Beautiful Geometry

A wonderful book for motivating young students and a very useful resource for teachers to inspire students. We need more such books to encourage mathematics learning a enjoyable experience among students.

A compelling read with beautiful illustrations.

This delightful book has 51chapters each devoted to a classical topic in geometry. Each chapter includes a beautiful colour plate and many chapters include additional illustrations. The topics are well chosen and the text is logical and eloquent. The book should be accessible to a very broad audience (there is an appendix with more mathematical details for those inclined). The attention to detail and the standard of production are both outstanding. This would make an excellent gift and would be enjoyed by anyone interested in math, the history of math, art or architecture.Here are 4 comments/observations:p. 44. It is often stated that there is no formula for the primes, but this is actually not the case. There are many explicit formulas. (To my mind the nicest is Ghandi's formula). For example, see Underwood Dudley's "Formulas for primes", Math. Mag. 56 (1983), no. 1, 17-22. There have also been other formulas obtained since Dudley's paper.p.101. For a geometric derivation of the formula for ln(2), see the proof without words by Matt Hudelson, Math. Mag. vol 83 (2010) p.294.p.120. Fig 36.3; in the 2nd and 4th figure the red dot should be in the centre of the figure, not on the rim of the circle.Chap 49. In my opinion the common popular treatment of the Koch curve is not entirely satisfactory, in that it may be unclear to the reader that its length is infinite, or in fact, what its length means. To clarify my concern, let alpha>0 and consider the curve: gamma_n : [01]->R^2 whose graph on each interval [m/n,(m+1)/n] is a little tent of height alpha/n, where m=0,1,2,...n-1. As n-> infty, the curve converges (in the sup norm) to the unit interval on the x-axis (which is a curve of length 1). But gamma_n has length sqrt(4 alpha^2+1), which is constant, and can be given any value >1 by appropriately choosing alpha. This example shows that where a curve is constructed as the limit of a sequence of curves, the length of the limit is not in general equal to the limit of the lengths. Further, a sequence of curves whose length tends to infinity, could well tend to a curve of finite length. I think an intelligent reader might wonder why this isn't also the case with the Koch curve.

This book has stunning visuals as well as a very readable narrative. Having graduated from college in 1971, I had not thought about many of these geometric concepts for about 50 years. The author describes mathematical principles and offers illustrations. Triangles of equal areas just fascinated me. Who knew the number 11 was so mysterious? And epicycloids.....too cool.

This is a beautiful book, especially for people who already possess an interest in math and who consider mathematics itself a beauty-filled discipline. I am a retired math educator, but if I were still teaching, I would definitely share this book with my high school geometry classes--it would provide great ideas for explorations and projects that integrate art and geometry. I would have given this lovely book 5 stars but there are formatting errors throughout such as extra spaces between words, lack of punctuation marks -- that I found rather distracting. Poor proofreading!

I bought this book intending to give it to a 7th grader who is good at math, because I am on the lookout for books that show kids that there is math beyond arithmetic -- arithmetic is like learning scales, before you can really experience playing sonatas. So to compare, I look for books that show kids that the sonatas exist, and give some idea of what they are like. To take the analogy one step farther, this book maybe assumes that you have heard the sonatas, and it gets into musical composition. Surely the title and reviews should have told me that this intended recipient might not be ready for it, but that didn't get through to me. The book is wonderful, but I think the content may be beyond someone who has not had algebra and geometry. I'll wait until then to give it to her.