Posted by:
Brother Of Jerry
(
)
Date: March 16, 2021 02:59PM
Then why is the area πr^2? The circumference of a circle is usually defined in terms of the radius, though it can obviously be defined in terms of the diameter. Essentially all other relationships regarding circles and spheres are defined in terms of the radius. Area = πr^2, area of sphere = 4πr^2, volume of sphere = 4/3 πr^3.
Also, a hexagon is exactly 6 copies of a radius as internal chords in a circle.
Feeling the definition or π is inappropriate is not new with me. Here's an article on the subject from Sci Am.
https://www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/https://tauday.comETA: when you get into calculus, all manner of quantities are expressed in terms of radians. One radian is the length of one radius rolled along the perimeter of a circle. Mathematics doesn't even have a word for rolling a diameter along the perimeter of a circle. (Diamian?). It's all radians, all the time.
Edited 2 time(s). Last edit at 03/16/2021 03:21PM by Brother Of Jerry.