Trigonometric Delights

This book is simply a delight. It explains theorems is a simple cogent manner. The historical content is a bonus. Egyptian clay tablets of right triangles, along with a table, in base 20 no less. Clear writing style, complete and easy to read. Written on a sophomore level, but in an exceedingly well manner. Discussion and proofs of identities are well written, clear and simple. The double angle formulas for sine and cosine are outstanding. I purchased three books. One for myself, and two for nephews who were taking trig related subjects. Eli Maor has other books which are excellent including (paraphrasing) Pi, e, Venus in Transit. Read Trigonometric Delights as it is a masterpiece. I have two degrees BSEE and MSEE so I know of what I speak. This was a simple and entertaining read for someone who has had a trig course, and is recommended as a supplement book when taking a trig course. Outstanding!

I accidentally stumbled upon this book when looking up "hypocycloids." This book literally blew me away! How many books do you know of that addresses De'Moivre's Theorem....and shows you how to use it? And, this little book also gives you the history of the concepts. This book starts out taking you on a trip thru Ancient Egypt and trigonometry's roots. It dissects a pyramid, mathematically. Cool. It then explores all facets of trigonometry from a fun point of view. You can't help but love this book. I can hardly put it down. So, if you ever want to know "why" you are doing anything trigonometrically, then this book is for you. Total amateur or PhD level person will love this little book!

The latest of a series by Eli Maor, this one is my favorite. For those who need more warming up to the mathematics, I would recommend reading Maor's earlier books first. Infinity and Beyond, The Story of a Number (e), and Trigonometric Delights have some overlapping subject matter. And, the author develops them in later books with new concepts. Although there is some content overlap (perhaps five percent), there is plenty original content in each book. The main reason this book is a favorite of mine is due to the subject, trigonometry is not covered so well by others. Also, this book has a more refined format than his earlier books. High school trigonometry, rarely taught in depth today, is good enough to make this an easy read. For young adults who have suffered the modern brush over, this book is priceless. For all readers, this book offers a fresh perspective. You will see the practical applications; and you will truly learn the purpose of a trigonometric function. If you appreciate graphical representations, you will appreciate this author's approach.. As in his earlier work's subject matter, Maor gives a good history of this subject matter. But, geometric solutions to problems are the gems of this book. Regiomontaus's maximum problem, a geometric solution to Zeno's paradox, and a geometric construction of an infinite product are developed. Also described is the contribution of trigonometry to the infinite series and De Moivre's theorem. If you ever owned a Spirograph, you will have wished a copy of this book to truly visualize what those circles and gears were truly doing and to learn to predict results through math. Any book by Eli Maor would not be complete without concepts of conformal mapping as applied to mapmaking. In this book, he cleverly shows in detail the conversion of a spherical map to a flat one while explaining the virtues of conformal mapping. In the penultimate chapter Sinx = 2, Imaginary Trigonometry, Maor illustrates the link between trigonometry, imaginary numbers, and the complex plane. Nowhere else have I seen a better description of conformal mapping of a complex valued function. The book's final chapter is a clear and interesting illustration of Fourier's theorem. These last two chapters contain the most challenging concepts; but they are clearly explained. I hope for another book by this author to be published soon.

What do sines, pyramids, music, and Fourier series all have in common? Eli Maor did an excellent job in explaining these dry and seemingly irrelevant terminologies to his readers. From Ahmes the Scribe to Fourier, Maor traced the development of trigonometry by juxtaposing different trig concepts with people and anecdotes. An inspiratoinal book.

If you think that trigonometry is boring and trivial, then read this book! He shows how central trig has been to many fields of math and science. A truly inspirational book!