Base 13
| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil |
Burmese Khmer Lao Mongolian Thai |
| East Asian numerals | |
| Chinese Japanese Suzhou |
Korean Vietnamese Counting rods |
| Alphabetic numerals | |
| Abjad Armenian Āryabhaṭa Cyrillic |
Ge'ez Greek Georgian Hebrew |
| Other systems | |
| Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit |
Kharosthi Mayan Quipu Roman Sumerian Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 20, 24, 30, 36, 60, 64 | |
| Balanced ternary | |
| Non-positional system | |
| Unary numeral system (Base 1) | |
| List of numeral systems | |
Base-13, tridecimal, tredecimal, or triskadecimal is a positional numeral system with thirteen as its base. It uses 13 different digits for representing numbers. Suitable digits for base 13 could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C, although any 13 characters could be used.
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[edit] Base 13 in fiction
In the end of The Restaurant at the End of the Universe by Douglas Adams, a possible question to get the answer "forty-two" is presented: "What do you get if you multiply six by nine?"[1] Of course, the answer is deliberately wrong, creating a humorous effect – if the calculation is carried out in base 10. People who were trying to find a deeper meaning in the passage soon noticed that in base 13, 613 × 913 is actually 4213 (as 4 × 13 + 2 = 54, i.e. 54 in decimal is equal to 42 expressed in base 13). When confronted with this, the author stated that it was a mere coincidence, famously stating that "I may be a sorry case, but I don't write jokes in base 13." See also The Answer to Life, the Universe, and Everything.
[edit] Base-13 calendar
The Maya calendar used a base system (the trecena), with 13x20 days for the Tzolkin cycle.[2]
[edit] Base-13 used in mathematics
The Conway base 13 function is used as a counterexample to the converse of the intermediate value theorem that is discontinuous at every point.[3]
[edit] References
- ^ The Restaurant at the End of the Universe, by Douglas Adams
- ^ Harvey M. Bricker, Victoria R. Bricker, Anthony F. Aveni, Michael P. Closs, Munro S. Edmonson, Floyd G. Lounsbury and Eric Taladoire (1983-02). Classic Maya Prediction of Solar Eclipses. JSTOR 2742481.
- ^ Willie Wong (2010-07-20). "Conway’s Base 13 Function". http://williewong.wordpress.com/2010/07/20/conways-base-13-function/.
