Wednesday, February 4, 2009

The Third Week

III. The Third Week - The Riemann Sphere

This meeting, we branched into a new way of thinking about the complex number system geometrically. In complex analysis, one learns that the complex numbers are graphed on a type of three-dimensional graph called a Riemann sphere (named after Bernhard Riemann). Fig. 3-1 below depicts the type of graph visually. 

[Fig 3-1 - The Riemann sphere, with labeled terms]. 

The illustration above attempts to show how a complex number is graphed onto the Riemann sphere - the complex number (e.g. 3 + 4i) is graphed with a coordinate of the form (x, y, z). 

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