Difference between revisions of "Pi"
(Created page with "=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...") |
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| + | 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= | ||
| + | [[Pi is irrational]]<br /> | ||
| + | [[Sum of values of sinc]]<br /> | ||
| + | [[Wallis product]]<br /> | ||
| + | |||
| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=JmnjjE0b5z0 The story of $\pi$ by Tom Apostol (1995)]<br /> | ||
| + | [https://www.youtube.com/watch?v=72N7yjcVFC8&feature=youtu.be&t=11s Proof that $\pi$ exists (2014)]<br /> | ||
| + | |||
=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] | + | [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://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]<br /> |
| + | [http://projecteuclid.org/download/pdf_1/euclid.bams/1183510788 A simple proof that $\pi$ is irrational by Ivan Niven]<br /> | ||
| + | [http://fredrikj.net/blog/2011/03/100-mpmath-one-liners-for-pi/ 100 mpmath one-liners for pi]<br /> | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 12:12, 29 August 2016
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
Pi is irrational
Sum of values of sinc
Wallis product
Videos
The story of $\pi$ by Tom Apostol (1995)
Proof that $\pi$ exists (2014)
References
Proof that $\pi$ is constant for all circles without using limits
Proof that $\pi$ exists
A simple proof that $\pi$ is irrational by Ivan Niven
100 mpmath one-liners for pi
