A Mathematical Gift III: The Interplay Between Topology, Functions, Geometry, and Algebra

The story of the birth of manifolds

• The prelude to the birth of manifolds
• The birth of manifolds

The story of area and volume from everyday notions to mathematical concepts

• Transition from the notion of "size" to the concept of "area"
• Scissors-congruent polygons
• Scissors-congruent polyhedra