What is Hardy Ramanujan number? (2024)

FAQs

Why is 1729 called the Ramanujan number? ›

The 2 ways 1729 can be a sum of two positive cubes. 1729 is the smallest nontrivial taxicab number, and is known as the Hardy–Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital.

The numbers with the desired property are seen to be: 1729, 4104, 20683, 39312, 40033, 64232, . . . . The next Ramanujan number after 1729 is thus 4104. Instead of a brute force method, can we not look for approaches that are more worthy of being called 'mathematical'?

Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed as the sum of two cubes in two different ways. Numbers obtained when a number is multiplied by itself three times are known as cube numbers or perfect cubes .

Is 1729 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.

Answer: Born in India in 1887, Srinivasa Ramanujan is one of the most influential mathematicians in the world. He made significant contributions to the analytical theory of numbers, as well as elliptic functions, continued fractions, and infinite series. He had an estimated IQ of 185.

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.

According to Physics Central, 1 + 2 + 3 + 4 + … only equals -1/12 because the mathematicians redefined the equal sign. In this style of mathematics, called analytical continuation, "=" stopped meaning “is equal to” and started meaning “is associated with.” Tricky mathematicians.

Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions. Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today.

In a lecture on Ramanujan, Hardy said that "my association with him is the one romantic incident in my life".

The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.

Who found zero? ›

The origin of zero in India came from a well-known astronomer and mathematician of his time, Aryabhatta. The well-known scientist used zero as a placeholder number. In the 5th century, Aryabhatta introduced zero in the decimal number system and hence, introduced it in mathematics.

1729, called the Hardy-Ramanujan Number is the smallest number which can be expressed in terms of sum of two cubes, namely: 1729 = 1^3 + 12^3. 1729 = 10^3 + 9^3.

Since the remainder obtained on dividing 1729 by 2 is 1, 1729 is an odd number.

The factors of 1729 can be listed as 1, 7, 13, 19, 91, 133, 247 and 1729.

1729 is the smallest number which can be expressed as the sum of two cubes in two different ways: 1³ + 12³ and 9³ + 10³. Ramanujan did not actually discover this fact. It was known in 1657 by the French mathematician Bernard Frénicle de Bessy.

Why is Srinivasan Ramanujan called 'The Man Who Knew Infinity'? Because he gave so many formulas on infinite. What is the sum of 1+0+5+6+8?

Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions. Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today.