Area of a circle, how to get the formula.

[acnelson12]

There's a simpler explanation. The area of a regular polygon is 1/2 apothem * perimeter.

Think of a circle as a polygon with an infinite number of sides. Perimeter = circumference. C = 2πr. The apothem = r. area = 1/2 2πr *r

simplified:

area = πr^2

If you don't understand the area formula for a regular polygon read this:

Any regular n-gon can be broken into n triangles with the apothem as their height. The base of the triangles is the perimeter, so you end up with 1/2 aP.

[Darthlego458]

awesome i love pi

[SenhoritaEueu25]

Ms.Kronish showed you this video didn't she? I know she did

[GSHBearXX]

Why is the base 1/2 the circumference?



[hi6747]

WOW

[sagor122]

i want to know why circumference = 2.pie.r,,,,,,,,,ty

[acnelson12]

@sagor122 Pi is defined as the circumference divided by the diameter. The diameter is two times the radius.

therefore: C = 2πr

[sagor122]

nice

[sidroxxable6]

great man

u solved my project of maths !!

thanzz a lot

[Randomasscrap223]

Cool thank you

[makotai]

superb work, very clear and pricised

[skulkid114]

that was a good lesson thnx

[agaclardan]

great educational video. what software did you use for the animations?

[fireball9ful]

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[ZOMBIEKILLAH500]

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[sds1997226]

man this is great now ill past my stupid test

[ZOMBIEKILLAH500]

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[ZOMBIEKILLAH500]

whos andrew?

[ammvid]

Nice video. Love it teacher showed me. Keep it up.

[fireball9ful]

i wuz tlk to andrew

[fireball9ful]

idiots

[cookiesmilk997]

good video:) well done

[ZOMBIEKILLAH500]

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[subfragelistic]

Excellent work! I have just finished reading a book entitled "The History of Pi." by Petr Beckman. (yes Mr. Beckman does spell his first name that way). His explanation is very similar to yours. I particulary like your use of animated graphics. I too make videos, ("Varietal Video"), but I do not know how to produce an animated presentation like yours. I'll be looking into that technique to learn. Again... very nice work... very comprehensive explanation of this subject. Sincerely, Anthony

[barnamah]

but you got away from the main question "where does pi R squared come from?". Many people are puzzled with the π in the formula. You simply cheated instead of answering the question, answered one unknown with other unknown. sorry.

[rolfch1p]

nice

[MolfitoMusic]

I wish everything had a cool video explanation like this! Great job!

[24thejessa]

.mahal n kita ,hehe

[FaradaysBirdCage]

Looks like Riemann Sums. ;)

[zx6rtt]

that was REALLY helpful

thanks

: ]

[Mathemaphysicist]

For anyone who's wondering, "Why does the Base of the rectangle = 1/2 circumference?"

The circle is split into infinitely many segments, which each have an infinitely small arclength. The sum of the arclengths is obviously equal to the circumference. You've gathered these together, and then split them in two. So half the gathering of the segments forms the base, which is therefore half the circumference.

[cmariefelts]

Wow!!! This is an amazing video and it is so helpful!!!

[ncbasspraise]

I showed them today. They liked it as much as 6th graders can. :-) It is so much more efficient than me doing it. I like to "show" why the formula works and this does so in great detail. Thanks again.

[Mathemaphysicist]

@ncbasspraise Not just that! It'd take you quite a while to divide a circle infinitely many times! :P

[ncbasspraise]

Excellent job. I use to have to show my middle-schoolers this with unit pieces that I made. Now, all I have to do is show your video. It's a sign of the times.

Thanks!!!!!

[mathematicsonline]

@ncbasspraise Nice! Let me know if they like it.

[OniLinkPlus]

Hax.

[EFRENURENAG]

neat