Generate 2D Math Objects by Collapsing 3D Math Objects

I had some excellent high school mathematics instructors. They both loved their field and took an interest in their students. Since high school, I have had a deep interest in collapsing 3D mathematical equations to derive equations for 2D mathematical objects or modifying 2D objects into other 2D, or 2D objects into 1D. A 3D sphere becomes a 2D circle. A 2D parabola becomes a 1D line. The 2D hyperbola shown, if collapsed along the x-axis, becomes two 1D line segments stretching at one end to infinity. The same hyperbola collapsed along the y-axis becomes a complete line. A 2D circle becomes a single 1D line segment of a length equal to the diameter. An Example of Collapsing 3D into 2D What can be obtained by collapsing 3D math objects…

Mathematical Equation for a Cone

You go to the mall and request a double scoop of Rocky Road ice cream. The fellow serving says "Yes," and then he asks you asks if you would like that on a wafer or a sugar cone? Since most have eaten ice cream since childhood (unless we are dairy or otherwise intolerant), the majority of people think of a simple v-shape hollow structure as a cone. It has a top. It has a bottom. But is this the kind of geometrical shape that mathematicians think of when they refer to deriving the mathematical equation of a cone? A Mathematics Cone The cone of the mathematician bears some resemblance to that, but there are differences. The figure included with this article demonstrates that there are two v-shaped portions, not one.…