A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

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Tiling the plane with congruent polygons
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…
 • 
Richard Green
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
1:11
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
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

Beginner Posts

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Tiling the plane with congruent polygons
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…
 • 
Richard Green
Anti-inductive dice
David and Goliath each have a six-sided die.
 • 
Richard Green
4
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
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Turning a triangle into a square
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A Piece of the Pi: mathematics explained
A Piece of the Pi: mathematics explained
For the intelligent general reader who likes mathematics.
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