What is the mathematical origin of Pi?

Question

I am trying to find the mathematical origin of Pi, but I cant quite seem to uncover it. Does anyone know? Thank you!

Answer 1

Pi History

www-groups.dcs.st-and.ac.uk/~history/.../Pi_through_the_ages.html

mathforum.org/dr.math/faq/faq.pi.html

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Answer 2

Pi is the ratio between the circumference of a circle and it's diameter.

Pi (π) has been known since antiquity - the Babylonians were using it in 1800BC. It was first called π in 1706 and the Greek name came into vogue in the late 1700's.

It had been noted that the circumference of a circle divided by its diameter always gave a constant ratio. This ratio was thought to be 256/81 by the ancient Egyptians, 25/8 by the Babylonians, 30/10 by the Bible (I Kings 7:23) all of which are varyingly accurate approximations of π

Answer 3

Interesting question, but by my guess is the origin is not known. It goes at least as far back as the ancient Egyptians - Archimedes was one of the first to estimate pi to reasonable accuracy. It also wouldn't surprise me if a Western civilization, e.g. the Mayans, discovered it independently.

Answer 4

Pi is a mathematical symbol which was invented in the ancient times to calculate circles.

Answer 5

Circumference of a circle=Pi X diameter.
Pi= circumference/diameter
Pi is ratio of a circle's circumference to its diameter

Answer 6

The mathematical constant π is a transcendental (and therefore irrational) real number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter in Euclidean geometry, and has many uses in mathematics, physics, and engineering. It is also known as Archimedes' constant (not to be confused with an Archimedes number) and as Ludolph's number.Main article: pi (letter)
The name of the Greek letter π is pi, and this spelling is used in typographical contexts where the Greek letter is not available or where its usage could be problematic. When referring to this constant, the symbol π is always pronounced like "pie" in English, the conventional English pronunciation of the letter.

The constant is named "π" because it is the first letter of the Greek words περιφέρεια 'periphery'[1] and περίμετρος 'perimeter', i.e. 'circumference'.

π is Unicode character U+03C0 ("Greek small letter pi").

Use of the symbol π
Often William Jones' book A New Introduction to Mathematics from 1706 is cited as the first text where the Greek letter π was used for this constant, but this notation became particularly popular after Leonhard Euler adopted it in 1737 (cf History of π).

Early approximations
Main article: History of numerical approximations of π
The value of π has been known in some form since antiquity. As early as the 19th century BC, Babylonian mathematicians were using π = 25⁄8, which is within 0.5% of the true value.

The Egyptian scribe Ahmes wrote the oldest known text to give an approximate value for π, citing a Middle Kingdom papyrus, corresponding to a value of 256 divided by 81 or 3.160.

It is sometimes claimed that the Bible states that π = 3, based on a passage in 1 Kings 7:23 giving measurements for a round basin as having a 10 cubit diameter and a 30 cubit circumference. Rabbi Nehemiah explained this by the diameter being measured from outside rim to outside rim while the circumference was the inner brim; but it may suffice that the measurements are given in round numbers. Alternately, the Hebrew word translated line can also mean measuring rod (cf Ezekiel 47:3). Five cubits is a convenient size for a measuring rod: long enough to be accurate, while not too long to be inconvenient. A five cubit measuring rod will mark off precisely six straight line segments around the brim of the basin. So the literal translation "a line of thirty cubits compassed it round about", meaning "a five cubit measuring rod marked off thirty cubits around the brim" would be precisely correct.


Principle of Archimedes' method to approximate πArchimedes of Syracuse discovered, by considering the perimeters of 96-sided polygons inscribing a circle and inscribed by it, that π is between 223⁄71 and 22⁄7. The average of these two values is roughly 3.1419.

The Chinese mathematician Liu Hui computed π to 3.141014 in AD 263 and suggested that 3.14 was a good approximation.

The Indian mathematician and astronomer Aryabhata in the 5th century gave the approximation π = 62832⁄20000 = 3.1416, correct when rounded off to four decimal places. He also acknowledged the fact that this was an approximation, which is quite advanced for the time period.

The Chinese mathematician and astronomer Zu Chongzhi computed π to be between 3.1415926 and 3.1415927 and gave two approximations of π, 355⁄113 and 22⁄7, in the 5th century.

The Indian mathematician and astronomer Madhava of Sangamagrama in the 14th century computed the value of π after transforming the power series expansion of π⁄4 into the form

By 1610, the German mathematician Ludolph van Ceulen had finished computing the first 35 decimal places of π. It is said that he was so proud of this accomplishment that he had them inscribed on his tombstone.

In 1789, the Slovene mathematician Jurij Vega improved John Machin's formula from 1706 and calculated the first 140 decimal places for π, of which the first 126 were correct [1], and held the world record for 52 years until 1841, when William Rutherford calculated 208 decimal places of which the first 152 were correct.

The English amateur mathematician William Shanks, a man of independent means, spent over 20 years calculating π to 707 decimal places (accomplished in 1873). In 1944, D. F. Ferguson found that Shanks had made a mistake in the 528th decimal place, and that all succeeding digits were incorrect. By 1947, Ferguson had recalculated pi to 808 decimal places (with the aid of a mechanical desk calculator).


Numerical approximations
Main article: History of numerical approximations of π
Due to the transcendental nature of π, there are no closed form expressions for the number in terms of algebraic numbers and functions. Formulæ for calculating π using elementary arithmetic invariably include notation such as "...", which indicates that the formula is really a formula for an infinite sequence of approximations to π. The more terms included in a calculation, the closer to π the result will get, but none of the results will be π exactly.

Consequently, numerical calculations must use approximations of π. For many purposes, 3.14 or 22/7 is close enough, although engineers often use 3.1416 (5 significant figures) or 3.14159 (6 significant figures) for more precision. The approximations 22/7 and 355/113, with 3 and 7 significant figures respectively, are obtained from the simple continued fraction expansion of π. The approximation 355⁄113 (3.1415929…) is the best one that may be expressed with a three-digit or four-digit numerator and denominator.

The earliest numerical approximation of π is almost certainly the value 3. In cases where little precision is required, it may be an acceptable substitute. That 3 is an underestimate follows from the fact that it is the ratio of the perimeter of an inscribed regular hexagon to the diameter of the circle.

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Answer 7

3.141592653589793238462643383279502884197169399
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