A detail from a painting by Raphael, showing an ancient Greek mathematician drawing a geometric figure with a compass and a straight edge.
A branch of math called algebraic geometry is about shapes made by certain equations. This shape, the ‘seahorse’, has the equation (x² − y³)² = z³(x + y²).
Geometric symmetry was very important to cathedral builders. Seen here is a rose window in Chartres cathedral; its shape has 12-fold symmetry.
One of the oldest fragments of Euclid's Elements that has been found, dating from 100 AD (about 400 years after it was written).
Évariste Galois was born in Paris in 1811. He was arrested for his democratic activism, invented a major new branch of mathematics, and died in a duel at the age of twenty.
With a few mirrors, you can make a pattern go on forever.
This marble floor mosaic is in Venice cathedral. It shows a shape called a stellated dodecahedron.
Seen here are instructions written by Thomas Jefferson for drawing part of an octagon. Jefferson’s house at Monticello, Virginia, which he designed, includes prominent octagonal structures.
For any three circles (drawn in black), there are exactly eight different circles that just touch all three of them.
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 Spain.
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 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 focus in a curved line, an example of a caustic.
The first page of the first printed edition of Euclid’s Elements, published in 1482 in Latin translation.