## Jane Bright Final Project

For our final project we made something that went along with our interests or our major, and was something that could be useful. As a physics and math double major, I decided to create something based off of my math methods for physical systems class with Dr. Tehver. One of the useful tools we learned in that class was how to use different coordinate systems. In 3D space, we usually refer to the position of a point by its x, y, and z coordinates, which is the standard Cartesian system. When trying to do things like integrate over the volume of a sphere, it can be much simpler to work in a different system of coordinates. We worked in three different alternate coordinate systems in the class: polar, cylindrical, and spherical. I found spherical to be the hardest to visualize based off of two dimensional board drawings, so for my project I decided to make a 3D representation of a spherical coordinate system. The coordinates to a point are r, ϕ, and θ . r is the length of a vector extending from the origin to the given point, θ is the angle between that vector and the z axis, and ϕ is the angle between the projection of the vector on the xy-plane (or r sin θ) and the x axis. I created a model with a vector that could rotate through the full rang of θ angles, which is half a circle or π radians, and made it so you can create a shadow of the vector as the projection on the xy-plane that could rotate through the full range of ϕ angles, which is a full circle or 2π radians.