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.
Chan, and S. –S. Huang [25] found proofs for all of Ramanujan's approximately 15 formulas employing only results from Ramanu- jan's notebooks [61] and lost notebook [62]. See also Chapter 15 of our book [10].
So the sum of all numbers is minus one twelfth AND is unity (1) and is infinity. The way 100 cents is one dollar and 60 seconds is 1 minute and is 60/3600 hour and is 0.01666 hour. Ramanujan's summation is presently being used to understand String Theory, showing it is true and very real.
Ramanujan identified a way to generate an infinite number of near misses of the form: x3 + y3 = z3 ± 1. 103 + 93 = 123 + 13; 63 + 83 = 93 − 1; 1353 + 1383 = 1723 − 1; 7913 + 8123 = 10103 − 1; 111613 + 114683 = 142583 + 1.
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.
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.
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.
The key reason behind Ramanujan's infinite series being wrong is the consideration that S equals 1/2, which in a real case scenario is impossible, even though it was proven to equal 1/2 with clever mathematical manipulations as S is not converging, i.e, even when we take the sum of infinite terms of S, we would either ...
Goldbach's Conjecture
Goldbach's Conjecture is, “Every even number (greater than two) is the sum of two primes.” You check this in your head for small numbers: 18 is 13+5, and 42 is 23+19. Computers have checked the Conjecture for numbers up to some magnitude.
Ramanujan's first Indian biographers describe him as a rigorously orthodox Hindu. He credited his acumen to his family goddess, Namagiri Thayar (Goddess Mahalakshmi) of Namakkal.
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.
The biopic will come and go, but what lingers in the mind is a quote in the book from Ramanujan: “An equation for me has no meaning unless it expresses a thought of God.”
The 3x+1 problem concerns an iterated function and the question of whether it always reaches 1 when starting from any positive integer. It is also known as the Collatz problem or the hailstone problem. . This leads to the sequence 3, 10, 5, 16, 4, 2, 1, 4, 2, 1, ... which indeed reaches 1.
Clay “to increase and disseminate mathematical knowledge.” The seven problems, which were announced in 2000, are the Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture.
“There are no whole number solutions to the equation xn + yn = zn when n is greater than 2.” Otherwise known as “Fermat's Last Theorem,” this equation was first posed by French mathematician Pierre de Fermat in 1637, and had stumped the world's brightest minds for more than 300 years.
Brilliant man. I would not even attempt to understand how a prodigy's mind works, I will just remain jealous.
Among his achievements in mathematics, Ramanujan built a bridge between number theory and analysis, another field in mathematics, which was extraordinary because the former mostly focuses on whole numbers and the latter on continuously-changing quantities.
Ramanujan was exceptionally gifted with it but mostly "self-taught" (he did get very basic mathematical education), he was able to pick up unusually much from books and other mathematicians he encountered, including Hardy, who published lectures on their collaboration amazon.com/Ramanujan-Lectures-Subjects-Suggested- ...
Ramanujan died on April 26, 1920, at the age of 32 years after suffering from tuberculosis. The self-taught genius lived a short but vibrant life and he is widely regarded as India's greatest mathematician. Srinivasa Iyengar Ramanujan is an inspiration for mathematicians across the globe.
Michael Angier (2005) [26] defines synergy as the phenomenon of two or more people getting along and benefiting one another, i.e., the combination of energies, resources, talents and efforts equal more than the sum of the parts. It is possible to describe this phenomenon by the expression 1 + 1 = 3.
{2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 351, 370, 407, 432, 468, 513, 520, 539, 559, 576, 637, 686, 728, 730, 737, ...}
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.
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.
For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."