**Parametric Potluck**

**Connecting Religion with Multivariable Calculus**

**For our project, we modeled a paper airplane moving through space using Mathematica's planes and polygons features. We also used parametric equations to create spheres to model planets surrounding the plane. **

**Using Mathematica, we compiled parabolas, spheres, and cylindrical shapes to create a bouquet with a rose, daisy, and bluebonnet. **

**For our project, we used Mathematica to create 3D shapes that model the Kazakh Yurt and the Siheyuan. **

**In our project, we used Mathematica to create a 3-D taro bubble tea that required 52 functions in total.**

**Slide content**

**For this project, I visualized the basic shape and form of the galaxy M74 using Mathematica. I used ContourPlot and Plot3D to capture these elements. **

**Our project used Mathematica to draw spirographs, a geometric drawing that creates mathematical curves called hypotrochoids and epitrochoids. **

**For our final project, we wanted to find the steepest route out of Park Science Building on Bryn Mawr's campus. To do this, we created a contour map using online software and Microsoft Excel. **

**For my project, I utilized Mathematica and Lagrange Multipliers to graph economic indifference curves. These curves are utility functions that mathematically map consumer preferences. **

**My project displays a variety of parametric 3D plot shapes modeled after candies using Mathematica. **

**Our poster has two manga demonstrating concepts and applications of calculus. The first manga demonstrates the conversion of cartesian to polar coordinates, while the second shows an application of gradient. **

**My project explains the history behind the contour plot and its applications. For this, I used Contourplot and Contourplot3D in Mathematica to illustrate multiple examples. **

**Our passion for music inspired us to visualize the patterns created when an oscillator is used with a loud speaker. For this, we used the Sound Lissajous Meter, Desmos and our vocalization and observed patterns from three notes. **

**Our project uses Mathematica to graph the three main parts of the brain. We then computed its volume and color coded the sections. **

**The application ofthe dot product in genetics for determining closeness of genetic relationships**

**We mapped the steepest and least steep paths up two fourteeners (hikes that have a peak about 14,000 feet) using contour maps found on Alltrails to find the average directional derivative and the average gradient.**

**This poster displays a tumbler ready for coffee to be added, complete with a lid, a straw, and ice cubes.**

**Mathematica model of a French press using parametric equations. **

**For this project, we investigated how we perceive the shapes around us and how mathematics helps us define them further. We made a 3D model of the studio ghibli character Totoro using the Mathematica function of ellipsoids. We also made his umbrella.**

**Using the program Mathematica, and what we learned in class about 3-dimensional modeling, we created equations that represented the components of an ice cream cone. These equations were then coded together to create the final ice cream cone.**

**Happy Valentine’s Day – How to draw roses and hearts in Mathematica**

**We have researched the “healing properties” of sound waves at 528, 432, and 320 Hz and created representations of these sound waves in 3D in Mathematica, as well as animations and sound files that live spectators can enjoy.**

**This poster looks at the equations that are theorized to be able to predict the patterns that form in nature based on the interaction between two chemical "morphogens," an activator and an inhibitor.**

**Mike the Bike---Mathematica bicycle created by the power of calculus**

**This poster showcases different types of electric fields based on the source charge. Because electric fields are vector fields, they can be graphed by Mathematica.**

**Modeling famous architectures in China using Mathematica. **

**Using Mathematica to graph Naturally Occurring Shapes.**

**The poster presents the magnetic field caused by interactions between parallel wires.**

**In our poster, we investigated the torus/bagel shape by using Mathematica and parametric equations.**

**When thinking about where your next meal comes from, always remember, math is everywhere. **

**Our poster shows how many languages are spoken in various countries around the world.**

**We created a 3D-model of two components of the International Space Station using the ParametricPlot3D and Graphics3D functions in Mathematica.**

**We used parametric equations in Mathematica to graph different pasta shapes.**

**My project was graphing Snoopy on his little red cabin, as well as using some other skills we learned in class to graph spirographs and other shapes. **

**This project aimed to show how the work on an object can be calculated using the dot product of the net force and displacement vectors by using a real-world example of balls being rolled down slides.**

**We used Mathematica the model the shape of a Pringle and calculate the volume of the Pringles in the container. **

We included some extra research about what genes are and how the dot product interacts. The dot product is very commonly used to determine genetic closeness and is helpful for predicting drug effects by testing them on closely related animals. The smaller the angle, the more closely related the two populations are. Due to the nature of randomly choosing four genes to do our calculations with, our data is not going to be as accurate as using more or all of the genes we found on the website. For example, our most closely related populations were white caucasian and Native American racial groups. This could have happened because the genes were not representative of the populations or because the racial groups were self-reported, and someone who is culturally one ethnicity isn’t necessarily genetically that ethnicity.

]]>We then decided to compute our model’s volume. Using integration, we derived formulas for each section’s volume. We then computed the volume of the brain using Mathematica. We then colored and labeled the model.

]]>Using Desmos, we began by plotting a basic parametric equation to create a similar shape to the curve that we got from the software. Then we adjusted the equations and the values of each variable to get closer to the shape of the curve. Each variable has different effects on the appearance of the final curve. Once we fit equations to the curves, we merged them onto one graph. Their overlap allows us to visualize our harmony.

]]>Next, I wanted to look into how we utilize contour lines in everyday math and science. Today, we use contour lines for visualizing ocean terrain, tracking temperature, salinity, and acidity, and environmental polluters. Contour lines are also used in solar sciences to show travel time, cost, and routes.

]]>The second manga focuses on the concept and real-world application of gradient. We picture a scenario where two people are trying to find the shortest route to reach a certain altitude. We humanize the coordinate (x,y,z) to introduce the concept of gradient in order to “tell” the two people the way they should be heading toward is where the gradient vector points to. The contour map models the mountain using the function *m(x)*, and it visualizes and identifies the group’s location in xy-coordination, and with every contour line marking the points that share the same altitudes (Panel 5). In order to calculate and find the exact direction of gradient and understand which way to go, we have to bring in the concept of partial derivatives of m(x,y) (Panel 8). As pointed out in Panel 11, in the real world, the direction of the steepest ascent may be the most time-saving route, but also causes risks in activities such as mountain climbing. After the “lecture” from X, Y, and Z, the two tourists thanked them and waved goodbye before going on their way, concluding the comic.