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…
Jun 16
•
Richard Green
7
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A Piece of the Pi: mathematics explained
Games in projective space
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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…
Jun 4
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Richard Green
10
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A Piece of the Pi: mathematics explained
Intersections of chords of a circle
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2
May 2025
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…
May 23
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Richard Green
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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…
May 21
•
Richard Green
22
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A Piece of the Pi: mathematics explained
The geometry of musical keys
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2
A robot that unknots knots
Imagine a robot walking a single lap of a knotted track in three dimensional space.
May 13
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Richard Green
2
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0:14
A robot that unknots knots
Imagine a robot walking one loop of a closed-circuit outdoor track.
May 12
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Richard Green
4
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A Piece of the Pi: mathematics explained
A robot that unknots knots
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5
April 2025
Anti-inductive dice
David and Goliath each have a six-sided die.
Apr 28
•
Richard Green
13
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A Piece of the Pi: mathematics explained
Anti-inductive dice
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4
Geodesics and polyhedra
A geodesic on a convex surface is a curve on the surface that is “locally straight”.
Apr 20
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Richard Green
9
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A Piece of the Pi: mathematics explained
Geodesics and polyhedra
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1
Venn diagrams and Winkler’s conjecture
A Venn diagram is an extremely well known device for representing the logical relationships between three sets.
Apr 6
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Richard Green
14
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A Piece of the Pi: mathematics explained
Venn diagrams and Winkler’s conjecture
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9
March 2025
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?
Mar 24
•
Richard Green
5
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A Piece of the Pi: mathematics explained
Which way is the bike going?
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2
Random coprime numbers
Two integers are called coprime, or relatively prime, if they have no factors in common other than 1.
Mar 14
•
Richard Green
12
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A Piece of the Pi: mathematics explained
Random coprime numbers
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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.
Mar 3
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Richard Green
9
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A Piece of the Pi: mathematics explained
Rubik’s abstract polytopes
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