The Meaning of Pi

[@sistajoseph]

Circumference is then the perimeter of a uniform one sided figure. Very helpful.

[@jamesoshea4444]

not sure anyone could explain pi as succinct and lucid as you did. thank you.

[@armorvestrus4119]

This was great and so well explained.❤❤❤

[@andredevouissexavierii8970]

elegantly explained

[@dipu6174-t8n]

Important viewpoint. Nicely explained....Thanks.

[@Hythloday71]

Very good. You show for all circles the ratio is between 3 and 4. But is there a 'simple' argument for why for all circles it must be the singular real number pi ? Simple via 'scaling' ?

[@pepemonjess]

This is fantastic, thank you!

[@Krishnan172]

which application are you using for this?

[@philipparanthoiene4892]

Archimedes continued by dividing the hexagon sides to get a dodecagon (12 sides), then 24 sides , then 48 sides etc. From memory , after 15 doublings it gave pi to 6 decimal places.

[@ffggddss]

Archimedes carried it out to 96 sides, so four doublings of the hexagon. And he calculated perimeters of both inscribed and circumscribed poygons, in order to get a bracketing pair of values between which π must fall. Not having decimal notation, he worked out a pair of fractions that he could prove bracketed π: 223/71 < π < 22/7 i.e., 3 + 10/71 < π < 3 + 1/7 This "squeezes" π down to about 3 significant figures, or 2 decimal places after the point. This video is actually doing a much simpler, easier-to-grasp version of that, using a circumscribed square and an inscribed regular hexagon, to arrive at 3 < π < 4 If he had used a circumscribed hexagon instead of a square, it would have complicated the process, and would have arrived at: 3 < π < 2√3 = 3.464... It was better to do it the way he did, because it's supposed to be an introduction to the concept, and his example was the easiest to comprehend, so as not to distract the student from the essence of the technique. Fred

[@davidschandler48]

This is just the first of a 3-part sequence of videos. The other two complete a variation of Archimedes' method. They are intended for students at different levels.

[@IsaacAsimov1992]

Excellent. Thanks!@@ffggddss

[@cutelilly1000vedios]

Thanks for the help

[@fireofevender5515]

You'll occasionally see a circle inside a square in certain temples throughout the world. Some believe that a squared circle represents a sacred place where heaven & earth meet.

[@nikobaka5272]

Thanks man

[@siten1]

Idk if I am wrong but your logic for saying that pi must be < 4 being it can fit inside the square is wrong because you can actually fit a square inside that circle that would still have a ratio of 4.

[@arthurkernkamp5062]

The important point that you are missing is that the circle and the square must have an equal diameter to use this visual argument. You're right, you could indeed fit a square inside of the circle, but that square would have a smaller diameter than the circle, meaning you cannot easily compare the ratios visually. The reason the creator of this video can say pi < 4 is because you can clearly see that when the shapes are of equal diameter, the perimeter of the square is larger than that of the circle.

[@flatearthasmr9034]

C/D = 3.17157

[@craftyourlife01]

I didn't understand 😕

[@davidschandler48]

I am establishing that there is a fixed ratio of perimeter to diameter, and that the first digit of that ratio is 3. Go to my other videos in this series to get more digits.

[@charleschoice4705]

Pi equals infinity!

[@oliviervos1216]

Charles Choice not true at all

[@charleschoice4705]

Alter Ego you need more study there is no end to pi

[@oliviervos1216]

Charles Choice Yes, it has an infinite amount of decimals, but it's not equal to infinitey. Infinity in an infinitly large quantety

[@oliviervos1216]

Unlike 3.141592653589793738462643383279502884197169399375105820974944592307816406......

[@johniec5282]

@@oliviervos1216 You are correct. I guess the OP meant infinite number of decimals.