Why 1729 is a special no?

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.

What is the story of Ramanujan number 1729?

I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

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.

Why 91 instead of 1729 could have been the Ramanujan number?

1729 is also the sum of the cubes of 12 and 1- a cube of 12 is 1728 and a cube of 1 is 1; adding the two results in 1729. 91 is the sum of the cubes of 6 and -5 i.e. the cube of 6 is 216 and the cube of -5 is 125; adding the two numbers results in 91.

Why 1728 is a special number?

It is a practical number as each smaller number is the sum of distinct divisors of 1728, and an integer-perfect number where its divisors can be partitioned into two disjoint sets with equal sum. 1728 is also an untouchable number where no other number contains a sum of proper divisors equal to 1728.

Why 1729 is a Special Number? | Hardy-Ramanujan Number Story | Magic Number | Cheenta

What is the magic 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.

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).

How did Ramanujan know so much?

He made mistakes all the time." Ramanujan quickly learned a great deal of formal mathematics at Cambridge and went from an amateur to writing world class mathematics papers. "Very quickly, within the span of a year or two, he was formally trained. He was very smart so he could catch up quickly.

Why was Ramanujan rejected?

Solution. Ramanujan would show his frayed notebooks to every officer. But no one could understand what was written in the notebooks. So, his applications for jobs were rejected.

Is 1729 a prime number or not?

This number is a composite. The largest number which is divisible by its prime sum of digits (19) and reversal (91) happens to be Ramanujan's famous taxi-cab number (1729 = 12³ + 1³ = 10³ + 9³).

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.

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?

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

What is Ramanujan paradox?

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 Ramanujan formula?

In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent.

Is 4104 a Hardy Ramanujan number?

1. Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed as sum of two cubes in two different ways.

What did Einstein say about Ramanujan?

Brilliant man. I would not even attempt to understand how a prodigy's mind works, I will just remain jealous.

Has Ramanujan been wrong?

Most of Ramanujan's mistakes arise from his claims in analytic number theory, where his unrigorous methods led him astray. In particular, Ramanujan thought his approximations and asymptotic expansions were considerably more accurate than warranted.

Where is Ramanujan's lost notebook now?

Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge.

What was the IQ level 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.

Did Ramanujan believe in God?

One could put this in the context of Ramanujan's religiousness and devotion to the family goddess in Namakkal, but equally, you could see it as a belief that truly inspired work gets done only when there is at least a hint of deeper meaning, when the mind talks to, or lives in, something bigger.

How intelligent was Ramanujan?

Srinivasa Ramanujan (1887-1920) was an Indian mathematician, who made great contributions in such areas as number theory, continued fractions, and infinite series, despite not having any formal education in math. His estimated IQ was 185.

What is the oldest number in the world?

What is the oldest number system? The oldest number system in the world is the Babylonian number system.

What is the greatest number to exist?

The thing is, infinity is not a number, but a concept or idea. A "googol" is the number 1 followed by 100 zeroes. The biggest number with a name is a "googolplex," which is the number 1 followed by a googol zeroes.

What is the most famous number ever?

Happy Pi Day! The annual celebration, held every March 14, is your chance to pay tribute to the most famous constant in math and physics: the number you get when you divide the circumference of a circle by its diameter. It's represented by the Greek letter “π” — in English, “pi.”