The author in this article compares two books on mathematical subjects that can help to provide a rich background on their developments. One book is about geometry by John Heilbron whereas the other one is about trigonometry by Eli Maor. The author elaborates that, “both writers share a belief that doing the mathematics is fun; both trace the origins of these subjects to a variety of cultures; and both glory in the achievements that geometry and trigonometry made” (Gray, 1998, p.333). The author claims that the books will leave any reader who is not frightened of mathematics with a deeper appreciation of the subjects (Gray, 1998).
Heilbron’s book on geometry is more substantial and covers Euclidean geometry from its conception. He presents material it in a way the reader will enjoy reading about mathematics and gives attention to the variety of cultural occasions for the math (Gray, 1998). Heilbron organized his book in an unconventional way that is typical of neither a textbook nor a history book, and uses special themes, such as cathedral windows and Islamic designs as well as difficult problems from historical texts. He keeps the reader engaged in the problems as a way to humanize the matter and show the reader the challenges that geometers and architects had to overcome in order to accomplish their work (Gray, 1998). The author mentions that, “modern American calculus textbooks like to insinuate that the subject is ‘really’ useful by similar devices, but they fail because the examples they use are all too often artificial questions dressed up to look like real ones.” (Gray, 1998, p.333). Heilbron succeeds in his efforts to capture the reader’s attention because of the many real life examples from history he employs and the way he presents them(Gray, 1998).
The author notes that Maor’s book of trigonometry focuses less on the cultural aspects of the topic and more on the history of the mathematics. (Gray, 1998). Topics included are Ptolemy’s tables, the Hindu origin of the trigonometric functions, shape of the earth, calculus of the trigonometric functions, de Moivre’s formula and many others (Gray, 1998). Gray (1998) suggests that Moar’s book is a great sources of historical accounts that the teacher may weave into their trigonometry lessons.
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The author states that both Maor and Heilborn state that “geometry and trigonometry were casualties of the ‘new maths’ reforms of the 1960s, and that the calculator-driven education of today is no better” (Gray, 1998). The author expresses his admiration for Heilbron’s book and calls it a deeply humanistic work for a book that deals with geometry. I agree with the author that our math books are written in a way that the students do not enjoy math or even hate it. I enjoyed reading this article and seeing the level of enjoyment and fun one can receive when one writes about mathematics which is something one rarely reads about. I will read these books and try to incorporate their teachings in my classes. The culture rich background and real problems faced in history will help students build a deeper meaning and connection to math they learn in class.
References
- Trigonometry and Sine by Leonard Merriman
- Nonfiction Books on Mathematics by Steven Goodman
- Forum discussion on Geometers and Modern Calculus Texts
- A History of Geometrical Methods by Julian Lowell Coolidge
- The History of Trigonometry and the Rise of Spatial Reasoning in Early Modern Europe by Roshdi Rashed
- Geometry in Islamic Art by Stefano Carboni
- Mathematical Association of America (MAA) eBooks
