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VilakkudY

B-Ed Maths Team

Semester 2nd

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The number π is a mathematical constant the ratio of a circle's circumference to its diameter

Represented By Greek Letter - π

C – circumferenceD – Diameter

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530582046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274…………………

prorperties π is an irrational number, meaning that it

cannot be written as the ratio of two integers (fractions such as 22/7 are commonly used to approximate π; no common fraction (ratio of whole numbers) can be its exact value.

Archimedes developed the polygonal approach to approximating π.

π can be estimated by computing the perimeters of circumscribed and inscribed polygons.

By calculating the perimeters of these polygons, Archimedes proved that 223/71<  < 22/7 

(that is 3.1408 < π < 3.1429).

Isaac Newton used Infinite series to compute π to 15 digits, later writing "I am ashamed to tell you to how many figures I carried these computations

Leonhard Euler popularized the use of the Greek letter π in works he published in 1736 and 1748.

Srinivasa Ramanujan, working in isolation in India, produced many innovative series for computing π.

3.14159265358979323846264338327950288.. Also called. "Ludolphine number"

Archimedes 

Archimedes' mathematical work exhibits great boldness and originality in thought, as well as extreme rigor. Among his mathematical accomplishments is the computation of pi, which is the ratio of the circumference of a circle to its diameter. His approach consisted of inscribing and circumscribing regular polygons with many sides in and around the circle, and computing the perimeter of these polygons. This provided him with an upper and a lower bound for pi…

Ludolph van Ceulen

Ludolph van Ceulen spent a major part of his life calculating the numerical value of the mathematical constant π, using essentially the same methods as those employed by Archimedes some seventeen hundred years earlier. He published a 20-decimal value in his 1596 book Van den Circkel ("On the Circle"), later expanding this to 35 decimals. After his death, the

"Ludolphine number",3.14159265358979323846264338327950288...,

π appears in formulae for areas and volumes of geometrical shapes based on circles, as ellipses, spheres, cones, and tori. Below are some ofthe more common formula that involve π.

1)The circumference of a circle with radius r is 2πr.2)The area of a circle with radius r is πr2.3)The volume of a sphere with radius r is 4/3πr3.4)The surface area of a sphere with radius r is 4πr2

Term Result (to 12 decimals)

1 3

2 3.166666666667

3 3.133333333333

4 3.145238095238

... ... etc! ...

.

Get a calculator (or use a spreadsheet) and see if you can get better results…

The symbol for pi has been regularly used for the past 250 years only.

In the Greek alphabets, Pi is the 16th letter.  In English p is also 16th letter.

Pi day is celebrated on March 14 every year.  It represents 3.14, which is pi value.  The first widely-attended pi day celebration was organized by Physicist Larry Shaw, also known as Prince of Pi, in the year 1988.

“Ludolph’s Number”, “Archimedes constant”, “Circular constant” are names by which Pi is referred.

Computing the value of Pi is a Stress test for a computer.