Schiller Institute Gauss Fundamental Theorem -Diagrams by Bruce Director

SCHILLER INSTITUTE

Figure 1: A succession of algebraic powers is generated by a self-similar spiral. For equal angles of rotation, the lengths of the corresponding radii are increased to the next power.

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Figure 2: Leibniz' construction of the algebraic powers from the hanging chain
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Figure 3: An example of the three solutions to the trisection of an angle
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Figure 4: The unit of action in Gauss' complex domain.
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Figure 5: In (a) the lengths of the radii are squared as the angle of rotation doubles.
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In (b) the lengths of the radii are cubed as the angle of rotation triples.
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Figure 6: Squaring a complex number.
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Figure 7: Cubing a complex number.
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Figure 8: The sin of x is zP and the cosine of x is 0P. The sine of 2x is QP' and the cosine is OP'.
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Figure 9: Variations of the sine and cosine from the squaring of a complex number.
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Figure 10: Gaussian surface for the second power.
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Figure 11: Gaussian surface for the third power.
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Figure 12: Gaussian surface for the fourth power.
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Figure 13: Combined Gaussian surfaces for algebraic equations. (a) combines the surfaces based on the variations of the sine and cosine for the second power.

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(b) combines the surfaces based on the variations of the sine and cosine for the third power.

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Figure 14: Roots of algebraic equations represented in a Gaussian surface. (a) is the intersection of the surfaces in 13(a) with the flat plane.

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(b) is the intersection of the surfaces in 13(b) with the flat plane.

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