A Piece of the Pi: mathematics explained

Subscribe now Share The Petersen graph is a famous graph with 10 vertices and 15 edges.

Subscribe now Share The picture above shows a set of seven dice designed by Oskar van Deventer.

Subscribe now Share Lights Out is a game that can be played on an equilateral triangular grid of buttons, each of which may be in a lit or unlit state.

Subscribe now Share The Matula arborification of a number is a way to represent that number as a rooted forest.

Subscribe now Share The golden ratio, φ=(1+√5)/2, is a famous example of an irrational number, which means that it cannot be expressed exactly as a ratio of two integers.

Subscribe now Share How many colours do we need to colour a fixed stack of identical cuboids with integer coordinates in such a way that no two cuboids of the same colour touch each other?

Subscribe now Share Consider the points of a clock face, numbered 1 up to 12, and for each point k, draw a straight line between k and 2k, taking remainders modulo 12.

Subscribe now A Steiner triple system consists of a set S (such as the set of seven letters {A, E, H, R, T, W, Y}) together with a set of 3-element subsets of S called blocks (such as {YEA, WHY, TRY, HER, RAW, WET, HAT}).

Subscribe now Share Consider a wheel with 21 evenly spaced positions, consecutively numbered 0, 1, 2, up to 20, and highlight the positions 1, 2, 5, 15, and 17 in bold, as in the picture.

Subscribe now In 1968, J.E.

Subscribe now Share The Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …) are one of the most famous sequences of integers.

Subscribe now Share Matroid bingo is a simplified version of the game of bingo.

Subscribe now Share A graph consists of a set of vertices, some of which are joined in pairs by edges.

Subscribe now A familiar fact from the game of pool is that 15 objects can be arranged in an equilateral triangle of side length 5.

Subscribe now Given a repeating wallpaper pattern in the Euclidean plane, is there a good algorithm to turn it into a wallpaper pattern in the hyperbolic plane, as in the Circle Limit series of pictures by M.C.

Subscribe now Suppose we have a 5×5 grid with 15 circled positions in a spiral shape as shown above.

What is the densest way to fill space with spheres of the same size?

Subscribe now It is impossible to tile the plane with regular pentagons of the same size, because the internal angle of a pentagon is 108°, and 360 is not a multiple of 108.

Subscribe now Projective geometry is a version of geometry in which there are points, lines, and planes, but in which there are no such things as distance or parallel lines.

Subscribe now The picture above shows a regular polygon with 15 vertices, including all the diagonals between the 15 vertices, and all the intersections between the diagonals.