Student Post: The Rabbit Hole of Graph Theory Terminology (Plus some Petersen Graphs)

My first ever exposure to any sort of graph theory was through this paper by Flapan, Mattman, Mellor, Naimi, and Nukkuni. If you've already clicked on the link, you might see how someone could get overwhelmed with terminology early on in the paper. Since I had no prior knowledge to graph theory, that person was me. …

A Student Post: An Interactive Application for (Inversive) Geometry Of Circles

Hello, For the past several months I have been working an interactive interface for the construction of inversive geometry of circles. Currently the working features are adding points, dragging points, and selecting three points to draw a disk. The past few weeks I was tasked with altering the code in order to implement a construction …

A Student Post: The Basic Mathematics of Quantum Computing

An Overview As discussed in the last post, the nature of superposition can be interpreted by the implementation of qubits. A qubit  can be interpreted as a matrix and mathematically applied to quantum gate transformations, thus allowing for the representation of quantum states. Qubit quantum state calculations can be represented using matrices and modeled by …

Student Post: The Basic Principles of Quantum Computing

What is Quantum Computing? The nature behind the implementation of quantum computers comes from the attempt to simulate and use principles of quantum mechanics to enhance computational run-time exponentially. Theoretically, any task given to a classical Turing machine can be completed with exponentially less computations on a quantum computer. In order to accomplish this, quantum …

Koebe-Lib Initial Release

The initial release of Koebe-Lib, our library for representing constructions in the inversive geometry of circles on the 2-sphere has just been uploaded to GitHub. Currently, the library contains one application, SphericalSketch, which allows a user to define and interact with geometrical objects on the 2-sphere using the python language. A screenshot of the interface …

Student Post: Variations in Size on General Petersen Graphs

Hello again! One more blog post dealing with Petersen Graphs. Last week we saw several examples of embeddings of Petersen graphs. Since one of the main goals behind creating those realizations is to 3D print them. As such, it is important that the dimensions of our embeddings are reasonable. In the previous embeddings, the graphs …