How to measure perimeter without pi?

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    Measure Perimeter Pi
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Discussion Overview

The discussion revolves around the concept of measuring the perimeter of a circle without using the mathematical constant pi. Participants explore historical methods of approximating pi and the implications of these methods on understanding perimeter measurement.

Discussion Character

  • Exploratory
  • Debate/contested
  • Historical

Main Points Raised

  • Some participants question the original inquiry about measuring perimeter without pi, expressing confusion about the intent of the question.
  • There is a discussion on how pi was historically discovered, particularly through the method of inscribing polygons within circles and summing their sides to approximate the circle's perimeter.
  • One participant argues that the approximation method used by Archimedes is insufficient for generalizing the value of pi, suggesting that there must have been another way to determine it accurately.
  • Another participant points out that the relationship between circumference and diameter is mentioned in Euclid's work, indicating that this concept predates Archimedes.
  • It is noted that Archimedes provided a more precise calculation of pi, establishing bounds for its value, while a biblical reference is mentioned that suggests an early approximation of pi as "3."

Areas of Agreement / Disagreement

Participants express differing views on the adequacy of historical methods for determining pi and the implications for measuring perimeter. There is no consensus on how to measure perimeter without pi or the historical accuracy of the methods discussed.

Contextual Notes

Some limitations include the lack of clarity on the original question's intent, the dependence on historical interpretations, and the unresolved nature of how accurately pi can be determined without using it directly.

menniandscience
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how to measure perimeter without pi? [before they knew about the pi ratio]
 
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I don't understand the question.
 
Hurkyl said:
I don't understand the question.

how pi was discovered?
 
meni ohana said:
how pi was discovered?

Look up some info on archimedes.

Basically the way that pi was discovered was to inscribe a polygon in the circle and measure the sum of the sides. So basically you approximate the circle by some uniform polygon (each side is the same size) and add up all the sizes.

Then you basically increase the number of sides that the polygon has and you find that the ratio of the perimeter of the circle against its diameter reaches pi.

The same kind of process is used in calculus.
 
chiro said:
Look up some info on archimedes.

Basically the way that pi was discovered was to inscribe a polygon in the circle and measure the sum of the sides. So basically you approximate the circle by some uniform polygon (each side is the same size) and add up all the sizes.

Then you basically increase the number of sides that the polygon has and you find that the ratio of the perimeter of the circle against its diameter reaches pi.

The same kind of process is used in calculus.

i know who is archimedes, can you narrow it?

calculus wan't invented - as much as i know- in ancient times. and approximation is not good enough to genralize and find pi. it had to be someother way.
right now if one wants to know how long is permiter he needs to use pi. but to know there is pi - you need to know the premiter in total acuratly and divide by diameter. problem
 
meni ohana said:
i know who is archimedes, can you narrow it?

calculus wan't invented - as much as i know- in ancient times. and approximation is not good enough to genralize and find pi. it had to be someother way.
right now if one wants to know how long is permiter he needs to use pi. but to know there is pi - you need to know the premiter in total acuratly and divide by diameter. problem

Here is a webpage about pi:

http://ualr.edu/lasmoller/pi.html

Also the analogy between Archimedes with pi and Newton/Liebniz with calculus is the concept of using limits to find certain quantities. That's what I mean when I use those two things with the same analogy.
 
the fact that circumference/diameter is the same for all circles is in Euclid, so it predates Archimedes.
 
Yes, but Archimedes was the first to give a really good calculation of pi- that pi is less that 3 and 1/7 but larger than 3 and 10/71.

In fact, in the bible (I forget which chapter and verse) there is a reference to a cauldron that has circumference 3 times the diameter- so you could say that the earliest approximation to pi was just "3".
 

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