For me, it was this video. It came out shortly after I graduated high school, and though I was pretty good at maths, I struggled to really conceptualise the fundamental intuition behind trigonometric functions and the (polar) complex plane. Instead, I was relying on brute memorisation of the unit triangles. Learning about tau and how it relates just instantly caused everything to click with me.
I can’t be arsed to check but I think it’s 2 pi which is useful when dealing with sine waves.
2 pi is tau, which is what I said it’s less than 0.1 away from, but still not equal to.
Reminds me of: https://www.explainxkcd.com/wiki/index.php/1292:_Pi_vs._Tau
And: https://www.tauday.com/tau-manifesto
For me, it was this video. It came out shortly after I graduated high school, and though I was pretty good at maths, I struggled to really conceptualise the fundamental intuition behind trigonometric functions and the (polar) complex plane. Instead, I was relying on brute memorisation of the unit triangles. Learning about tau and how it relates just instantly caused everything to click with me.
That’s a fantastic video. I follow Numberphile but never saw this one, thanks for sharing.