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Invitation to topology (Viewing figures globally): Introduction

The Euler characteristic Vortices created by winds and the Euler characteristic Curvature of a surface and the Euler characteristic

The story of dimension: Introduction

Learning to appreciate dimension

What is dimension? Three-dimensional figures Physics and dimension

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

The legacy of trigonometric functions: Introduction

Trigonometric functions and infinite series

Elliptic functions Intersection of geometry and algebra: Introduction

The Poncelet closure theorem

The Poncelet theorem for circles

The Poncelet theorem in the world of complex numbers

Proof of the Poncelet theorem using plane geometry

Conclusion

Invitation to topology (Viewing figures globally): Introduction

The Euler characteristic Vortices created by winds and the Euler characteristic Curvature of a surface and the Euler characteristic

The story of dimension: Introduction