Taxicab number

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 1³ + 12³ = 9³ + 10³.

1. How do I find my taxicab number?
2. How many taxicab numbers are there?
3. Why is 1729 called Ramanujan number?
4. What is the second taxicab number?
5. What is taxicab geometry used for?
6. Why is it called taxicab number?
7. Why is 1729 a magic number?
8. What is the smallest taxicab number?
9. What is the special of 1729?
10. Why is 1728 a special number?
11. Who wrote book on Ramanujan?
12. Is taxicab one word or two?
13. What is a taxicab circle?
14. Where can I find Ramanujan number?

How do I find my taxicab number?

The nth Taxicab number Taxicab(n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Taxicab(2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).

How many taxicab numbers are there?

Sloane defines a slightly different type of taxicab numbers, namely numbers which are sums of two cubes in two or more ways, the first few of which are 1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, ... (OEIS A001235).

Why is 1729 called Ramanujan number?

The Hardy-Ramanujan number is named such after an anecdote of the British mathematician G.H. Hardy who had gone to visit S. Ramanujan in hospital. ... 1729 is the sum of the cubes of 10 and 9 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

What is the second taxicab number?

The second is 1729, which can be written as the sum of two cubes in two different ways. The third taxi cab number is 87539319, the smallest number that is equal to the sum of two cubes in three different ways. The fourth one is the sum of two cubes written in four different ways.

What is taxicab geometry used for?

Taxicab geometry can be used to assess the differences in discrete frequency distributions. For example, in RNA splicing positional distributions of hexamers, which plot the probability of each hexamer appearing at each given nucleotide near a splice site, can be compared with L1-distance.

Why is it called taxicab number?

The most famous taxicab number is 1729 = Ta(2) = 1³ + 12³ = 9³ + 10³. The name is derived from a conversation in about 1919 involving mathematicians G. H. ... 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen.

Why is 1729 a magic number?

It is 1729. Discovered by mathemagician Srinivas Ramanujan, 1729 is said to be the magic number because it is the sole number which can be expressed as the sum of the cubes of two different sets of numbers.

What is the smallest taxicab number?

So 729+1000=1729 There are other numbers that can be shown to be the sum of two cubes in more than one way, but 1729 is the smallest of them.

What is the special of 1729?

1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 - a cube of 10 is 1000 and a cube of 9 is 729; adding the two numbers results in 1729.

Why is 1728 a special number?

1728 is the cube of 12 and, as such, is important in the duodecimal number system, in which it is represented as "1000". It is the number of cubic inches in a cubic foot. 1728 occurs in the algebraic formula for the j-invariant of an elliptic curve. ... The number 1728 is one less than the Hardy–Ramanujan number 1729.

Who wrote book on Ramanujan?

5.0 out of 5 stars Makes you realise what a Genius Srinivas Ramanujan was ! This biography of respected Shri S. Ramanujan by Robert Kanigel gives detailed insight on the life, character and the Genius of Ramanujan.

Is taxicab one word or two?

"Taxicab" is a compound word formed from contractions of "taximeter" and "cabriolet".

What is a taxicab circle?

The Circle in the Taxicab world

We can define a circle to be the set of points which are a constant distance from a centre. For example if we take all the points which are a distance of 4 units from a point A, then we have a circle of radius 4 with a centre at point A.

Where can I find Ramanujan number?

Ramanujan Numbers are the numbers that can be expressed as sum of two cubes in two different ways. Therefore, Ramanujan Number (N) = a³ + b³ = c³ + d³. Explanation: The number 1729 can be expressed as 12³ + 1³ and 10³ + 9³.