Collatz Conjecture

The Collatz Conjecture : Unsolved but Useless

The Collatz Conjecture is one of the Unsolved problems in mathematics, especially in Number Theory. The Collatz Conjecture is also termed as 3n+1 conjecture, Ulam Conjecture, Kakutani’s Problem, Thwaites Conjecture, Hasse’s Algorithm, Syracuse Problem. Statement: Start with any positive integer. • Halve it, if it is even. Or • triple it and add 1, if it is odd. If you keep repeating this procedure, you shall reach the number 1 at last. Illustrations » Starting with 1 — we get…

Understanding Poincaré Conjecture

Introduction & Statement of Poincaré Conjecture In 1904, the french Mathematician Henri Poincaré posed an epoch-making question in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Explanation The statement can be explained by considering the analogous two-dimensional situation. Let us think of a rubber band stretched around the spherical surface of an apple (or any other spherical body like ball) . It is easily seen that it can…