## Icons of Mathematics: An Exploration of Twenty Key ImagesCertain geometric diagrams play a crucial role in visualizing mathematical proofs. Twenty of these icons of mathematics are presented in this book, where the authors explore the mathematics within them and the mathematics that can be created from them. A chapter is devoted to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus and puzzles from recreational mathematics. Each chapter concludes with a selection of challenges for the reader to explore further properties and applications of the icon. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning. |

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a2 C b2 ABCD altitude AM-GM inequality bicentric quadrilateral bisects bride’s chair cardioid cevians Challenges CHAPTER chord circle circumcenter circumcircle circumradius congruent cosine cyclic quadrilateral denote diagonals diameter draw equal equilateral triangles Euclid formula geometric mean golden ratio gray triangle hence hexagon hexagram Honsberger hypotenuse icon illustrated in Figure inequality inscribed integer intersection isosceles length line segments mathematics medians midpoint n-gon Napoleon’s Nelsen parallelogram pentagon pentagram perpendicular Polygonal Lines proof prove Pythagorean theorem Pythagorean triples radius ratio rectangle rectangular hyperbola result Reuleaux triangle right angle right triangle semicircle shaded triangles shown in Figure sides similar Similarly sinĀ Solutions square star polygons suan jing tangent tatami mats tiling trapezoid triangle ABC triangle in Figure Vecten configuration vertex vertices vesica piscis yields yin and yang Zhou bi suan α β