I need help with a Math problem

[Danjen]

Okay, so what I'm trying to do is have three dots that can rotate on a circle, with a line drawn between them, forming a triangle inside the circle. What I need to figure out is a formula for calculating the percent of the circle that the triangle takes up. So like, when the points are at any given position on the circle, the formed triangle will take up X% of that circle.

[ericfourfour]

Area of triangle / Area of Circle * 100

To calculate the area of a triangle the formula (I think) is:

code:

Area of Triangle = abs (x1 * y3 + x2 * y1 + x3 * y2 - x3 * y1 - x1 * y2 - x2 * y3)

[BenLi]

ever heard of (down product - up product) divided by 2?

[BenLi]

btw, that works for any polygon in which any point can be connected to any other point with an uninterrupted line.

[neufelni]

The Formula for area of a triangle is A = (b * h) / 2.
So in Turing that would be:

code:

area := (x2 - x1) * (y3 - y2) / 2

And the area of a circle is A = pi r ** 2.

And then you just use the formula ericfourfour gave:
Area of triangle / Area of Circle * 100

[ericfourfour]

Nick try using that formula with this triangle:

code:

A(0, 0), B(10, 5), C (5, 10)

[BenLi]

Okay, if you use the (abs(down product - up product)) divided by 2, you don't have to find the height and the base and stuff

[Danjen]

Ok, that works. But what's with down product and up product?

[BenLi]

its hard to explain but in a nutshell:

1. List numbers on the polygon in a counterclockwise fashion repeating one point
2. Downproduct is the sum of all the numbers in the first column multiplied by those in the second column one row down.
3. Upproduct is the sum of all the numbers in the first column multiplied by those in the second column one row up.
4. Follow the formula abs(dp - up) / 2

Note: the abs is just an extra, done properly, you could omit the abs.

[Danjen]

Well you explained it in a coherent manner, so I'm pretty sure I get it .