Difference between revisions of "Chapter 2: An ancient theorem and a modern question"

The explanation for this is simple. <math> \pi </math> is simply used as a shorthand for <math> \pi R </math> where <math> R </math> stands for radian. An arc of a circle with the same length as the radius of that circle subtends an '''angle of 1 radian''' (roughly 57.29). Adding three radians together brings you almost '''180 degrees''' around. <math> \pi </math> radians brings you ''exactly'' 180 degrees around. The circumference subtends an angle of <math> 2\pi </math>. To summarize:

The explanation for this is simple. <math> \pi </math> is simply used as a shorthand for <math> \pi R </math> where <math> R </math> stands for radian. An arc of a circle with the same length as the radius of that circle subtends an '''angle of 1 radian''' (roughly 57.29). Adding three radians together brings you almost '''180 degrees''' around. <math> \pi </math> radians brings you ''exactly'' 180 degrees around. The circumference subtends an angle of <math> 2\pi </math>. To summarize:

<math> 1 Radian = 1R = 57.29^\circ </math>:

<math> 1 Radian = 1R = 57.29^\circ </math>:

So just remember, <math> \pi = 180^\circ </math>. Further explanations are given in the [[Preliminaries]| preliminaries] section.

So just remember, <math> \pi = 180^\circ </math>. Further explanations are given in the [[Preliminaries]| preliminaries] section.