What is so special about 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 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

Why 1729 is a great number?

It's the smallest number expressible as the sum of two cubes in two different ways." 1729 is the sum of the cubes of 10 and 9. Cube of 10 is 1000 and the cube of 9 is 729. Both the cubes, therefore, add up to 1729.

Is 1729 a perfect cube?

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.

What is the mystery of 1729?

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.

Why is 1728 a special number?

1728 is the number of daily chants of the Hare Krishna mantra by a Hare Krishna devotee. The number comes from 16 rounds on a 108 japamala bead.

Hardy Ramanujan Number | Discovery of this number - 1729

What is the rarest 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).

Why is 1729 a taxi cab number?

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Ramanujan–Hardy 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 did Ramanujan find out?

Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics.

What did Ramanujan find?

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.

How was Hardy Ramanujan number found?

The number derives its name from the following story G. H. Hardy told about Ramanujan. "Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it.

Is 1729 even or odd?

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

Can 1729 be divided?

The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729. Therefore, 1729 has 8 factors.

Is there any other number like 1729?

{1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, ...} A018850 Numbers that are the sum of 2 cubes in more than 1 way (primitive solutions).

What is Ramanujan's magic square?

Ramanujan magic square is a special kind of magic square that was invented by the Indian mathematician Srinivasa Ramanujan. It is a 3×3 grid in which each of the nine cells contains a number from 1 to 9, and each row, column, and diagonal have the same sum.

Who invented infinity?

Infinity is a mathematical concept originating from Zeno of Elia (~450 BC) who tried to show its “physical” impossibility. This resulted in the “arrow paradox”, but which was solved later on. Many mathematicians and physicists went on to try understanding infinity and to explain it by various theories and experiments.

Why was Ramanujan so brilliant?

Drawing upon deep intuition, Ramanujan created new concepts in the theory of numbers, elliptic functions and infinite series. Even full-blown mathematicians take years to grasp his complex ideas. Exceptional genes plus fortunate circumstances is why some become maths-science superstars.

Who found zero?

Therefore it is said that Aryabhatta found zero.

Why did Ramanujan died?

He was diagnosed with tuberculosis and a severe vitamin deficiency, and confined to a sanatorium. In 1919, he returned to Kumbakonam, Madras Presidency, and in 1920 he died at the age of 32.

Who invented algebra?

Muhammad ibn Musa al-Khwarizmi was a 9th-century Muslim mathematician and astronomer. He is known as the “father of algebra”, a word derived from the title of his book, Kitab al-Jabr. His pioneering work offered practical answers for land distribution, rules on inheritance and distributing salaries.

What is the IQ of Ramanujan?

Srinivasa Ramanujan: IQ 185

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.

How did Ramanujan become genius?

He spent much of his spare time scribbling formulae in notebooks or on a small blackboard. By the age of 23 Ramanujan was convinced he was making important new discoveries in mathematics, and was enterprising enough to write a letter to the eminent Cambridge Professor of Mathematics G.H. Hardy.

What is the Ramanujan theory of infinity?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.

What is 1729 as sum of two cubes?

1729=1000+729=103+93.

What is Ramanujan formula?

Ramanujan obtained a general expression using three variables that can generate an infinite number of such equations, like the ones sent in by some readers. Just define f(x) = x + n + a, giving f(x)²= ax + (n + a)² + x f(x + n).

What is the smallest number in the world?

Answer: Solution 3: The smallest whole number is "0" (ZERO).