Math Department (Thesis/2009-10)

Topics in the History of Mathematical Astronomy

Under the direction of: Kim Plofker

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The topics in this set have a math-historical focus. History of mathematics is still a very under-studied field, and even a one-semester undergraduate thesis can potentially uncover new and interesting results that researchers and teachers in the field would be eager to know. Students interested in these topics are encouraged to consider planning and structuring their theses for publication, with the assistance of the instructor.

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Understanding the perceived motions of the universe has for thousands of years been one of the major driving forces behind the development of new mathematics. Topics in this area that could be the focus of an undergraduate thesis include (but are not limited to) the following:

- History of trigonometry. How did ancient models of the universe as a set of spheres lead to the development of the trigonometric functions that we know today? How were they computed and used? A thesis project in this area might focus, for example, on the development of early plane and spherical trigonometry in antiquity, or on the invention of power series for trigonometric functions in the early modern period.

- The astrolabe: an ancient astronomical "computer". Long before astronomers could feed dates and times into an electronic computer and see pictures of the heavens in the future, their predecessors were doing the same thing with the first "analog computer", a device known as the astrolabe. These beautiful and complex instruments used ingenious math and mechanics to make difficult computations as easy as turning a dial.

- From circles to ellipses: the mathematics of computing orbits. Many people know that Johannes Kepler came up with the concept of elliptical planetary orbits with the sun at one focus. But what inspired him to arrive at this idea, and how did he manage it mathematically? We will explore how Kepler's revolutionary (no pun intended) idea changed the role of the humble ellipse in mathematics forever.

Math Department web pages Created: 11 May 2009 Last modified: May 11, 2009 10:27:58 AM Comments to: math@union.edu

Thesis Topics -J. Wang Thesis Topics for 2009-2010 Thesis Topics - K. Plofker