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Icon...and Sometimes I Can't....

An icon is defined as "a picture that is universally recognized to be representative of something." So begins Claudi Alsina and Roger Nelson's Icons of Mathematics: An Exploration of Twenty Key Images.

On first reaction, what are your suggested icons in mathematics? Perhaps a right triangle, two overlapping circles, similar triangles, angles, etc. But, for each, can you explore the mathematics attached to them?

Alsina and Nelson explore twenty icons...many of their choices will surprise you. That is, in addition to those mentioned above, consider this list of icons and I expect you will draw a blank on many of them:

  • The Bride's Chair
  • Zhou Bi Suan Jing
  • Garfield's Trapezoid
  • Cevians
  • Napoleon's Triangles
  • Overlapping Figures
  • Yin and Yang
  • Polygonal Lines
  • Star Polygons
  • Self-Similar Figures
  • Tatami
  • Rectangular Hyperbola
  • Tiling
In many cases, you may recognize the icon's words, but are unsure as to even what the particular icon looks like. And, can you suggest the mathematics connected to each icon?

For each geometric icon, the authors discuss its presence in real-life (with some stretching!), its main mathematical attributes, and its important role in visual proofs. Every icon also is complemented by a series of related problem challenges, that can get quite difficult.

Overall, the text is an enjoyable romp though plane geometry, numeric properties of integers, trig identities, calculus notions, history of mathematics, and even puzzles from recreational mathematics. Personally, I found each chapter (i.e. icon), an interesting surprise.