4 ms·
The statement about the diameter being the interesting parameter is kind of exactly wrong. This is true for all the same reasons Tau is a better constant than P
by sebastos 11y ago
The statement about the diameter being the interesting parameter is kind of exactly wrong. This is true for all the same reasons Tau is a better constant than Pi.
For example, how does one derive the area of a circle? The most natural way is to integrate with respect to radius. When using Tau and radius, you get A = (1/2)Taur^2, which is nice since it looks a lot like the integral of, say, momentum, which gives you kinetic energy. If you use Pi or diameter or both, then weird factors of 2 start to creep in. It's also much more natural to think about defining the radial extent at each angle, rather than the diameter, especially if you're dealing with something other than a circle that has changing radius.
- gaze 11y agoTau is not happening.
- justinlardinois 11y agoStop trying to make tau happen. It's not going to happen.
- delish 11y agoI'll echo what gp said to help make tau happen: tau : the circumference (perimeter) of a circle. (1/2)tau^2 : the area of a circle. Beautiful. To go from one to the other, you integrate or take a derivative. Like gp said, there's no weird factor of two. Just the power rule in action.
- drdeca 11y agoYou seem to have left out the r in both of those expressions. Tou r. .5 tou r^2 .
- cmiller1 11y agoNope, all circles have a perimeter of 19.7392088022.
- Someone 11y ago(1/2)tau^2? I assume that's not what you meant to write, and just mention: 2pi r : the circumference (perimeter) of a circle. pi r^2: the area of a circle. Beautiful. To go from one to the other, you integrate or take a derivative. There's no weird factor of 1/2. Just the power rule in action.
- deleted 11y ago[deleted]