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That was an EXCELLENT read, thank you. I was a math major in college, and somethings you learn how to work out mechanically and understand intellectually. I d
by gxs 6y ago
That was an EXCELLENT read, thank you.
I was a math major in college, and somethings you learn how to work out mechanically and understand intellectually.
I dont do anything remotely close to academic, undergraduate mathematics, but it's interesting how now that I'm older i seem to understand things better, to internalize them beyond something mechanical or simply accepting them because they make logical sense.
Wish I'd had that type of understanding in school.
This explanation is very intuitive - and the author makes a good point. There might be better ways to introduce pi other than the ratio of the circumference of a circle to its diameter.
- jonsen 6y ago> There might be better ways to introduce pi other than the ration of the circumference of a circle to it's radius. Sure, the ratio of the circumference of a circle to it's diameter ;-)
- gxs 6y agoHa! I thought I corrected it before anyone saw :)
- qsort 6y ago> There might be better ways to introduce pi To be fair that's the elementary school way of defining pi. I'm somewhat rusty myself, but I'm pretty sure even undergraduate real analysis courses define pi in terms of the complex exponential. "Ratio of circumference to diameter" is insanely hard to make rigorous.
- Tainnor 6y agoMy undergraduate real analysis course didn't, probably because here, I don't think complex numbers are necessarily part of the high school curriculum. Instead, we defined sin and cos via power series, and then IIRC, pi as the first positive zero of the sin function or something similar.
- sgdpk 6y agoIndeed! I highly recommend following the author.