Base 13
Encyclopedia
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.
by Douglas Adams
, a possible question to get the answer "forty-two" is presented: "What do you get if you multiply six by nine?" 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.
used a base system (the trecena
), with 13x20 days for the Tzolkin cycle.
is used as a counterexample to the converse of the intermediate value theorem
that is discontinuous at every point.
Positional notation
Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...
numeral system
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
with thirteen
13 (number)
13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....
as its base
Radix
In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...
. It uses 13
13 (number)
13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....
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.
Base 13 in fiction
In the end of The Restaurant at the End of the UniverseThe Restaurant at the End of the Universe
The Restaurant at the End of the Universe is the second book in the Hitchhiker's Guide to the Galaxy comedy science fiction trilogy of five by Douglas Adams. It was originally published by Pan Books as a paperback. The book was inspired by the song "Grand Hotel" by British rock band Procol Harum...
by Douglas Adams
Douglas Adams
Douglas Noel Adams was an English writer and dramatist. He is best known as the author of The Hitchhiker's Guide to the Galaxy, which started life in 1978 as a BBC radio comedy before developing into a "trilogy" of five books that sold over 15 million copies in his lifetime, a television...
, a possible question to get the answer "forty-two" is presented: "What do you get if you multiply six by nine?" Of course, the answer is deliberately wrong, creating a humorous effect – if the calculation is carried out in base 10
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
. 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.
Base-13 calendar
The Maya calendarMaya calendar
The Maya calendar is a system of calendars and almanacs used in the Maya civilization of pre-Columbian Mesoamerica, and in many modern Maya communities in highland Guatemala. and in Chiapas....
used a base system (the trecena
Trecena
A trecena is a 13-day period used in pre-Columbian Mesoamerican calendars. The 260-day calendar was divided into 20 trecenas. Trecena is derived from the Spanish chroniclers and translates to 'a group of thirteen' in the same way that a dozen relates to the number twelve...
), with 13x20 days for the Tzolkin cycle.
Base-13 used in mathematics
The Conway base 13 functionConway base 13 function
The Conway base 13 function is a function created by British mathematician John H. Conway as a counterexample to the converse of the intermediate value theorem. In other words, even though Conway's function f is not continuous, if f ...
is used as a counterexample to the converse of the intermediate value theorem
Intermediate value theorem
In mathematical analysis, the intermediate value theorem states that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is at least one point in its domain that the function maps to that value....
that is discontinuous at every point.