>>12511974you mean that C/D = pi. which imo is the incorrect form of the equation. we do not define circles by their diameter. the definition of a circle if all points equidistant from a given center, which is defined by the length of the RADIUS. my point is that 2pi*r = C makes more sense considering how you integrate the circumference formula to get the formula for the area of the circle.
theta = s/r.
when theta = 2pi (the entire circle) it yields:
2pi*r = s, which is the length of the sector around the entire circle (the circumference)
if you integrate the circumference you get the area.
C = 2pi*r
int C dr = 2pi *int r dr = A
A = 2pi*(r^2/2)
do you see that? it's the factor of two being cancelled out. when you integrate x dx you get x^2/2. you see that all the time as a common integral form, like the kinetic energy equations or hooke's law. by using pi you're introducing an anomalous factor of 1/2 and making radians a pain in the ass.
1/4 of a circle should just be tau/4 instead of pi/2. why do we intentionally make things more painful than they have to be?
