A fun one involving 3 dimensions, two circles, and right triangles.
I could use some help here. I have tried to figure this out on my own but my math is just too rusty. I believe it will require trig using both right triangles and the unit circle. I am trying to make a spreadsheet that will do this for me automatically, but if you can show me how to set up the formulas for my own calculation I can get it into the spreadsheet myself.
The setup goes like this. Imagine two discs (circles) with the same radius (r) placed on top of each other at a given distance apart (d). The top circle has 7 evenly spaced points along the circumference. (1 point every 360/7 degrees).
The second circle has 6 points on it evenly spaced along the perimeter (1 point every 360/6 degrees). The difference is at the points on this one, there is a right triangle reaching into the z plane for (o) distance from the bottom circle and (a) length along the circumference of the bottom circle. These triangles will extrude towards the top circle. Note: the triangles do not necessarily span the length of the angle (IE, there can be a gap between triangles). The triangle is curved so if you were to straighten the circle into a straght line with the triangles coming off it, they would still look like perfect right triangles.
I need to find the distances from the 7 points of the top circle to the closest surface of the object in the bottom circle (be it a triangle or the circle itself).
The givens are...
The radius of the circles (which are the same)
The distance between each circle
The height of the right triangle
The length of the right triangle
7 points on the top circle evenly spaced
6 triangles on the bottom circle evenly spaced
If I left a variable out, or if you need me to explain more so you can understand what I am looking for, PLEASE ask. :) Thanks.
It is a fun problem for me, just too many variables for my mind to wrap around at the moment.