Marcus du Sautoy explains how Egyptians discovered pi through activities of their everyday life.

In a court case, the plaintiff claims that the defendant is unfairly compensating him for his lawn work. He asserts that he should be paid the same amount for mowing the triangular lawn and the rectangular lawn because they have the same area. He proves his claim by using a cardboard representation of the two lawns and comparing their areas.

Jim al-Khalili shows us how the man who invented algebra, Al-Khwarizmi, would use his mathmatical discoveries during his time period, when things were much different.

You've probably seen a few cubes sitting in an art gallery and questioned why they were there. How could cubes be important? How did we get here? Minimalist art can still impart a strong feeling. A feeling for space, light, for presence and absence. You are aware of your own body in the gallery as you've never been before. You appreciate the architecture and the spareness, and in a world filled with complexity and information. This is the case for Minimalism.

It is described how many tribes were drawn to live near the Nile River, and how these were united to form Egypt under Menes. The narrator then describes how canals were built, and how they became ancient Egypt's main system of transport. It is then detailed how ancient Egyptians took advantage of canals and what particular commodities were transported through the canals.