Starting with the age-old challenge of measuring awkward shapes (think ancient Egyptian farmers re-mapping flood-washed land!), the session builds up to a powerful idea: break any irregular region into simple rectangles or trapezoids, add them up, and you have a surprisingly accurate estimate. This technique, known as numerical integration, is the gateway into calculus and the foundation behind how engineers and scientists analyze changing quantities in the real world.

It opens with a riddle: a photographer spots a bear to their east, runs north, and photographs it looking south. The bear turns out to be a polar bear, because the only place this geometry works is the North Pole. That one puzzle sets the tone for everything that follows. From there, the session explores how circles and the number π appear everywhere in the shape of the Earth, in the distorted sizes of continents on flat maps, in the curved flight paths arcing over Greenland, and in the celestial sphere of stars rotating overhead. The session then scales up dramatically, moving from the surface of the Earth to the fabric of the universe. Drawing on Einstein’s General Relativity, it shows how space-time itself curves — and how π, the constant born from a simple circle drawn on paper, turns out to be woven into the very geometry that governs gravity, planetary orbits, and the structure of the cosmos.