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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