Question

Could someone please post all the circle related formulas or theorems. i heard that there are around 20-30 of them. Thanks

Answer 1

http://openstudy.com/study?login#/updates/4fd43dcde4b057e7d222c127

Answer 2

a website is also acceptable, but they must have ALL of the formulae or theorems!!!

Answer 3

@samyflashy that was only a mere 4 or so... what i need is like 20-30 theorems

Answer 4

im sorry i was just trying to help u :S, i really dont know, i just thought maybe that will help u something :/

Answer 5

ok thanks anyways

Answer 6

http://mathworld.wolfram.com/Circle.html

That website has a good survey of them. It's impossible to have literally every possible formula for a circle, because there are infinite ways that I could rewrite a formula in a slightly different notation.

Answer 7

To be clear: this is an extremely broad and vague question. Circles are a fundamental geometric object, and have been studied for thousands of years using thousands of different approaches and methods. It would be much easier to help you if your question was more specific.

Answer 8

i dont really mind what format you give of each formulae. i just want all the formulas which have different purposes which are related to circle geometry

Answer 9

The surface area of a sphere
\[\text{---------}\]\[x=r\sin\theta\cos\phi\qquad\qquad y=r\sin\theta\sin\phi\qquad\qquad z=r\cos\theta\]\[x_r=\sin\theta\cos\phi\qquad x_\theta=r\cos\theta\cos\phi\qquad x_\phi=-r\sin\theta\sin\phi\]\[y_r=\sin\theta\sin\phi\qquad y_\theta=r\cos\theta\sin\phi\qquad y_\phi=r\sin\theta\cos\phi\]\[z_r=\cos\theta\qquad\qquad z_\theta=-r\sin \theta\qquad\qquad z_\phi=0\]
\[\frac{\partial(x,y,z)}{\partial ( r,\theta, \phi)}=\left|\begin{matrix} x_r&x_\theta&x_\phi\\{y}_{r}&y_{\theta }&y_{\phi}\\{z}_{r}&{ z}_{\theta }&{z}_{\phi}\end{matrix}\right|={r^2\sin\theta}\]\[=x_r\left((y_\theta\times z_\phi)-(y_\phi\times z_\theta)\right)-x_\theta\left((y_r\times z_\phi)-(y_\phi \times z_r)\right)+x_\phi\left((y_r\times z_\theta)-(y_\theta \times z_r)\right)\]\[=x_r\left((r\cos\theta\sin\phi\times 0)-(r\sin\theta\cos\phi\times -r\sin\theta )\right)-x_\theta\left((\sin\theta\sin\phi\times 0)-(r\sin\theta\cos\phi \times \cos\theta)\right)+x_\phi\left((\sin\theta\sin\phi\times -r\sin\theta )-(r\cos\theta\sin\phi \times \cos\theta)\right)\]\[=x_r\left(0+r^2\sin^2\theta\cos\phi)\right)-x_\theta\left(0-r\sin\theta\cos\phi\cos\theta\right)-x_\phi\left(r\sin^2\theta\sin\phi+r\cos^2\theta\sin\phi\right)\]\[=x_rr^2\sin^2\theta\cos\phi+x_\theta r\sin\theta\cos\phi\cos\theta-x_\phi r\sin\phi\]\[=\sin\theta\cos\phi\ r^2\sin^2\theta\cos\phi+r\cos\theta\cos\phi\ r\sin\theta\cos\phi\cos\theta+r\sin\theta\sin\phi r\sin\phi\]\[=r^2\sin\theta\left(\sin^2\theta\cos^2\phi-\cos^2\theta\cos^2\phi+\sin^2\phi\right)\]\[=r^2\sin\theta\left((\sin^2\theta+\cos^2\theta)\cos^2\phi+\sin^2\phi\right)\]\[=r^2\sin\theta\left(\sin^2\phi+\cos^2\phi\right)\]\[={r^2\sin\theta}\]\[\text{---------}\]
\[SA_{\text{sphere}}=\int\limits_0^{2\pi}\int\limits_{ -\pi/2}^{\pi/2}\text dA\]
\[=\int\limits_0^{2\pi}\int\limits_{ -\pi/2}^{\pi/2}r^2\sin\theta\text d\theta \text d\phi\]\[=r^2\int\limits_0^{2\pi}\int\limits_{ -\pi/2}^{\pi/2}\sin\theta\text d\theta \text d\phi\]\[=2r^2\int\limits_0^{2\pi}\int\limits_{ 0}^{\pi/2}\sin\theta\text dr\text d\theta \text d\phi\]\[=2r^2\int\limits_0^{2\pi}\left.-\cos\theta \right|_{0}^{\pi/2}\text d\phi\]\[=2r^2\int\limits_0^{2\pi}-\left(\cos(\pi/2)-\cos(0)\right) \text d\phi\]\[=2r^2\int\limits_0^{2\pi} \text d\phi\]\[=2r^2\left.\phi \right|_0^{2\pi}\]\[=4\pi r^2\]

Answer 10

lol how do i view it... it has come up as code D:

Answer 11

if u wait the image will appear :)

Answer 12

You're still not getting my point. There aren't just some 20-30 formulas that are "the circle formulas." Circles are studied in a broad array of mathematical disciplines. Look at this article:
http://en.wikipedia.org/wiki/List_of_circle_topics