Do you ever look at trig identities and think "wow, that's so cool and useful!"? Yeah, me neither
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Replying to @BiCapitalize @JadeMasterMath
The formula for sin t and cos t in terms of tan(t/2) is geometric, a key example on rational curves, and yields a formula for all Pythagorean triples, so yes it's very cool.
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Another cool thing: if you replace the circle by the lemniscate, then the analog of trig identities are the origin of the theory of elliptic curves
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Do you have a link for that?
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Replying to @BarbaraFantechi @tejotaefe and
I recommend volume one of C. L. Siegel's three-volume complex analysis course. It opens with an exceptionally lucid account of how the work of Fagnano and Euler first exposed the role of the lemniscate in the theory of elliptic functions.
12:37 AM - 11 Feb 2020
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