How Archimedes Found Pi to be 3.14

A ten minute lesson on how Archimedes "triangulated" the value of Pi, or "squared the circle" I think is also a correct reference.

Category:

Education

Tags:

• Mrcropper
• archimedes
• value
• pi
• math
• circle
• circumference
• diameter
• radius

[zardozcs]

How did archimedes construct the outside 96-polygon?  Is there any mention of what he used to construct it? I imagine he must have used a very large compass and a flat section of ground to construct the circle.

[MrCropper]

"How did archimedes construct the outside 96-polygon?"

By drawing a triangle around the outside of the circle, then collapsing it in the exact way he did the inside edge, but in reverse. After the outside triangle is drawn, the next three lines cut the tips of the triangle off into three perfect triangles, and so on...

Does that make sense? It seems a bit unclear...

[nine9s]

"...how Archimedes 'triangulated' the value of Pi, or 'squared the circle' I think is also a correct reference."

Squaring the circle was the problem of using a circle to create a square with the same area as the circle, using only a compass and a straightedge. It was impossible to get it precisely right because pi is an irrational number.

[MrCropper]

"Squaring the circle was the problem of using a circle to create a square with the same area as the circle"

That sounds more like it. Archimedes more 'triangulated' the circle. Even that's probably a stretch.

[hughtub]

As I watch this video, the thought occurred to me that maybe the atmosphere in schools should be very degraded, so that the content of the lesson would be so interesting that kids would pay more attention. All the modern conveniences take away the feeling of necessity that kids might otherwise develop, for this education. Kids just don't care to learn when everything is already so well developed, like video games and buildings. A dirt floor hut school might be a good thing.

[Prostock1489]

These kids thought they were going to learn about pie, not pi...

[UFOGEAR]

Go to Google and type

did archimedes study in egypt

click on second result. The 3rd and 4th paragraphs in that article say that he studied in Egypt. The value of pi is encoded in several places in the construction of the Great Pyramid at Giza. Archimedes may have been an initiate into the Egyptian mystery system and the Pythagoreans. 22/7 is an approx. of pi. It is the 22 letters of the Hebrew aleph beth divided by the holy number 7.

[11Agamemnon235]

Yeah, the method of exhaustion was absolutely ingenuious for its time. Archimedies as an incredible geometer.

[richardcadbury]

shout out for my favourite biblical verse. pi is exactly 3 lol

[makedonas86]

(8 months ago) =)

[kevinkim44]

1000th viewer =)

[bluehighlighterfreak]

yeah way to think. because kids care more about pi than the atmosphere.

[zardozcs]

Yes, though I'm unsure how he did it technically. The inside triangles are easy because bisection of a line can be done with a compass set to side length of the triangle. Cutting the tips off the outside triangles seems to me like he has to eye the ruler to get the right tangent. Maybe I just don't know enough geometry to compute where he would draw the lines exactly. Sadly, formal geometry not taught any more.