Summary: The Forgotten Art Of Spherical Trigonometry

Book Overview

The book that I chose to read is called Heavenly Mathematics: The Forgotten art of Spherical Trigonometry. This book talks about the history of spherical trigonometry. It also talks about how trigonometry is connected with astronomy and geography. Not only does this book provide theorems and proofs of various trigonometric formulas and identities used in ancient times, it also talks about the people that came up with these ideas and why. In the beginning, the author says that “for more than 1500 years, spherical trigonometry was the big brother to plane trigonometry that high school students slog through today” (preface). It was also created mostly for astronomy because back then they were more interested in the location of the

“When the Sun is at one of the intersection points, day and night are equal length, so these two points are called the equinoxes” (pg 25). There is also an important scientist mentioned, Hipparchus, who examined the Sun’s motion. He moved the Earth away from the center of the Sun’s orbit. He came up with the idea that the Sun does travel at constant speed, it just takes more time in the spring because it has a longer distance to travel. The third chapter in this book is called The Ancient Approach. The most important thing to know that spherical trigonometry is very old. This does not mean that we do not completely use it today or that it is incorrect. It just means that some of the functions that we use today have changed. This chapter also mentions Hipparchus once again. He was known to be an astronomer, but not a lot is known about his personal life. He was born in Bithynia, which is now Turkey. He also talks about Claudius Ptolemy “who described some of Hipparchus’s achievements in the Almagest” (pg 42). The other important mathematician is Menelaus. He wrote a book called Sphaerica, which involved applications in the study and the geometry of the sphere. Menelaus also invented the plane theorem, which is useful in finding

The author tries to explain the qibla problem in this book, by using the positions of the worshippers and Mecca itself. He does this using al-Bīrūnī’s methods. He used the Rule of Four Quantities and the Law of Sines. The author tries to go through some applications of it. The fifth chapter of this book is called The Modern Approach: Right-Angled Triangles. The author gives us a definition of trigonometry, which means triangle measurements. He also says that spherical trigonometry comes from European science and mostly all theorems were established around the 17th century. The author mentions that a man from Scotland became famous for coming up with many ideas in math that were not even related to trigonometry. He was not even a mathematician. He wrote a book called Trigonometria, which according to the author, “it included the first appearance of the word trigonometry” (pg 73). The author also mentions John Napier, who developed the trigonometry of right-triangles on the sphere. This was all a hobby for him. He was actually a “landholder, who was widely known for his commitment to Protestant causes against the Catholics” (pg 74). He was interested in finding ways to navigate around the