# The Taxi number

TaxinumberAndere Eigenschaften[edit] Driving in a taxi with the number 1729, I noticed that the number seemed rather boring to me and that I was hoping it wasn't an accident. "No, " he said, "it's a very interesting number; it's the smallest number that can express as the total of two dice in two different ways.

This quote is sometimes referred to as a "positive cube", since accepting negatively perfected dice (the die of a negativ integer) gives the smallest possible result as 91 (which is a divider of 1729): Figures that are the smallest number that can be summed up as the number of two dice in n different ways[5] are called "Taxicab numbers".

This number was also found in one of Ramanujan's journals dating from years before the event and was noted by FrÃ©nicle de Bessy in 1657. 1729 is the first in the series of " Fermat near misseses " (series A050794 in the OEIS), which is in relation to Fermat's last theorem as numbers of the formula 1 + z3, which can also be expressed as the total of two other dice.

In 1729 there is also the third Carmichael number and the first Euler pseudoprim number. It' also a symbolic number. Seventeen hundred nine nine nine is a Zeisel number. It is a centred number of cubes,[7] and a twelve-ecagonal number,[8] a 24-gonale[9] and 84-gonale number. When examining couples of different integers of square shapes that equally often represented each whole number, Schiemann found that such square shapes must be present in four or more variable values, and the least possible discrimination against a four-variable couple is 1729 (Guy 2004).

Since the number 1729 is dividable by the total of its numbers in basis 10, it is a Hashad number. There is also this feature in degrees of octality (1729 = 33018, 3 + 3 + 0 + 1 = 7) and hexidecimal ( 1729 = 6C116, 6 + C4 + 1 = 1910), but not in degrees of binarity and two-decimal.

1729 is recorded as 1001 in basis 12, so its inverse in this basis has only 6 periods. In 1729, Masahiko Fujiwara showed that one of four positives numbers (the other ones being 81, 1458 and the trite case being 1) is one of four whole numbers (the other ones being 81, 1458 and the trite case being 1) which, when their numbers are added together, give a total which, when multiplicated by their inversion, gives the initial number: it is sufficient to verify totals which are identical to 0 or 1 (mod 9) to 19.

An A Disappearing Number, a 2007 piece about Ramanujan in England during World War I. 4104, the second affirmative whole number that can be summed up as two affirmative dice in two different ways. Guy, Richard K. (2004), Unsolved Problems in Number Theory, Problem Books in Mathematics, Volume 1 (3rd edition), Springer, ISBN 0-387-20860-7 - D1 refers to the Hardy Ramanujan number.

"The number 1,729 is why it' tucked away in Futurama episodes? It'?s number history: "A051015 ( Zeisel numbers)" series. Online-encyclopedia of the whole sequences. Online-encyclopedia of the whole sequences. Online-encyclopedia of the whole sequences. Online-encyclopedia of the whole sequences. "Tessellation of the Hardy-Ramanujan Taxicab number, 1729, bedrock of the whole A198775 sequence".

"1729: Taxi cabin number or Hardy Ramanujan number". Number phile.