How exactly is Pi Calculated? Who was the first to calculate it and how did they use it?

Question

I want to know because I have no clue as 2 how Pi was calculated and would like to see if I can come up with another way to do it.

Answer 1

As you may know, pi is the ratio of a circle's circumference to its diameter. It is an irrational number so there is no an exactly way to prove it..
Even Euclides, who was the first one to discover it, and Euler, who popularized it, couldn't give the exactly result for pi.
Even though, there are some methods to prove that definition.
Wanna try?

Draw una a circunference with ratio R. Inside an hexagon and take triangle OEG. Draw a parallel to EG through A, taking it trough OE, and resulting D. From this point D and above that line, move 3 times the ratio of the circunference resulting point C. Line BC is aproximately the half of the circunference...

BC^2 = AB^2 + (3 - DA)^2

part from here to prove that BC= 3.141533

As a gift there you have the firs 100 decimals of pi

π ≈ 3,141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 9

Answer 2

Hi!
A simple and suggestive way of calculating pi is the following:
Measure the perimeter of a square which is inscribed in a circle with the radius equal to one.Divide the perimeter at twice the radius,thus you obtain an approximative value of pi. Repeat the same procedure with a polygon obtained by braking the edges of the square in two, and positioning the braking point as to obtain an regular octagon. The new obtained value of pi is more accurate. The more edges the inscribed polygon has the more accurate is the pi value obtained. Just multiply by two the edges of the regular polygon starting from the square and thus obtain a more accurate pi.Doing so infinite times and you obtain the real
value of pi. With the help of some geometric calculations you may find the actual formula for obtaining the pi.
As for who was the first I can't tell. The egyptians new pi with one decimal precision (3.160),also the babylonians(3.125) , but it seams that the mayans and the aztecs had calculated some more precise values. Arhimede had also calculated pi and found the value of 3.14(using a polygon with 96 edges).Than in the 5th century India Aryabatha found the value of 3.1416. In China in the 3rd century BC Liu Huei found pi with five decimals 3.14159(using a polygon with 3072 edges) and also a method for calculating even more precise values.In the middle ages more precise values were calculated.In 1873 William Shanks had calculated pi with 707 decimals,and none had tried after to calculate a more precise value on paper.
In conclusion just use a circle if you want to find out a new way of calculating pi, or even better trigonometry.

Answer 3

The most famous series to calculate pi is:

pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

Unfortunately, this series converges too slowly to be very useful. Until computers came along (in other words, back when these calculations had to be done by hand), the most popular formulas utilized inverse tangent identities. For example, Machin developed a popular one in 1706, which he used to calculate pi to 100 places:

pi = 16 arctan(1/5) - 4 arctan(1/239)

http://ic.net/~jnbohr/java/Machin.html

Also, if you are interested in how the calculation of pi has progressed historically, you will love the following Web site:

http://documents.wolfram.com/v5/Demos/Notebooks/CalculatingPi.html


Also, you mention trying to come up with an original way to calculate pi. During my junior year of college, I remember once coming up with an approximation of pi during breakfast by counting the squares in my Eggo waffle. I'll never understand why the two girls sitting at the table thought that was weird (heh heh).

Answer 4

The Egyptian Method: this consisted of drawing a square, drawing an irregular octagon inside the square and then inscribing a circle touching the sides of the square. The theory was the area of the octagon = area of the circle. This method gave a value for pi of 3.11

The Hindu Method: This involved drawing a circle then inscribing a square. The distance between the sides of the square and the circle was divided into three equal parts. A second circle was drawn connecting the inner third of this divided area.
Theory: the area of the inner circle = area of the square
This method gave a value for pi pf 3.09

Method of Archimedes: The theory is if polygons of increasing number of sides are inscribed and circumscribed about a circle, the area of he circle will be a number somewhere between the area of the outer polygon and the area of the inner polygon.

Using the appropriate equation for determing the length of the sides of the two polygons and using increasing numbers of sides, the value for pi was calculated to be somewhere between 3.13100 and 3.14256.

Finally there was the method of Cusanus. This involved drawing a circle of radius, r and a chord, h. Add the length of the chord to the radius and then draw a second circle whose center is the mid-point of h+r. Draw an equilateral triangle in the new circle.
Theory: the circumference of the triangle = circumference of the original circle.

This method gave a value for pi of 3.1136.

Perhaps the oldest recorded data is to be found in the Bible.
In 1 Kings 7:23 and 2 Chronicles 4:2:is recorded
"Then he made the molten sea; it was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference.

From this information, 2 x pi x r = 30 and r = 5
This gives a value for pi of 3

You can probably find drawings of the constructs and the math used to solve them (its simple geometry).

Answer 5

Well, there are several ways. Really, it was a lot of trial and errors, and by people all over the world.

The first really interesting method came from archimedes, using an algorithm in which he substracted the area of a polygon inside a circle and the same number-sided polygon outside the same circle. That technique doesn't converge very fast, but it gave a 3 decimal precision.

That was pretty much the best that was achieved for a very long time by mathematicians. Some Arabs mathematicians using the archimedes method made it even more accurate. Some chinese and indians did pretty good too around the 5th century

More recently, Indians mathematicians (around the 14th century) started using infinite series-expansions of known functions to evaluate pi to the 11th decimal. Europeans, such as De moivre, using similar methods as that indian did pretty good too.

Nowadays, we use very specific algorithms made for computers. We have several billions Pi decimals by now.

Answer 6

in accordance to a million Kings, he thinks that's 3. that is a susceptible argument at the same time as Christians declare that the diameter replaced into affected because the diameter replaced into measured tip to tip, besides the indisputable fact that the circumference replaced into the interior circumference of the bowl. How do they understand how thick the bowl replaced into? Adam - The instruments do not count number. Pi is a courting between a circle and a circumference. If a circle has a diameter of one million cubit, the circumference is pi cubits. If a circle has a diameter of one million boodings, then that circle's circumference is pi boodings. truth: you may't have a circle with a given diameter that's a million/3 the dimensions of its circumference. Biblically-superb perfect circles can not exist.

Answer 7

Pi is defined as the ratio of the circumference of a circle to its diameter. So, Pi = C/d and C = d*Pi
3.1416 and 22/7 are your most common approximtions.

Hope that helps.

Answer 8

There are many ways to calculate pi. Check the following source.

Answer 9

Archimedes first discovered pi, which is the ration of the circumference of a circle to its diameter.

Answer 10

22/7

it's a ratio...

there is no other way to do it...

I promise