Our poster displays the iconic sculpture Balloon Dog by Jeff Koons juxtaposed against our group’s interpretation of the piece. The poster outlines details about Koons, his art, the original Balloon Dog sculpture, and our process of recreating it.
My poster used Mathematica to model different flowers. I used hypotrochoid curves (like the Spirograph toy) to model a ranunculus and a peony, then illustrated them as flowers online.
Our poster models three different types of dumplings: Polish pierogies, Japanese gyoza, and Chinese xiaolongbao using Mathematica. Our primary focus involved manipulating surfaces created by functions of 3-variables including elliptical paraboloids, hyperbolic paraboloids, ellipsoids, logarithmic cones, and various trigonometric functions. Our calculations also included conversions in polar and spherical coordinates.
Our poster includes the six Mathematica models we created of each of the kinds of chess pieces needed for a full set. We additionally included the calculations for the models and a brief description of our methods.
We approximated the sizes of our heads using multivariable calculus to determine who has the larger head. We used shapes that we were familiar with integrating in the past in order to set up the integrals and models that appear on the poster.
For my project, I wanted to explore the trefoil knot. I found different ways to represent it in Mathematica, and researched the history of its presence in Celtic art.
My poster is about partial differential equations and their applications. The graphs are about x, temperature, time, and the heat equation.
This project focuses on the mathematical theory behind spirographs. A spirograph kit was used to draw hypocycloids and then parametric equations were used to model these drawings in Mathematica.
This poster models the various curves of a string around a needle as you create a single crochet loop. There are four “snapshots” of the different curves and their corresponding parameterized equations.
This poster reviews the physics of the eyewalls of a hurricane and the importance of ocean temperature, as well as a hypothetical situation that practically applies flux in terms of a hurricane.
We explore the relationship between temperature, humidity, and productivity using partial derivatives and local linearization. By clearly defining variables T (temperature), H (humidity) and P (labor productivity), and means of multivariable calculus, we reveal the direct influence of temperature and humidity on efficiency of working in construction based on the local linearization as the useful tool to interpret non-linear functions and predict a way how temperature and humidity influences the working efficiency.
I created Rapunzel’s tower from Tangled using the shapes or surfaces that include cylinders, disks, cones, spheres, and even a hyperboloid of one sheet. Only a cone, cylinder, sphere, and hyperboloid of one sheet are displayed on the poster as they are the main surfaces that are used and seen at first glance.
We used equations in Mathematica to create 3D chairs, some based off of reference images, some not - just anything we thought would be comfortable to sit in!
The poster shows the connection between Mathematics and Economics in the field of Lagrange Multiplier. Lagrange Multiplier is used as an important mathematical tool in economic calculation such as profit maximization.
The project demonstrates electric field intensity – force allied on per unit charge – as a vector field. It also explores the meaning of differential or integrated calculation in the context of an electric field.