How did archimedes discover pi? we know that pi is:3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953........but how did he find it!!!!!??????
2007-11-22 04:23:15 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Archimedes found a method for finding good approximations to the ration of the circumference of a circle to the diameter. He did this by inscribing polygons inside the circle and finding how the perimeter changes when the number of sides is doubled.
Archimedes came up with an approximation that is equivalent to saying that pi is between 3 1/7 and 3 10/71. This is quite far from being as accurate as what you showed.
2007-11-22 04:33:33 · answer #1 · answered by mathematician 7 · 3⤊ 0⤋
A circle's circumference or perimeter is the distance around the circle. The diameter is the longest line segment that you can have inside a circle. The line segments go through the center of the circle and have their endpoints on the circle.
Now that you know what circumference and diameter are, here are a few questions for you.
Think of many circles of different sizes. Do you think there is a relationship between the circumference and the diameter?
If so, what might the relationship be? In this way PI was discovered.
2007-11-22 04:51:42 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Take a circle of diameter D = 1.
A square can be circumscribed outside this circle, such that its sides are barely tangent to the circle.
The sides of such a square will be exactly the same as the circle's diameter (D).
Therefore, the outside square's perimeter will be 4*D.
A square placed inside the same circle will have it's corners touching the circle. It's diagonal will measure D. Each side will be D/√2 = 0.7071*D.
The perimeter of the inscribed square is the sum of four sides = 2.8284
The circumference of the circle (its perimeter) is, by definition, D*pi, except that we do not know the value of pi.
However, we know that the value of the circumference is somewhere between the perimeter of the outer square (4) and the inner square (2.8284).
Repeat the procedure, using octogons this time (8 sided regular figure). You will get a perimeter for the outer octogon (less than 4) and one for the inner octogon (more than 2.9) and you now have tighter limits for the value of pi.
Continue with regular polygons with more and more sides, until you get a value that satisfies your curiosity and the limits get tighter and tighter.
You can approximate the value of pi to a great number of decimals (but, of course, in those days, you better have lots of time for the calculations)
2007-11-22 04:50:02 · answer #3 · answered by Raymond 7 · 0⤊ 0⤋
Although Pi is equal to the Circumference of a circle divided by its Diameter, it can be found with a simple formula.
PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 ...
One fourth of pi is equal to the reciprocals of the odd numbers added and subtracted from each other in order.
Pi never ends because there is an infinite number of odd numbers.
2007-11-22 05:31:15 · answer #4 · answered by A A 3 · 1⤊ 1⤋
He knew that if he inscribed a regular polygon in a circle and circumscribed another one, then the area of the circle would be between the areas of the two polygons. As he increased the number of sides on the polygons that he used, he found that the gap between the two gave him more accuracy.
Archimedes is thought to be the first person to understand the idea of limits. It is thought that he understood many of the principles behind the Calculus.
2007-11-22 04:31:01 · answer #5 · answered by Ranto 7 · 4⤊ 0⤋
Or, as a curt answer: He used two 96-sided polygons. One he inscribed in the circle with perimeter P1, and one he circumscribed about the circle with perimeter P2. He knew the circumference of the circle, C must be P1 < C < P2. He knew the radius R of the circle, so all he had to do was P1 / 2*R and P2 / 2*R. Then pi must lie between these two bounds.
2016-05-25 00:42:03 · answer #6 · answered by ? 3 · 0⤊ 0⤋
He looked at the circumference, and divided it by the diameter. If he experimented with circles of different circumferences and diameters, he still got the answer 3.14159....etc. That's how he found it.
2007-11-22 05:06:41 · answer #7 · answered by little louie 2 · 0⤊ 1⤋
Archimedes was drawing circles, we don't know for sure.
Some sources say that he just used a simple way as 22/7.
Other's say that he was using circles to calculate PI, the method is quite long and you should find it somewhere on the internet.
Why do you need to know? He didn't find it that exactly...
2007-11-22 04:28:06 · answer #8 · answered by Sir Rogers 2 · 0⤊ 2⤋
Who knows
2007-11-22 04:39:49 · answer #9 · answered by THe CW 1 · 0⤊ 3⤋
It's the circumference divided by the diameter. ...I don't know why he chose to look at that, though....
2007-11-22 04:27:24 · answer #10 · answered by Amelia 6 · 0⤊ 2⤋