The trigonometry we learned in high school is a mere shadow, the part that is needed to do calculus, of this beautiful and ancient discipline. Beginning in ancient Greece to resolve astronomical needs, trigonometry began not on the flat surface we are accustomed to, but on the celestial sphere. On this new surface the theory changes; the results are always elegant and often surprising. The subject developed through several cultures, especially medieval India and Islam, finding uses in a variety of contexts including the determination of the direction of Mecca and ocean-going navigation.
Glen Van Brummelen A mathematics historian, is known particularly for his works dedicated to Trigonometry and Astronomy in the Ancient Greek and Medieval Islamic civilisations. He has authored the first book on the history of trigonometry in over a century called The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. The courses he has taught reflect the richness of his field and he has merged fields such as democracy and trigonometry, music and trigonometry, spherical trigonometry (using a 19th-century textbook), and also how to use the tools an ancient astronomer would and achieve the same results.
Van Brummelen has also been the receiver of the Haimo award, the highest teaching award for undergraduate mathematics in North America.