Probably everyone has at least seen the Mandelbrot set in some form, as it’s a popular object of mathematical artists. Here’s a picture from Wikipedia: The formal definition is as follo…

It seems everyone’s heard of Pascal’s triangle. However, if you haven’t then it is an infinite triangle of integers with 1’s down each side and the inside numbers determined…

Problem: Optimally pack n unit circles into the smallest possible equilateral triangle. Let L(n) denote the length of the side of the smallest equilateral triangle in which n circles have been pack…

A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. For example,  1 + 2 + 3 = 6 i…

In 1911, Otto Toeplitz asked the following question. Inscribed Square Problem: Does every plane simple closed curve contain all four vertices of some square? This question, also known as the square…

In 1937 Lothar Collatz proposed the 3n+1 conjecture (known by a long list of aliases), is stated as follows. First, we define the function $f$ on the set of positive integers: If the number \$…

Recall the Fibonacci numbers $F_n$ given by 1,1,2,3,5,8,13,21… There is no need to define them. You all know. Now take the Euler numbers (OEIS) $E_n$ 1,1,1,2,5,16,61,272… Th…

Source: Fibonacci times Euler

On Thursday, the first in a series of public discussions on scientific topics was put on by an organisation called Mass Interaction (the name comes from a statement by Richard Feynman that “a…

Source: The nature of infinity, 2

This blog aims to show that mathematics is beautiful, useful and fun. The singular value decomposition has all these qualities. It is very elegant, and has a wide range of useful applications

Schur complement