Circle segment

[Rotenurrov]

I know the maximum area of the circle segment that I can have in the following formula: A= 0.5*r^2*(v-sin(v)). I have forgotten how to break out v to get the angle. Help is appreciated.

 

[Rotenurrov]

I solved this by iteration but there has to be a more a more elegant way of doing this (since the only unknown variable i v)?

 

[pka]

I solved this by iteration but there has to be a more a more elegant way of doing this (since the only unknown variable i v)?

Here is the standard material on circular segments. Look at formulas $14-#18.

Are you using the vocabulary correctly?

 

[Rotenurrov]

Here is the standard material on circular segments. Look at formulas $14-#18.

Are you using the vocabulary correctly?

It could be that I'm stupid, but whenever you have a forumla with only one unknown variable; shouldn't you be able to rework the equation so that you have the unknown on the left side of the equal sign and then just plug in the values in the equation to get an answer? In the forumla I wrote above, A and R are known. I just don't know how to "break out" the v when it's presented like this; v-sin(v). If it was v-vx I would get v(1-x) and then devide by (1-x) so to speak. I'm laughing to myself at how stupid this must sound to someone who actually knows math .

 

[Ishuda]

It could be that I'm stupid, but whenever you have a forumla with only one unknown variable; shouldn't you be able to rework the equation so that you have the unknown on the left side of the equal sign and then just plug in the values in the equation to get an answer? In the forumla I wrote above, A and R are known. I just don't know how to "break out" the v when it's presented like this; v-sin(v). If it was v-vx I would get v(1-x) and then devide by (1-x) so to speak. I'm laughing to myself at how stupid this must sound to someone who actually knows math .

What you are talking about is called closed form solutions. Closed form solutions do not exist for all problems. For example the simple looking equation
x⁵ − x + 1 = 0.
is considered to have no closed form solution using elementary functions [+, -, *, /, log, exponential, power, root, etc.], see
http://en.wikipedia.org/wiki/Closed-form_expression