The History of Pi: Archimedes

[@ffggddss]

Kudos for something that virtually every other YT treatment of Archimedes' method fails to mention - that he also used *circumscribed,* in addition to inscribed polygons; and that rather than just get *an* approximation for π, he found upper & lower *bounds* for it. Fred

[@charlemagnepacquiao6454]

Thanks for the awesome video

[@w2quick]

i love to hear the story and methods behind mathematical discoveries. great video. might include the link to the next one please

[@emirselman3984]

Am I right to say the only difference between the calculations between the cir. and in. polygon is that with the inscribed its C bigger than P, whereas with the cir. its C smaller than P? This is the only difference you make if you want to prove the upper and lower boundary - otherwise the calculations are the same, right?

[@ffggddss]

Not quite. The amount by which the circumscribed polygon is bigger, is about twice the amount by which the inscribed polygon is smaller. P(cir) - C ≈ 2(C - P(ins)) Also, the method for calculating the next polygon's perimeter from the current one, is a little different for the circumscribed ones than for the inscribed ones. [He didn't get into how to do that in this video.] Basically, for inscribed polygons, the "radius" (half the diagonal) remains constant; while for circumscribed polygons, the apothem (altitude of each constituent isosceles triangle) remains constant. Both are equal to the radius of the circle. But both methods use the Pythagorean Theorem. Fred

[@pas618]

What program are you using?

[@nagarmalsharma9992]

Why not just take a thread of known length and arrange it in a circular shape...then calculate it's diameter using a scale and then divide ? Wouldn't that give us the value of Pi?

[@EulersAcademy]

I believe that is what people essentially did before Archimedes. This method will get you an answer very close to pi, but it will only be an approximation. Archimedes and subsequent mathematicians were concerned with finding the exact value for pi.

[@O-Kyklop]

Where are the historical sources that corroborate that Archimedes was looking for Pi up to four decimal places, in the upper and in the lower limit?

[@becnal]

O. Kyklop en.m.wikipedia.org/wiki/Archimedes_Palimpsest

[@vitakyo982]

Taking the average value of the boundaries , & you are even closer to pi . 3.1418... in the case of 96 sides

[@srimantaroy78]

pi= 3, to equilibrium of a loci fixed to the fixed point, origin of the circle without overlapping and this proves it.