Glen Van Brummelen | |
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 Photo of Van Brummelen holding a t-shirt. |
Glen Robert Van Brummelen (born May 20, 1965) is a Canadian historian of mathematics specializing in the history of trigonometry and historical applications of mathematics to astronomy.
He is president of the Canadian Society for History and Philosophy of Mathematics, [1] and was a co-editor of Mathematics and the Historian's Craft: The Kenneth O. May Lectures (Springer, 2005).
Van Brummelen earned his PhD degree from Simon Fraser University in 1993, [2] and served as a professor of mathematics at Bennington College from 1999 to 2006. He then transferred to Quest University Canada as a founding faculty member. In 2020, he became the dean of the Faculty of Natural and Applied Sciences at Trinity Western University in Langley, BC. [3]
Glen Van Brummelen has published the first major history in English of the origins and early development of trigonometry, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. [4] His second book, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, concerns spherical trigonometry. [5] [6]
In 2016 he received a Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics. [7]
Spherical geometry or spherics is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of higher dimensional spheres.
The versine or versed sine is a trigonometric function found in some of the earliest trigonometric tables. The versine of an angle is 1 minus its cosine.
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
Abu Mahmud Hamid ibn al-Khidr al-Khujandi was a Muslim Transoxanian astronomer and mathematician born in Khujand who lived in the late 10th century and helped build an observatory, near the city of Ray, in Iran.
Theodosius of Bithynia was a Hellenistic astronomer and mathematician from Bithynia who wrote the Spherics, a treatise about spherical geometry, as well as several other books on mathematics and astronomy, of which two survive, On Habitations and On Days and Nights.
In spherical trigonometry, the law of cosines is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.
Dennis M. DeTurck is an American mathematician known for his work in partial differential equations and Riemannian geometry, in particular contributions to the theory of the Ricci flow and the prescribed Ricci curvature problem. He first used the DeTurck trick to give an alternative proof of the short time existence of the Ricci flow, which has found other uses since then.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function, cosine function, and versine function.
The Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics are awards given by the Mathematical Association of America to recognize college or university teachers "who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions." The Haimo awards are the highest teaching honor bestowed by the MAA. The awards were established in 1993 by Deborah Tepper Haimo and named after Haimo and her husband Franklin Haimo. After the first year of the award up to three awards are given every year.
Michael P. Starbird is a Professor of Mathematics and a University of Texas Distinguished Teaching Professor in the Department of Mathematics at the University of Texas at Austin. He received his B.A from Pomona College and his Ph.D. in mathematics from the University of Wisconsin–Madison.
MathPath is a mathematics enrichment summer program for students ages 11–14. It is four weeks long, and moves to a different location each year. MathPath is visited by mathematicians such as John H. Conway and Francis Su. It was probably the original, and is still one of the few, international residential high-end summer camps exclusively for mathematics and exclusively for students of middle school age.
Frank Morgan is an American mathematician and the Webster Atwell '21 Professor of Mathematics, Emeritus, at Williams College. He is known for contributions to geometric measure theory, minimal surfaces, and differential geometry, including the resolution of the double bubble conjecture. He was vice-president of the American Mathematical Society and the Mathematical Association of America.
Jyā, koṭi-jyā and utkrama-jyā are three trigonometric functions introduced by Indian mathematicians and astronomers. The earliest known Indian treatise containing references to these functions is Surya Siddhanta. These are functions of arcs of circles and not functions of angles. Jyā and koti-jyā are closely related to the modern trigonometric functions of sine and cosine. In fact, the origins of the modern terms of "sine" and "cosine" have been traced back to the Sanskrit words jyā and koti-jyā.
Āryabhata's sine table is a set of twenty-four numbers given in the astronomical treatise Āryabhatiya composed by the fifth century Indian mathematician and astronomer Āryabhata, for the computation of the half-chords of a certain set of arcs of a circle. The set of numbers appears in verse 12 in Chapter 1 Dasagitika of Aryabhatiya. It is not a table in the modern sense of a mathematical table; that is, it is not a set of numbers arranged into rows and columns. Āryabhaṭa's table is also not a set of values of the trigonometric sine function in a conventional sense; it is a table of the first differences of the values of trigonometric sines expressed in arcminutes, and because of this the table is also referred to as Āryabhaṭa's table of sine-differences.
Muḥammad ibn Muḥammad ibn al-Ḥasan al-Ṭūsī, also known as Naṣīr al-Dīn al-Ṭūsī or simply as (al-)Tusi, was a Persian polymath, architect, philosopher, physician, scientist, and theologian. Nasir al-Din al-Tusi was a well published author, writing on subjects of math, engineering, prose, and mysticism. Additionally, al-Tusi made several scientific advancements. In astronomy, al-Tusi created very accurate tables of planetary motion, an updated planetary model, and critiques of Ptolemaic astronomy. He also made strides in logic, mathematics but especially trigonometry, biology, and chemistry. Nasir al-Din al-Tusi left behind a great legacy as well. Tusi is widely regarded as one of the greatest scientists of medieval Islam, since he is often considered the creator of trigonometry as a mathematical discipline in its own right. The Muslim scholar Ibn Khaldun (1332–1406) considered Tusi to be the greatest of the later Persian scholars. There is also reason to believe that he may have influenced Copernican heliocentrism.
A Lénárt sphere is an educational manipulative and writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard. It can be used for visualizing the geometry of points, great and small circles, triangles, polygons, conics, and other objects on a sphere, and comparing spherical geometry to Euclidean geometry as drawn on a flat piece of paper or blackboard. The included spherical ruler and compass support synthetic straightedge and compass construction on the sphere.
Gerald Lee Alexanderson (1933–2020) was an American mathematician. He was the Michael & Elizabeth Valeriote Professor of Science at Santa Clara University, and in 1997–1998 was president of the Mathematical Association of America. He was also president of The Fibonacci Association from 1980 to 1984.
Deborah Tepper Haimo (1921–2007) was an American mathematician who became president of the Mathematical Association of America (MAA). Her research concerned "classical analysis, in particular, generalizations of the heat equation, special functions, and harmonic analysis".
Annalisa Crannell is an American mathematician, and an expert in the mathematics of water waves, chaos theory, and geometric perspective. She is a professor of mathematics at Franklin & Marshall College.
Jacqueline M. Dewar is an American mathematician and mathematics educator known for her distinguished teaching and her mentorship of women in mathematics. She is a professor emerita of mathematics at Loyola Marymount University.
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