# Rational Linear Combinations of Pure Geodetic Angles, Part 2

Rational Linear Combinations of Pure Geodetic Angles, Part 2

A "pure geodetic" angle is an angle such that any of the six squared trigonometric functions of is rational or infinite. This Demonstration shows how an angle whose tangent is of the form /+/+/+/ can be expressed as a rational linear combination of pure geodetic angles and an integral multiple of , that is, it finds rational , ,, and , such that +++ is a sum of a rational linear combination of (), , , and plus an integer multiple of .

α

α

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0

b

1

a

1

d

1

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a

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a

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π/4

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-1

tan

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a

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a

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-1

tan

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-1

tan

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-1

tan

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-1

tan

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π/4