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1729 is known as the Hardy-Ramanujan number, after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan. In Hardy's words [1]:
| |||
| 1729 | |||
|---|---|---|---|
| Cardinal | One thousand seven hundred [and] twenty-nine | ||
| Ordinal | 1729th | ||
| Factorization | |||
| Divisors | 7,13,19,91,133,247 | ||
| Roman numeral | MDCCXXIX | ||
| Binary | 11011000001 | ||
| Hexadecimal | 6C1 | ||
The quote is sometimes expressed using the term "positive cubes", as the admission of negative perfect cubes (the cube of a negative integer) gives the smallest solution as 189:
Of course, equating "smallest" with "most negative", as opposed to "closest to zero" gives rise to solutions like -189, -1729, and further negative numbers. This unclearness is eliminated by the term "positive cubes".
Numbers such as
which can be expressed as the sum of cubes in distinct ways have been dubbed taxicab numbers. The number was also found in one of his notebooks dated years before the incident.
1729 is the third Carmichael numberIn number theory, a Carmichael number is a composite positive integer n such that for any integer a relatively prime to n with 1 ≤ a ≤ n it is true that a n ≡ a (mod n (see modular arithmetic). Overview Fermat's little theorem states that all, and a Zeisel numberA Zeisel number is a square-free integer k with at least three prime factors which fall into the pattern where a and b are fixed constants and x is the index number of each prime factor in the factorization, sorted from lowest to highest. For the purpose.
It is a centered cube numberA centered cube number is a centered figurate number that represents a cube. The centered cube number for n is given by the equation The first few centered cube numbers are 1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471,, as well as 12- gonalIn mathematics, a polygonal number is a number that can be arranged as a regular polygon. Ancient mathematicians discovered that numbers could be arranged in certain ways when they were represented by pebbles or seeds. The number 10, for example, can be a, 24-gonal and 84-gonal number.
1729 has another property -- the 1729th decimal place is the beginning of the first occurrence of all ten digits consecutively in the decimal representation of eThe mathematical constant e (occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms) is the base of the natural logarithm function., although, of course, this fact would have been unknown to either mathematician, since the computer algorithms used to discover this weren't implemented till much later. [2]
Because in base 10 the number 1729 is divisible by the sum of its digits, it is a Harshad numberA Harshad number or Niven number is an integer that is divisible by the sum of its digits in a given number base. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997. All numbers between zer. It also has this property in octalThe octal numeral system is the base 8 number system, and uses the digits 0 7. According to Donald Knuth's The Art of Computer Programming it was invented by King Charles XII of Sweden. Octal numerals can be made from binary numerals by grouping consecuti and hexadecimal, but not in binary.
Bender, the robot on the television show Futurama, has a serial number of 1729. Ken Keeler, a writer on the show with a Ph. D. in Applied Math, said that "that 'joke' alone is worth six years of grad school." The serial-number on the ship Nimbus (which also is from Futurama), contains this magic number as well.