Table of Contents

Algebra and arithmetics: Arithmetic and combinatorics: Can a number be approximately rational? Arithmetical properties of binomial coefficients On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities Equations: Equations of degree three and four Equations of degree five How many roots does a polynomial have? Chebyshev polynomials Geometry of equations Geometry and topology: Envelopes and singularities: Cusps Around four vertices Segments of equal areas On plane curves Developable surfaces: Paper sheet geometry Paper Mobius band More on paper folding Straight lines: Straight lines on curved surfaces Twenty-seven lines Web geometry The Crofton formula Polyhedra: Curvature and polyhedra Non-inscribable polyhedra Can one make a tetrahedron out of a cube? Impossible tilings Rigidity of polyhedra Flexible polyhedra Two surprising topological constructions: Alexander's horned sphere Cone eversion On ellipses and ellipsoids: Billiards in ellipses and geodesics on ellipsoids The Poncelet porism and other closure theorems Gravitational attraction of ellipsoids Solutions to selected exercises Bibliography Index.