Difference between revisions of "Pi"
(→References) |
|||
| Line 11: | Line 11: | ||
=References= | =References= | ||
[http://math.stackexchange.com/questions/3198/proof-that-pi-is-constant-the-same-for-all-circles-without-using-limits Proof that $\pi$ is constant for all circles without using limits]<br /> | [http://math.stackexchange.com/questions/3198/proof-that-pi-is-constant-the-same-for-all-circles-without-using-limits Proof that $\pi$ is constant for all circles without using limits]<br /> | ||
| + | |||
| + | [https://www.youtube.com/watch?v=72N7yjcVFC8&feature=youtu.be&t=11s Proof that $\pi$ exists (video)] | ||
[http://www.oocities.org/cf/ilanpi/pi-exists.html Proof that $\pi$ exists] | [http://www.oocities.org/cf/ilanpi/pi-exists.html Proof that $\pi$ exists] | ||
[https://www.youtube.com/watch?v=2fCTnF75AL0#t=142 The story of $\pi$ by Tom Apostol (video)] | [https://www.youtube.com/watch?v=2fCTnF75AL0#t=142 The story of $\pi$ by Tom Apostol (video)] | ||
Revision as of 17:14, 14 March 2015
A circle in Euclidean plane geometry is defined to be the set of points equidistant from a center point. The length around a circle is called its circumference and the length a line from the circle through the center is called a diameter of the circle. All diameters have the same length by definition of the circle. Let $A$ be a circle. The number $\pi$ is defined to be the ratio $\dfrac{C}{D}$ where $C$ is the circumference of $A$ and $D$ the diameter of $A$. It requires proof to show that the value obtained from the circle $A$, call this $\pi_A$, is the same number one obtains from another circle $B$, the value $\pi_B$.
Properties
Theorem: The value of $\pi$ is independent of which circle it is defined for.
Proof: █
References
Proof that $\pi$ is constant for all circles without using limits
