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2006-09-15 13:02:16 · 9 answers · asked by Brandon K 2 in Education & Reference Higher Education (University +)

how do we know it goes 141592 after 3. please tell me wikipedia not accepted

2006-09-15 13:03:11 · update #1

also 22/7 does not work it is 3.14857....

2006-09-15 13:07:22 · update #2

9 answers

it's posted all over the web

2006-09-15 13:44:02 · answer #1 · answered by yofatcat1 6 · 0 0

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609

What is pi ()? Who first used pi? How do you find its value? What is it for? How many digits is it?

By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it.
For the sake of usefulness people often need to approximate pi. For many purposes you can use 3.14159, which is really pretty good, but if you want a better approximation you can use a computer to get it. Here's pi to many more digits: 3.14159265358979323846.

The area of a circle is pi times the square of the length of the radius, or "pi r squared":


A = pi*r^2
A very brief history of pi

Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3; the Babylonians had an approximation of 3 1/8 (3.125), and the Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484), which is slightly less accurate and much harder to work with. For more, see A History of Pi by Petr Beckman (Dorset Press).
The modern symbol for pi [] was first used in our modern sense in 1706 by William Jones, who wrote:


There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to (16/5 - 4/239) - 1/3(16/5^3 - 4/239^3) + ... = 3.14159... = (see A History of Mathematical Notation by Florian Cajori).
Pi (rather than some other Greek letter like Alpha or Omega) was chosen as the letter to represent the number 3.141592... because the letter [] in Greek, pronounced like our letter 'p', stands for 'perimeter'.

About Pi
Pi is an infinite decimal. Unlike numbers such as 3, 9.876, and 4.5, which have finitely many nonzero numbers to the right of the decimal place, pi has infinitely many numbers to the right of the decimal point.
If you write pi down in decimal form, the numbers to the right of the 0 never repeat in a pattern. Some infinite decimals do have patterns - for instance, the infinite decimal .3333333... has all 3's to the right of the decimal point, and in the number .123456789123456789123456789... the sequence 123456789 is repeated. However, although many mathematicians have tried to find it, no repeating pattern for pi has been discovered - in fact, in 1768 Johann Lambert proved that there cannot be any such repeating pattern.

As a number that cannot be written as a repeating decimal or a finite decimal (you can never get to the end of it) pi is irrational: it cannot be written as a fraction (the ratio of two integers).

Pi shows up in some unexpected places like probability, and the 'famous five' equation connecting the five most important numbers in mathematics, 0, 1, e, pi, and i: e^(i*pi) + 1 = 0.

Computers have calculated pi to many decimal places. Here are 50,000 of them and you can find many more from Roy Williams' Pi Page.

2006-09-15 13:06:49 · answer #2 · answered by Anjanette A 3 · 0 2

obviously, 22/7 is just an approximation and will not give you a correct value beyond 3 decimal points

although you seem to have something against the wikipedia, it has a good description of one of the simpler algebraic techniques

there are also caluculus techniques and statistical techniques (and experimental ones where you draw a really big circle and accurately measure the circumference and diameter)

Calculating π

The formulae often given for calculating the digits of π have desirable mathematical properties, but are often hard to understand without a background in trigonometry and calculus. Nevertheless, it is possible to compute π using techniques involving only algebra and geometry.

For example, one common classroom activity for experimentally measuring the value of π involves drawing a large circle on graph paper, then measuring its approximate area by counting the number of cells inside the circle. Since the area of the circle is known to be

a = \pi r^2,\,\!

π can be derived using algebra:

\pi = a/r^2.\,\!

This process works mathematically as well as experimentally. If a circle with radius r is drawn with its center at the point (0,0), any point whose distance from the origin is less than r will fall inside the circle. The pythagorean theorem gives the distance from any point (x,y) to the center:

d=\sqrt{x^2+y^2}.

Mathematical "graph paper" is formed by imagining a 1x1 square centered around each point (x,y), where x and y are integers between -r and r. Squares whose center resides inside the circle can then be counted by testing whether, for each point (x,y),

\sqrt{x^2+y^2} < r.

The total number of points satisfying that condition thus approximates the area of the circle, which then can be used to calculate an approximation of π. Mathematically, this formula can be written:

\pi \approx \frac{1}{r^2} \sum_{x=-r}^{r} \; \sum_{y=-r}^{r} \Big(1\hbox{ if }\sqrt{x^2+y^2} < r,\; 0\hbox{ otherwise}\Big).

In other words, begin by choosing a value for r. Consider all points (x,y) in which both x and y are integers between -r and r. Starting at 0, add 1 for each point whose distance to the origin (0,0) is less than r. Divide the sum, representing the area of a circle of radius r, by r2 to find the approximation of π. Closer approximations can be produced by using larger values of r.

For example, if r is set to 2, then the points (-2,-2), (-2,-1), (-2,0), (-2,1), (-2,2), (-1,-2), (-1,-1), (-1,0), (-1,1), (-1,2), (0,-2), (0,-1), (0,0), (0,1), (0,2), (1,-2), (1,-1), (1,0), (1,1), (1,2), (2,-2), (2,-1), (2,0), (2,1), (2,2) are considered. The 9 points (-1,-1), (-1,0), (-1,1), (0,-1), (0,0), (0,1), (1,-1), (1,0), (1,1) are found to be inside the circle, so the approximate area is 9, and π is calculated to be approximately 2.25. Results for larger values of r are shown in the table below:
r area approximation of π
3 25 2.777778
4 45 2.8125
5 69 2.76
10 305 3.05
20 1245 3.1125
100 31397 3.1397
1000 3141521 3.141521

Similarly, the more complex approximations of π involve repeated calculations of some sort, yielding closer and closer approximations with increasing numbers of calculations.

before computers, calculating pi was rough work, but now, they are cranking out pi digits like crazy

2006-09-15 13:12:11 · answer #3 · answered by enginerd 6 · 0 0

There are formulas for computing pi but any calculator you have would not have enough digits and the formula has a endless number of terms that converge very slow. You can find the formula on the internet. You are required to add ever decreasing fractions.

Below is a site with some formulas.

2006-09-15 13:15:39 · answer #4 · answered by Barkley Hound 7 · 0 0

3.141592653589793
23846264338327950
28841971693993751
05820974944592 (64 places).

Get the free Power calculator from Microsoft (you need to run Windows XP) it goes to 512 decimal places!

I split the lines above, because yahoo blanks after a certain number of places on one line! See the other answers with 3 dots after each line?

To actually calculate PI you need the algorithm they use on super computers.

2006-09-15 13:06:40 · answer #5 · answered by Anonymous · 0 0

get out your calculator and go 22/7

2006-09-15 13:04:19 · answer #6 · answered by maisyday07 3 · 1 2

Ask arthur of king of queens, that way he will stop irritating dug, and ask steve paul and bruce cooper from UCSF, if they are free to give u a helping hand.

2006-09-15 13:12:03 · answer #7 · answered by weirdoonee 4 · 0 2

392699/125000

2006-09-15 13:34:14 · answer #8 · answered by hector 4 · 0 0

http://www.learner.org/exhibits/dailymath/pi.html

3.141592653589793238462643383279502884
19716939937510582097494459230781640628
62089986280348253421170679821480865132
82306647093844609550582231725359408128
48111745028410270193852110555964462294
89549303819644288109756659334461284756
48233786783165271201909145648566923460
34861045432664821339360726024914127372
45870066063155881748815209209628292540
91715364367892590360011330530548820466
52138414695194151160943305727036575959
19530921861173819326117931051185480744
62379962749567351885752724891227938183
01194912983367336244065664308602139494
63952247371907021798609437027705392171
76293176752384674818467669405132000568
12714526356082778577134275778960917363
71787214684409012249534301465495853710
50792279689258923542019956112129021960
86403441815981362977477130996051870721
13499999983729780499510597317328160963
18595024459455346908302642522308253344
68503526193118817101000313783875288658
75332083814206171776691473035982534904
28755468731159562863882353787593751957
78185778053217122680661300192787661119
59092164201989

2006-09-15 13:06:25 · answer #9 · answered by gravytrain036 5 · 0 1

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