A reading report about π (Pi)

The number pi (Greek letter π) is a mathematical constant which occurs in many areas of mathematics and physics. It is also known as Archimedes' constant and is equal to the ratio of a circle's circumference to its diameter in Euclidean geometry.
The symbol π for the number 3.14... was introduced in 1706 by William Jones, although the same symbol had been used earlier to indicate the circumference of a circle. In either case, π is the first letter of περιμετρον (perimetron), meaning 'to measure around' in Greek.
Properties
The number π is an irrational number: that is, it cannot be written as the ratio of two integers. This was proved in 1761 by Johann Heinrich Lambert. In fact, the number is transcendental, as was proved by Ferdinand Lindemann in 1882. This means that there is no polynomial with integer (or rational) coefficients of which π is a root.
Open questions
It is not known which of the digits 0,...,9 occur infinitely often in the decimal expansion of π.
The nature of π
In non-Euclidean geometry the sum of the angles of a triangle may be more or less than π, and the ratio of a circle's circumference to its diameter may also differ from π. This doesn't change the value of π, but does affect many formulae in which it appears. So in particular, the shape of the universe does not affect the value of π at all: it is a mathematical constant, not a physical value.
Pi culture
There is an entire field of humorous yet serious study that involves the use of mnemonic techniques to remember the digits of π, which is known as Piphilology.
The most famous example of this is from Isaac Asimov :
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!
March 14 marks Pi Day which is celebrated by many lovers of π. On July 22, Pi Approximation Day is celebrated .

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