A circle is a set of points equidistant from a Center Point called the radius.
Polar coordinates in two dimensions were made for circles. Find the distance between the radius and one of the points of the circle, and that value is ‘r’.
After that, stipulate that the angle theta must be zero degrees or higher, up to but not including 360 degrees.
However, we like Cartesian space with ‘x’ and ‘y’ because vector addition is so easy in Cartesian space.
The circle with a radius of ‘r’ consists of all the points for which
For something simple like a+b=c, it is obvious that after the values for two of the variables are known, the other one is locked into some calculation.
The same is true for x,y and r. We can solve for y:
From the above equation, it should make sense that x can equal r but it can never be greater than r.
Appendix
We could have a math problem we want the X and Y values of a particular Circle to be the independent variables for something. In this situation we call the circle a manifold.
A circle is a one dimensional manifold embedded in two dimensions. Think of a circle as being a line that’s been twisted around and brought together to touch itself. Likewise a sphere (all points in three dimensions a distance r from the origin) is a plane.
Vectoreverything 