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There are thirteen special shapes with completely symmetrical...

There are thirteen special shapes with completely symmetrical flat sides that look the same at every meeting point. They were discovered by the ancient Greek mathematician Archimedes.
This beautiful tiling is from the palace of the Alhambra in...

This beautiful tiling is from the palace of the Alhambra in Spain.
This is a woodcut called Circle Limit III by the Dutch artist...

This is a woodcut called Circle Limit III by the Dutch artist M.C. Escher, of which he said that “fish shoot up like rockets from infinitely far away … and fall back again whence they came”.
A model of a surface called a hyperbolic plane made by...

A model of a surface called a hyperbolic plane made by crocheting. Hyperbolic planes are surfaces that are curved like leaves of holly at every point.
If you shine a flashlight into a coffee cup, the light will...

If you shine a flashlight into a coffee cup, the light will focus in a curved line, an example of a caustic.
The first page of the first printed edition of Euclid’s...

The first page of the first printed edition of Euclid’s Elements, published in 1482 in Latin translation.
A drawing of a shape called a stellated octahedron by Leonardo...

A drawing of a shape called a stellated octahedron by Leonardo da Vinci.
Ada Lovelace — daughter of the poet Lord Byron — helped write...

Ada Lovelace — daughter of the poet Lord Byron — helped write the first computer program, in 1843.
A drawing of an imaginary sculpture by Renaissance artist Wenzel...

A drawing of an imaginary sculpture by Renaissance artist Wenzel Jamnitzer. The shape in the center is a stellated great dodecahedron.
A film of soap between two hoops settles into a shape that has a...

A film of soap between two hoops settles into a shape that has a smaller area than any other possible shape that could stretch between the two hoops. This shape is an example of a minimal surface.