended to use base-13 numeral systems.

Base 13 000102030405060708090A0B0C
Base 10 00010203040506070809101112
Base 13 101112131415161718191A1B1C
Base 10 13141516171819202122232426
Base 13 202122232425262728292A2B2C
Base 10 26272829303132333435363738
Base 13 303132333435363738393A3B3C
Base 10 39404142434445464748495051
Base 13 404142434445464748494A4B4C
Base 10 52535455565758596061626364
Base 13 505152535455565758595A5B5C
Base 10 65666768697071727374757677
Base 13 606162636465666768696A6B6C
Base 10 78798081828384858687888990
Base 13 706172737475767778797A7B7C
Base 10 919293949596979899100101102103
Base 13 808182838485868788898A8B8C
Base 10 104105106107108109110111112113114115116
Base 13 909192939495969798999A9B9C
Base 10 117118119120121122123124125126127128129
Base 13 A0A1A2A3A4A5A6A7A8A9AAABAC
Base 10 130131132133134135136137138139140141142
Base 13 B0B1B2B3B4B5B6B7B8B9BABBBC
Base 10 143144145146147148149150151152153154155
Base 13 C0C1C2C3C4C5C6B7C8C9CACBCC
Base 10 156157158159160161162163164165166167168
Base 13 100
Base 10 169

Multiplication Table in Base-13

Base 1310 102030405060708090A0B0C0100
Base 1013 13263952657891104117130143156169
Base 130C 0C1B2A39485766758493A2B1C0
Base 1012 1224364860728496108120132144156
Base 130B 0B19273543515C6A788694A2B0
Base 1011 112233445566778899110121132143
Base 130A 0A1724313B4855626C798693A0
Base 1010 102030405060708090100110120130
Base 1309 0915212A36424B57636C788490
Base 1009 0918273645546372819099108117
Base 1308 08161B263139444C57626A7580
Base 1008 081624324048566472808896104
Base 1307 0711182229333A444B555C6670
Base 1007 07142128354249566370778491
Base 1306 060C151B242A33394248515760
Base 1006 06121824303642485460667278
Base 1305 050A12171C242931363B434850
Base 1005 05101520253035404550556065
Base 1304 04080C13171B22262A31353940
Base 1004 04081216202428323640444852
Base 1303 0306090B1215181B2124272A30
Base 1003 03060912151821242730333639
Base 1302 020406080A0C11131517191B20
Base 1002 02040608101214161820222426
Base 1301 0102030405060708090A0B0C10
Base 1001 01020304050607080910111213
0102030405060708090A0B0C10

Borean Measurements in Base-13

UnitEquivalentsImperial conversionMetric conversion
Inch1/10th Borean foot0.975 inches2.413 cm
Hand½ span
Span9¾ inches; ¾ foot; ½ cubit9.5125 inches; 0.79 feet
Foot10 inches; ⅔ cubit; ⅓ yard12.675 inches; 1.05625 feet32.1945 cm; 0.321945 m
Cubit16½ inches; 1½ feet; ½ yard19.0125 inches; 1.584375 feet0.4829175 m
Ell23¼ inches; 2¼ feet; 1½ cubits ¾ yard28.51875 inches; 2.3765625 feet0.4829175 m
Yard30 inches; 3 feet; 2 cubits38.025 inches; 3.16875 feet0.965835 m
Furlong
Mile
League
Fathom

The average height for a Borean male was about 5½ Borean feet or 3⅔ cubits (about 5.8 Imperial feet or 5’9”), with 6 feet or 4 cubits (about 6.34 imperial feet or 6’4”) being regarded as unusually tall and 5 feet or 3⅓ cubits (about 5.3 Imperial feet or 5’3”) being regarded as unusually short. Average height for a Borean female was about 5 Borean feet or 3⅓ cubits (about 5.3 Imperial feet or 5’3”), with 5½ feet or 3⅔ cubits (about 5.8 Imperial feet or 5’9”) being regarded as unusually tall and 4½ feet or 3 cubits (about 4.75 Imperial feet or 4’9”) being regarded as unusually small.

Borean Currency

The Borean shale was the standard, primary unit of currency all over ancient Borea. In western Borean societies, the shale tended to be divided into five pents, in keeping with the western Borean base-5 numeral system. In eastern Borean and Elfish societies, the shale was more often divided into thirteen lots, in keeping with the eastern Borean base-13 numeral system.

Pictured here is an "Elfin Solar", originally worth 1 shale but eventually a modest collector's piece that could be traded for several times its original value. On the left is the "skyward" side, with a 5-pointed star most likely representing the planet Venus, and wreathed with what looks strikingly like laurel. On the right is the "earthward" side, with a 5-pointed star representing the Earth-womb and surrounded by an ouroboros, which normally represented the yearly cycle of the Sun. The gold circle in the center on both sides surrounded by a field of silver represents the Sun in the sky.


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