How did we measure the Earth?

Nobody had walked all the way round the Earth, and nobody had gone into space to look at it from outside. Yet about 2,250 years ago a scholar in Alexandria worked out the size of our planet to the right order of magnitude. All he had was a shadow, an estimated distance between two cities and the geometry of parallel lines. Linking what you cannot measure to what you can: that idea was handed down to every observer of the next two thousand years.

This journey begins by reminding you what an angle is and how it is measured. Next you calculate the Earth's circumference yourself from Eratosthenes's shadow. Then, in Samarkand, the city of Ulugh Beg's great stone arc with a radius of about 40 metres, you find latitude from the height of the Pole Star, and in Istanbul, at Taqi al-Din's observatory, you see why a clock can work as an angle-measuring instrument. At every stop you follow how knowledge passed from one culture to the next, and who added what.

In the last step you try to put what you have measured on paper: Piri Reis's map of 1513 shows why flattening a globe onto a plane always distorts something. Along the way you'll pick up a useful habit too: telling apart what is documented, what is an estimate and what is legend.