All cinematic journeys
Cinematic map journey15 scenes
When Sameness Became a Law — From Patterns to the Universe
Symmetry means more than a beautiful mirror image. When a specified relation survives a transformation, mathematics studies the motion and the invariant together. This journey follows more than 2,300 years from regular solids and crafted patterns through permutations, geometry, continuous transformations, crystals, conservation laws, and particle physics.
3 min300 BCE–2012
Scene 1 of 15
c. 300 BCE
Alexandria
Placing Five Perfect Forms inside One System — Euclid’s Regular Solids
Book XIII of the Elements constructs and classifies the five convex regular polyhedra whose congruent regular faces meet alike at every vertex. The language of modern group theory was absent, but geometric sameness entered a durable system of construction and proof. A modern umbrella term should not be projected unchanged onto Euclid.
Replay on the map from scene 1Scene index