A Piece of the Pi: mathematics explained

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How to build a computer using origami
 • Richard Green
1
Curves and L-systems
 • Richard Green
5
The Thue–Morse sequence
 • Richard Green
The number 163
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No three in a line
This picture shows how to place 20 points on the vertices of a 10×10 grid in such a way that no three of the points lie on a straight line. So what is…
 • 
Richard Green
1
Derangements and the number e
If a teacher randomly hands back 20 homework assignments to the 20 students who wrote them, what is the probability that none of the students receives…
 • 
Richard Green
1
Automorphic numbers
An automorphic number is a number whose square ends in the digits of the number itself. For example, 625 × 625 = 390625 ends in the digits 625, and 376…
 • 
Richard Green
Curves and L-systems
The picture above shows an approximation to the Gosper curve, which was discovered by Bill Gosper in 1973. The Gosper curve is a space-filling curve…
 • 
Richard Green
5
Fractional Sudoku
The diagram on the left of the above picture shows a completed 6×6 Sudoku puzzle using colours instead of numbers. What makes this a valid solution to…
 • 
Richard Green
Misleading diagrams
The picture above appears to show a triangle that can be cut into four smaller shapes and rearranged to form a shape with a different area. The red…
 • 
Richard Green
Diophantine m-tuples
A Diophantine quadruple of integers is a set of four integers, such as {1, 3, 8, 120}, with the property that if we multiply any two of them and add 1…
 • 
Richard Green
1
The Proth–Gilbreath conjecture and absolute differences of integers
The Proth–Gilbreath conjecture is an easily stated open problem about prime numbers. Start by writing the first n prime numbers (for example, 2, 3, 5…
 • 
Richard Green
1
Dissecting polygons into squares and rectangles
The Wallace–Bolyai–Gerwien theorem in geometry says that whenever two polygons have the same area, it is possible to cut one of the polygons into a…
 • 
Richard Green
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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A Piece of the Pi: mathematics explained

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