THE PYTHAGOREAN THEOREM
Here is a fact seemingly not worth mentioning for its triviality: Still water in a resting container, with no disturbances, shall remain at rest. I think it is remarkable that this fact has the Pythagorean theorem as a corollary (p. 17). In addition, this seeming triviality implies the law of sines (p. 18), the Archimedian buoyancy law, and the 3D area version of the Pythagorean theorem (p. 19).
The proof of the Pythagorean theorem, described in section 2.2, suggested a kinematic proof of the Pythagorean theorem, described in section 2.6. The motion-based approach makes some other topics very transparent, including
• The fundamental theorem of calculus.
• The computational formula for the determinant. ...