|The trigonometric identities |
come from the Pythagorean theorem.
|You can write out the algebraic statements|
but a picture is worth a thousand words.
|Descartes is credited with uniting algebra and geometry. |
His work reflects the seemingly intractable
analytic-synthetic dichotomy of philosophers.
In truth, it should have erased the distinction
between the logically consistent and the empirically verifiable.
See the works of Gregory Browne on this blog here and here.
Long ago, at Curious Books in East Lansing, I found a old manual for apprentice carpenters that showed sines, cosines, and tangents to 32nds of an inch for triangles of given measurement. Many times I have regretted not buying it then. Even before that, when Laurel and I were first married, her father asked us what calculus was all about. We told him. He asked, "Do you mean like this?" and took out a foot-sized caliper and showed us how he measured stair cases. Rise over Run. Ain't no doubt.
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