The 20th annual Symposium will be held on Thursday, April 23, 2009.

The Biangular Coordinate System as Seen Through Complex Numbers
Norris 100, 10:15 AM

Whitney  Patton,   '09 8
   Major: Mathematics
   Hometown: Bloomfield Hills, MI

Sponsor(s): Mark Bollman
Support:  

Abstract: 
Visual representations of mathematical functions are a melding of algebra and geometry that form into structures called coordinate systems. These systems include the Cartesian or rectangular, the polar, and the biangular coordinate systems. Each has a different representation for the real numbers and the complex numbers. I will briefly explain the similarities and differences between the structures and then delve deep into the biangular coordinate system, as it is mostly unknown. The description of the biangular coordinate system will rely mostly on how functions are formed and a few function representations such as circles, lines, angels, and devils. This leads nicely into a discussion of how complex numbers are represented in the biangular plane verses their depiction in the Cartesian and the polar structures. The final matter of discussion will be research topics or questions that would be a good base to start another such project in the biangular coordinate system.

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