Pi (π)

pi in maths is the most common constant. discover more about it.

1. Pi ( π) Name : Shama Singla Class : X-B Roll No. : 27

2. INDEX Introduction Value Type of number Formula History of Pi Uses Facts Pi day

3. Introduction Pi is a mathematical constant that is used to solve problems generally related to circles. Its value is fixed . Pi is basically the ratio of a circle's circumference to its diameter.

4. Value Its value is fixed universally. It is 3.14 or 22/7. Actually the value of Pi is endless i.e. 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128

5. Type of number Pi is an irrational number. It is non-terminating and repeating.

6. Formula π is commonly defined as the ratio of a circle's circumference C to its diameter d: The ratio C/d  is constant, regardless of the circle's size .

7. History of Pi European mathematicians in the early modern period developed new arithmetical formulae to approximate the value of pi, such as that of James Gregory (1638-1675), which was taken up by Leibniz: /4 = 1 - 1/3 + 1/5 - 1/7 + . . . . . . . . . . .

8. One problem with using this formula to calculate the value of pi is that you would have to add 5 million terms to work out a value of /4 that extends to 6 or 7 decimal places. In 1706, another mathematician named John Machin developed a refinement on Gregory's formula, yielding the formula still used today by computer programmers to compute pi. Using this formula, an Englishman named William Shanks calculated pi to 707 places, a labour of many years, which he published in 1873.

9. Uses π appears in formulae for areas and volumes of geometrical shapes based on circles, such as ellipses, spheres, cones, and tori. Below are some of the more common formulae that involve π. The circumference of a circle with radius r is 2πr. The area of a circle with radius r is πr2. The volume of a sphere with radius r is 4/3πr3. The surface area of a sphere with radius r is 4πr2.

10. Facts Pi is the most recognized mathematical constant in the world. Scholars often consider Pi the most important and intriguing number in all of mathematics. The symbol for pi (π) has been used regularly in its mathematical sense only for the past 250 years. In the Greek alphabet, π (piwas) is the sixteenth letter.

11. Albert Einstein was born on Pi day. Hiroyuki Goto of Tokyo, Japan has the world record for most memorized digits of pie with 42,195 digits in d4ecimal place. Value of pi has been found till 2 trillion decimals.

12. Pi day Pi Day is an annual celebration of the mathematical constant π. Pi Day is observed on March 14 (3/14 in the month/day date format) since 3, 1, and 4 are the first three significant digits of π. In 2009, the United States House of Representatives supported the designation of Pi Day.

13. Pi Approximation Day  is observed on July 22 (22/7 in the  day/month  date format), since the fraction  22 ⁄ 7  is a common approximation of π, which is accurate to two decimal places and dates from  Archimedes.

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