John Carlos Baez on Nostr: If you're a serious mathematician who has been suffering through all this pop math ...
If you're a serious mathematician who has been suffering through all this pop math fluff, wondering what's *really* going on here, let me finally come out and say:
The reason ϖ and its mutant trig functions are important is that they're connected to one of the most symmetrical elliptic curves of all, the Gaussian elliptic curve!
You can get this taking the complex plane and modding out by the lattice of Gaussian integers. Any lattice in the complex plane gives an elliptic curve and elliptic functions. But this particular case is especially nice.
Gauss discovered that this elliptic curve is connected to the 'arithmetic-geometric mean', defined below. And the arithmetic-geometric mean of 1 and √2 is the ratio π/ϖ.
This number is called lemniscate constant!
https://en.wikipedia.org/wiki/Lemniscate_constant
I could go on, but I will spare you. Happy holidays!
(4/n, n = 4)
The reason ϖ and its mutant trig functions are important is that they're connected to one of the most symmetrical elliptic curves of all, the Gaussian elliptic curve!
You can get this taking the complex plane and modding out by the lattice of Gaussian integers. Any lattice in the complex plane gives an elliptic curve and elliptic functions. But this particular case is especially nice.
Gauss discovered that this elliptic curve is connected to the 'arithmetic-geometric mean', defined below. And the arithmetic-geometric mean of 1 and √2 is the ratio π/ϖ.
This number is called lemniscate constant!
https://en.wikipedia.org/wiki/Lemniscate_constant
I could go on, but I will spare you. Happy holidays!
(4/n, n = 4)