||General Inverses in 2-D, 3-D, applications inspired by Technology
||Wei-Chi YANG and Min-Lin LO
We first generalize the concept of inverse images with respect to the line y = x to the inverse images with respect to y = mx + b, and we extend the idea to three dimensions. Next, we find the reflection of a point on curve C1 with respect to a moving point P on C2: We find the locus of the point P; which links to the concept of orthotomic and caustic curves. The concepts can be extended to the corresponding ones in 3-D. It is interesting to see how technological tools have prompted us to relate Mathematics to similar concepts used in Physics.