10 Mathematician's Favorite place:
- Gauss: I will gonna going to Gottingen, Germany~ Maybe I should became a teacher in here~
- Cantor: ..... Haale, Germany..... I leave from born place (he means Russia 'cause Cantor is not Russian)
- Pascal: Paris~ City of model~
- Newton: London.
- Abel: Maybe I going to Paris too~ But I'm too gloomy...
- Cauchy: I always going to Germany, Czech, or anything! (he was exlied from France before he back to Paris)
- Archimedes: I'm tired, I should I take a bath...
- Hamilton: I'm drunk, hic... (has drinking problems)
- Descartes: I going to around the world~! (Holland, Sweden, Poland, etc.)
- Euler: St. Petersburg, Russia~
A000217 - Triangular numbers
A000217 - Triangular numbers
0, 1, 3, 6, 10, 15, 21, …
Triangular numbers appear in at least two very common games. In bowling, the pins are arranged into rows of 1, 2, 3, and 4 pins each, depicting T4 = 10. When setting up eight-ball on a billiard table, the triangular rack arranges the balls into T5 = 15. The largest repdigit triangular number is T36 = 666. Not only is 36 = 62, but it’s also triangular itself (T8 = 36). All even perfect numbers are triangular. Amazingly, they all have a prime index (i.e. T7 = 28).
Fermat’s Last Theorem is only the most well-known case where he claimed to have a solution to a problem but never published it. In 1638, he claimed to have a proof showing that every positive integer was equal to the sum of three triangular numbers, or four square numbers, or five pentagonal numbers, etc. A proof for the triangular case wasn’t published until Gauss did so 130 years after Fermat’s death. Jacobi and Lagrange each independently devised proofs of the square case around the same time. But it wasn’t until 1813 — almost 150 years after Fermat died — that his Polygonal Number Theorem was finally proved in its entirety.
Carl Friedrich Gauss (1777-1855)
Mathematics is the queen of the sciences and number theory is the queen of mathematics
- At just ten years old, his abilities were made apparent after his teacher asked the class to add all numbers from 1-100, as a way to keep them occupied for a while. Gauss correctly answered 5050 almost immediately. It’s presumed he used the equation m(m+1)/2
- At 18 he made a brilliant discovery and proved you can construct a 17 sided polygon with a ruler and compass, something that was thought impossible for over two thousand years. The equilateral triangle, regular pentagon, as well as certain other polygons with numbers of sides that are multiples of 2, 3 and 5, are constructable. Hence, no other polygon with a prime number of sides were thought to be constructable.
- Gauss proved the law of quadratic reciprocity in number theory
- He worked on the Fundamental Theorem of Algebra
- He made many contributions on number theory
- He wrote Disquisitions Arithmeticae in 1798, and then it was published in 1801. It consists of his particular results in number theory as well as filling gaps and inconsistencies in others results.
- Gaussian Integers: a complex number a + bi where a and b are integers
- On the back page of a copy of a table of his logarithms, Gauss presumably wrote the equation Primzahlen unter a( = ∞) a/1a
This is a statement of the prime number theorem: the number of primes less than a given integer a approaches asymptotically the quotient a/1n a as a increases indefinitely.