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The Pythagorean Theorem:

The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the two shorter sides.

I.e. for the Left Hemisphere we have

c² = a² + b² (4.1)

where a, b and c are defined by the labelled picture of a right triangle, shown in Fig. 4.2, which cathects the Right Hemisphere and gets the two working together.

  

Figure: A right triangle with hypotenuse c and short sides a and b. The right angle is indicated and the angle $\theta$ is defined as shown. Note that a is always the (length of the) side ``across from'' the vertex forming the angle $\theta$. This convention is essential in the trigonometric definitions to follow.