Professor Jim Al-Khalili shows how chaos theory can answer a question that mankind has asked for millennia - how does a universe that starts off as dust end up with intelligent life? It's a mindbending, counterintuitive and for many people a troubling idea.
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.
In Egypt, professor Marcus du Sautoy uncovers use of a decimal system based on ten fingers of the hand and discovers that the way we tell the time is based on the Babylonian Base 60 number system. In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a counting tool into the analytical subject of today.
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.
From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted physical law. And today’s theorists are pursuing an even more exotic symmetry that, mathematically speaking, could be nature’s final fundamental symmetry: supersymmetry.
Mathematical formulas can be found in the arrangement of seeds on a sunflower, the structure of the spirals in the shells of certain marine animals, and the distribution of leaves around a plant stem. These formulas recur in nature from snowflakes to the stripes on a zebra.