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Chapter 2: An ancient theorem and a modern question: Difference between revisions
Chapter 2: An ancient theorem and a modern question (edit)
Revision as of 21:22, 16 May 2020
, 16 May 2020→Radians and \pi
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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>: | ||
<math> \pi \cdot 57.29 = \pi r = 180^\circ </math> | <math> \pi \cdot 57.29 = \pi r = 180^\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. | ||