The typical shape of a bagel is fairly recognizable as a doughy-looking circle with a hole straight through the middle. Although the shape is fairly simple, it is interesting when graphed with parametric equations. The formula for graphing a bagel shape, also known as a torus is: ParametricPlot3D[{Cos[x] (2 + Cos[y]), Sin[x] (2 + Cos[y]), Sin[y]}, {x, 0, 2 \[Pi]}, {y, 0, 2 \[Pi]}] which might seem daunting at first glance. A torus is defined as the area between a larger outer circle and a small inner circle which both are centered at the same point, which explains the bounds of y and x being from 0 to 2Pi. Additionally, the center circle includes the points which make up the circles that move around the inner circle to create the bagel shape.
Besides the equation for graphing, we investigated the history of the torus and its real life application. We found that it dates back to an ancient Greek mathematician, Pappus of Alexandria who formulated a theory about calculating the surface of a torus. In terms of real life application, the torus can be seen as the popular breakfast foods of a bagel and donut but also in the popular toy called a fidget spinner which represents a triple torus.
