A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

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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…
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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…
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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…
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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…
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Richard Green
2
A robot that unknots knots
Imagine a robot walking a single lap of a knotted track in three dimensional space.
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Richard Green
0:14
A robot that unknots knots
Imagine a robot walking one loop of a closed-circuit outdoor track.
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Richard Green
5
Geodesics and polyhedra
A geodesic on a convex surface is a curve on the surface that is “locally straight”.
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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
Random coprime numbers
Two integers are called coprime, or relatively prime, if they have no factors in common other than 1.
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Richard Green
2
Counting dimer tilings
A dimer is a 2×1 domino-shaped rectangle.
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Richard Green
2
The maximum number of SETs for 12 cards
SET is a card game that is played with a deck of 81 cards.
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Richard Green
Identifying bottlenecks in networks
A large network, such as an infrastructure network or a social network, may contain highly connected regions that are linked to each other by…
 • 
Richard Green
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