A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

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Geometry 📐

Games in projective space
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…
 • 
Richard Green
2
Intersections of chords of a circle
The picture above shows a regular polygon with 15 vertices, including all the diagonals between the 15 vertices, and all the intersections between the…
 • 
Richard Green
2
Audio Note: Companion to “The geometry of musical keys”
The relationships between musical keys can be described either by means of the triangles in the “Tonnetz”, or by carefully designed geometric…
 • 
Richard Green
1:11
The geometry of musical keys
The Tonnetz (German for “tone network”) is a diagram representing musical tonal space, in which each vertex represents a musical note, and each small…
 • 
Richard Green
2
Geodesics and polyhedra
A geodesic on a convex surface is a curve on the surface that is “locally straight”.
 • 
Richard Green
1
Venn diagrams and Winkler’s conjecture
A Venn diagram is an extremely well known device for representing the logical relationships between three sets.
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Richard Green
9
Which way is the bike going?
Is it possible to deduce the direction of motion of a bicycle just by looking at the shape of the tracks it leaves?
 • 
Richard Green
2
Rubik’s abstract polytopes
The well-known puzzle Rubik’s Cube can be generalized in a number of ways, for example by turning it into a 4×4×4 or 5×5×5 puzzle.
 • 
Richard Green
Turning a triangle into a square
In 1902, Henry Dudeney showed that it is possible to cut an equilateral triangle into four polygonal pieces, and then to rotate and translate those…
 • 
Richard Green
3
Penny graphs
A penny graph can be created from a non-overlapping arrangement of unit circles on a flat surface.
 • 
Richard Green
2
How many triangles are there?
A well-known type of brain teaser invites the reader to count the number of triangles formed by dividing up a larger triangle using straight lines.
 • 
Richard Green
3
Facially complete graphs
The Four Colour Theorem proves that no more than four colours are required to colour the regions of any map in such a way that no two adjacent regions…
 • 
Richard Green
8
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