Pi | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-04

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Pi


00:03:06 1 Fundamentals
00:03:15 1.1 Name
00:03:56 1.2 Definition
00:04:42 1.3 Irrationality and normality
00:08:00 1.4 Transcendence
00:09:56 1.5 Continued fractions
00:10:18 1.6 Approximate value and digits
00:11:01 1.7 Complex numbers and Euler's identity
00:15:52 2 History
00:17:55 2.1 Antiquity
00:20:19 2.2 Polygon approximation era
00:20:28 2.3 Infinite series
00:21:22 2.3.1 Rate of convergence
00:22:00 2.4 Irrationality and transcendence
00:23:31 2.5 Adoption of the symbol spanπ
00:25:37 3 Modern quest for more digits
00:31:56 3.1 Computer era and iterative algorithms
00:34:58 3.2 Motives for computing spanπ
00:36:42 3.3 Rapidly convergent series
00:38:35 3.4 Monte Carlo methods
00:39:29 3.5 Spigot algorithms
00:39:38 4 Role and characterizations in mathematics
00:42:20 4.1 Geometry and trigonometry
00:43:24 4.2 Eigenvalues
00:48:04 4.3 Inequalities
00:50:29 4.4 Fourier transform and Heisenberg uncertainty principle
00:53:25 4.5 Gaussian integrals
00:53:54 4.6 Projective geometry
00:56:32 4.7 Topology
00:57:05 4.8 Vector calculus
00:57:21 4.9 Cauchy's integral formula
00:57:48 4.10 The gamma function and Stirling's approximation
00:58:20 4.11 Number theory and Riemann zeta function
00:59:41 4.12 Fourier series
01:00:20 4.13 Modular forms and theta functions
01:02:32 4.14 Cauchy distribution and potential theory
01:05:30 4.15 Complex dynamics
01:07:43 5 Outside mathematics
01:09:55 5.1 Describing physical phenomena
01:11:31 5.2 Memorizing digits
01:16:15 5.3 In popular culture
01:18:52 5.4 In computer culture
01:20:33 6 References
01:24:33 7 Further reading
01:29:10 8 External links
01:30:37 Modular forms and theta functions
01:33:23 Cauchy distribution and potential theory
01:35:57 Complex dynamics
01:36:42 Outside mathematics
01:36:51 Describing physical phenomena
01:41:44 Memorizing digits
01:43:21 In popular culture
01:45:34 π/2, to simplify formulas. However, no other authors are known to use τ in this way. Some people use a different value, τ
01:45:44 6.28318..., arguing that τ, as the number of radians in one turn, or as the ratio of a circle's circumference to its radius rather than its diameter, is more natural than π and simplifies many formulas. Celebrations of this number, because it approximately equals 6.28, by making 28 June "Tau Day" and eating "twice the pie", have been reported in the media. However, this use of τ has not made its way into mainstream mathematics.In 1897, an amateur mathematician attempted to persuade the Indiana legislature to pass the Indiana Pi Bill, which described a method to square the circle and contained text that implied various incorrect values for π, including 3.2. The bill is notorious as an attempt to establish a value of scientific constant by legislative fiat. The bill was passed by the Indiana House of Representatives, but rejected by the Senate, meaning it did not become a law.
01:46:40 In computer culture



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SUMMARY
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The number π () is a mathematical constant.  Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics.  It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes' constant.
Being an irrational number, π cannot be expressed as a common fraction (equivalently, its decimal representation never ends and never settles into a permanently repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed. In particular, the digit sequence of π is conjectured to satisfy a ...