Why is 1729 called Ramanujan number?

The Hardy-Ramanujan number stems from an anecdote wherein the British mathematician GH Hardy had gone to meet S Ramanujan in hospital. Hardy said that he came in a taxi having the number '1729', which the British mathematician described "as rather a dull one".

Why 1729 is a Ramanujan number?

Ramanujan said that it was not. 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 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

Why is 1729 a taxi cab 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.

What is the Ramanujan number and why?

THE MYSTERY OF RAMANUJAN NUMBER

Ramanujan explained that 1729 is the only number that is the sum of cubes of two different pairs of numbers: 12³ + 1³, and 10³ + 9³. It was not a sudden calculation for Ramanujan.

Is 1729 is a perfect cube?

The number 1729 on prime factorization gives 7 × 13 × 19. Here, the prime factor 7 is not in the power of 3. Therefore the cube root of 1729 is irrational, hence 1729 is not a perfect cube.

Hardy Ramanujan Number | Discovery of this number - 1729

Who is the father of maths?

Archimedes is known as the Father Of Mathematics. He lived between 287 BC – 212 BC. Syracuse, the Greek island of Sicily was his birthplace. Archimedes was serving the King Hiero II of Syracuse by solving mathematical problems and by developing interesting innovations for the king and his army.

Why is 6174 a magic number?

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).

Who invented 0 in India?

"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.

Why is 2520 a special number?

2520 is: the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple. half of 7! (5040), meaning 7 factorial, or 1×2×3×4×5×6×7.

Where is Ramanujan Math park in India?

The Ramanujan Math Park is an Indian museum and activity center dedicated to mathematics education inside the Agastya Campus Creativity Lab located in Kuppam, in Chittoor, Andhra Pradesh.

What is Ramanujan square?

In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n².

Why is it called taxicab number?

A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways. It has nothing to do with taxis, but the name comes from a well-known conversation that took place between two famous mathematicians: Godfrey Hardy and Srinivasa Ramanujan.

Is 2520 discovered by Ramanujan?

[7 × 30 × 12 = 2520] This is the characteristic and dominance of time. These secrets about the number 2520 were discovered by the great Indian mathematician Sri Srinivasa Ramanujan. 2520 is the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple.

Who invented maths?

Archimedes is known as the Father of Mathematics. Mathematics is one of the ancient sciences developed in time immemorial. A major topic of discussion regarding this particular field of science is about who is the father of mathematics.

Who invented infinity?

infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1655.

What did Ramanujan discovered?

He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he found a value for the sum of such series using a technique he invented that came to be called Ramanujan summation.

What is the LCM of 1729?

The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729 and factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. Therefore, the Lowest Common Multiple (LCM) of 1729 and 192 is 331968 and Highest Common Factor (HCF) of 1729 and 192 is 1. Example 3: Find if 1, 19, 133, 370 and 1729 are factors of 1729.

What is the formula of Ramanujan?

(1961). "The Diophantine equation x² + 7 = 2ⁿ".

Who invented 1?

Hindu-Arabic numerals, set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century.

Who invented pi?

The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.

Is 888 a happy number?

The distinct combinations of digits that form 10-happy numbers below 1000 are (the rest are just rearrangements and/or insertions of zero digits): 1, 7, 13, 19, 23, 28, 44, 49, 68, 79, 129, 133, 139, 167, 188, 226, 236, 239, 338, 356, 367, 368, 379, 446, 469, 478, 556, 566, 888, 899. (sequence A124095 in the OEIS).

What is Black Hole number?

The number is pretty jaw-dropping: 40 quintillion, or 40,000,000,000,000,000,000 black holes, roughly making up 1 percent of all the normal matter in the observable Universe.

What is the 1089 Trick?

The mystery is this: first, take any three digit number, where the first and last digits differ by two or more and reverse the number to produce a new one. Then subtract the smaller from the larger producing another new number. If you reverse this number and this time add the two, the result will always be 1089.