To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China
Visualizing the Dynamics of Complex Functions with The Geometer's Sketchpad
KCP Technologies, Inc.
The development and understanding of complex analysis has often benefited from innovative use of visualization, from the earliest geometric interpretations of Argand and Wessel to contemporary pedagogic treatments such as Needham's Visual Complex Analysis (Oxford University Press, 1997). This presentation demonstrates applications of the Dynamic Geometry visualization approach pioneered by The Geometer's Sketchpad software to a variety of introductory topics in the field. When graphing complex functions, the central concern is one of four-dimensional visualization: since both domain and range are two-dimensional, illustrations of domain to range projections need four visual dimensions in which to describe a function's behavior! Temporal dynamics, parametric color, animation, and other Sketchpad capabilities are tools offering greater traction on these visualization problems than traditional textbook methods.
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