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Introduces the Pythagorean theorem, explaining its geometric significance and applications in calculating areas.
Covers the concept of distance in the plane, distance axioms, triangle construction, and triangle side properties.
Explores remeshing in geometric computing, emphasizing equal edge lengths and valence close to 6.
Explores the construction of a regular pentagon using Euclid's method and discusses historical constructions by Euclid and Ptolemy.
Explores Fubini's theorem in multiple dimensions, demonstrating integration over rectangles and closed unit balls with practical examples.
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
