පයිප්ප සාදන්නා

[chathuranirmal]

bum[

 

[imhotep]

Please prove area of a circle using integrals, differentials, and other advanced formulas

There should be many isn't it?
The simplest proof - without any of the above is below.
The area of any regular polygon is (a*p)/2 where a is the apothem (the line drawn from the centre of the polygon, perpendicular to any of the sides) and p is the perimeter.
In the case of the circle a becomes the radius r snd p becomes 2(pi)r. Therefore the area is (pi)(r squared).

Also there's a simple, just a couple of steps proof using the line integral for the area inclosed of a simple, closed and smooth curve, use the polar form for the curve as r cos(theta), r sin(theta), for theta to 0 to 2(pi)

The more famous or popular one is the Onion Proof.

 

[upulpdn]

There should be many isn't it?
The simplest proof - without any of the above is below.
The area of any regular polygon is (a*p)/2 where a is the apothem (the line drawn from the centre of the polygon, perpendicular to any of the sides) and p is the perimeter.
In the case of the circle a becomes the radius r snd p becomes 2(pi)r. Therefore the area is (pi)(r squared).

Also there's a simple, just a couple of steps proof using the line integral for the area inclosed of a simple, closed and smooth curve, use the polar form for the curve as r cos(theta), r sin(theta), for theta to 0 to 2(pi)

The more famous or popular one is the Onion Proof.

There are Many methods. But there is a condition.
With integral, differential and advanced formulas

WITHOUT-
GEOMETRY,
" PI" (Because pi prooved using circle )

Anyway, I'm not completely against you. I just love discussion

 

[imhotep]

There are Many methods. But there is a condition.
With integral, differential and advanced formulas

WITHOUT-
GEOMETRY,
" PI" (Because pi prooved using circle )

Anyway, I'm not completely against you. I just love discussion

That would be difficult...with integrals yes. with added differential (??). advanced methods yes, possibly using Gaussian curvatures with integrals - there is But to have them together in one (????)
Thanks.. I love mathematical problems too. - at least you get your brain into gear - rather than !@#$ politics.

 

[upulpdn]

That would be difficult...with integrals yes. with added differential (??). advanced methods yes, possibly using Gaussian curvatures with integrals - there is But to have them together in one (????)
Thanks.. I love mathematical problems too. - at least you get your brain into gear - rather than !@#$ politics.

Im Covering all topics except "asahana thread"
Very less people attracting to post in mathematic threads now.
Will see