Self-assembly is the process during which a collection of relatively simple components, starting in a disorganized state, autonomously combine into a more complex structure. During self-assembly, there is no external guidance or direction, and the self-assembling components experience only local interactions and typically obey a simple set of rules that govern how they combine. We…Continue Reading Using Computation to Self-Assemble Patterns
Are you a fan of the game SET? Are you a master? Have you never, ever, ever played it before? Great! Come learn about this amazing math game and try your hand at beating our SET masters! Additional Resources: A website where you can play SET against human or AI players: https://playset.netlify.app/ A website with…Continue Reading The Game of SET
How many colors do you need to color a map so that no two adjacent regions are colored the same? It turns out that no matter how complicated the map is, you only ever need four! Come try your hand at 4-coloring! Videos: A YouTube video from Numberphile about the Four Color Theorem: https://www.youtube.com/watch?v=NgbK43jB4rQ Additional…Continue Reading The Four Color Theorem
This sculpture by Shalese Fitzgerald demonstrates the “ruling” of the hyperbolic paraboloid by lines. You can find other works by Fitz on instagram at @SFitzgerald_Art https://www.instagram.com/SFitzgerald_Art/ Additional Resources: An article describing how to create your own hyperbolic paraboloid: https://mathcraft.wonderhowto.com/how-to/make-hyperbolic-paraboloid-using-skewers-0131751/ An demonstration of hyperbolic paraboloids as ruled surfaces: https://demonstrations.wolfram.com/HyperbolicParaboloidAsARuledSurface/ A Wikipedia article about ruled surfaces: https://en.wikipedia.org/wiki/Ruled_surface…Continue Reading Ruled Hyperbolic Paraboloid
Given a needle (or stick), what is the smallest area shape that we need to rotate the needle 360 degrees? We will look at this problem from the perspective of several different shapes, we will start with a circle and slowly shave off parts of the shape to see that we can get smaller and…Continue Reading Kakeya Needle Problem
Before Google, search engines didn’t have a great way to rank their results in order of importance. Instead most of them just found every single website containing your search terms and listed them in an arbitrary order. As you can imagine, this was not very user friendly. Search results were jammed full of insignificant and…Continue Reading Google’s First Great Idea: PageRank
Parabolas, circles, and hyperbolas may look vastly different on a graph, but there is a way to paint these pictures on a ball such that they all turn into circles? It turns out that all quadratic curves turn into circles, and we can see this by copying a graph onto a balloon. What happens to…Continue Reading Projective Geometry of Elliptic and Quadratic Curves
Experience mind bending hyperbolic geometry through virtual reality and craft activities. Come prepared to test your limits on reality with Hyperbolica, a virtual reality puzzle adventure game that visualizes what hyperbolic space is and how it can be interacted with. Then we will create a fun model of the hyperbolic plane to remember your time…Continue Reading Experiencing Hyperbolic Geometry
Platonic Solids are 3D shapes that: have faces identical in shape and size have the same number of faces meeting at each vertex, and are convex. How many such solids do you think meet these criteria? Surprisingly, there are precisely 5 and you can easily make them at home. With a hands-on approach through construction…Continue Reading Platonic Solids
Using everyday items and liquids that can be found at the local grocery store we can investigate complex fluid flows and fluid mixing that is important to many areas of science. With hands-on experimentation we observe the interaction of mixing fluids of varying density. Videos: Floating and Falling Flows: https://youtu.be/9IFwZu6xQrM?si=hZKM1-B2bX47FDf- Kelvin-Helmholtz Instability: https://youtu.be/qgamfo86FQo?si=JnB3s4LKlXQNTafi What is…Continue Reading Mixing Fluids