Wherever we find patterns and symmetry in nature, we also find that nature conforms to certain rules. Rules that combine elegance with efficiency. Rules that shape trees and river estuaries alike, and that continue to baffle scientists by their often unfathomable ubiquity.

Why are manhole covers round?

Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there’s another, more compelling reason, involving a peculiar geometric property of circles and other shapes. Marc Chamberland explains curves of constant width and Barbier’s theorem.

The Frontiers of Space

By the 17th century, Europe had taken over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss.

The Joy of Logic

A sharp, witty, mind-expanding and exuberant foray into the world of logic with computer scientist Professor Dave Cliff.

How many ways can you arrange a deck of cards?

One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.

Part 1

Wherever we find patterns and symmetry in nature, we also find that nature conforms to certain rules. Rules that combine elegance with efficiency. Rules that shape trees and river estuaries alike, and that continue to baffle scientists by their often unfathomable ubiquity.

2017 • Nature's Mathematics • Math

Shapes

Marcus du Sautoy uncovers the patterns that explain the shape of the world around us. Starting at the hexagonal columns of Northern Ireland's Giant's Causeway, he discovers the code underpinning the extraordinary order found in nature - from rock formations to honeycomb and from salt crystals to soap bubbles.