Slightly OT: I remember reading about a Real World empirical way of solving quadratic equations. Basically it involves a fishtank, a balance beam and some uniform shapes (a sphere, a cylinder, a cone and a parabolic cone).

For 3x^2 + -1x + 4 = 0, the user set up, hanging each by a thread -
-the sphere at position 4 on the beam
-the cylinder at position -1 (with 0 being the fulcrum)
-the cone at position 3

Then add water and adjust strings such that sphere is submerged and the cylinder and cone are only just touching the water, and beam is balenced. Mark level of water.

Then add water. The beam will become unbalenced. Keep adding water until it balences again. The difference in water level gives a solution for x.

I can't remember the name of the book, but it had several other examples of analog devices.

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