Update contact.md

Author: saramaloni

geolab/contact.md

@@ -8,12 +8,16 @@ permalink: /geolab/current_projects/
 
 ### Mentors for Spring 2025:
 
+- [Bakhyt Aitzhanova](https://math.virginia.edu/people/axh7cj/)
 - [Michael Wills](https://sites.google.com/view/michael-wills/)
+- [Brandon Shapiro](https://brandontshapiro.github.io/)
 
 ### Faculty Advisors:
 - [Evangelia Gazaki](https://sites.google.com/view/valiagazakihomepage/home)
 - [Sara Maloni](https://sites.google.com/view/sara-maloni)
+- [J. D. Quigley](https://sites.google.com/view/sara-maloni](https://quigleyjd.github.io/)
 
 ### Projects Spring 2025:
-1. **Compass and Straightedge Constructions** ([Evangelia Gazaki](https://sites.google.com/view/valiagazakihomepage/home), [Michael Wills](https://sites.google.com/view/michael-wills/))
-This project will examine compass and straightedge constructions in the plane. We will use these tools to carry out explicit constructions (bisecting an angle, drawing a regular hexagon) as mathematicians have been doing for over 2000 years. Even as more and more constructions were discovered, some (such as constructing a square with the same area as a given circle) remained elusive. This project will also examine the seemingly distant branch of math known as _Galois theory_, and how it was used in the 1800's to show the mathematical impossibility of these famous open problems.
+1. **Compass and Straightedge Constructions** ([Evangelia Gazaki](https://sites.google.com/view/valiagazakihomepage/home), [Michael Wills](https://sites.google.com/view/michael-wills/)): This project will examine compass and straightedge constructions in the plane. We will use these tools to carry out explicit constructions (bisecting an angle, drawing a regular hexagon) as mathematicians have been doing for over 2000 years. Even as more and more constructions were discovered, some (such as constructing a square with the same area as a given circle) remained elusive. This project will also examine the seemingly distant branch of math known as _Galois theory_, and how it was used in the 1800's to show the mathematical impossibility of these famous open problems.
+2. **Computer graphics and Robotics** ([Bakhyt Aitzhanova](https://math.virginia.edu/people/axh7cj/)): We will learn a standard method for solving the forward and inverse kinematic problems for a given robot “arm”. The forward kinematic problem is a fundamental concept in robotics and computer graphics that involves determining the position and orientation of the hand of a robot arm based on its joint parameters. Unlike forward kinematics, where the hand position is computed from known joint parameters, inverse kinematics works in reverse: given the hand position, we find the joint parameters. The inverse kinematic problem is more challenging because it often requires solving a system of non-linear polynomial equations.
+4. **Zome and polyhedra** ([Brandon Shapiro](https://brandontshapiro.github.io/)): The Zome toolkit makes it easy to build toy models of polyhedra, 3 dimensional solid shapes like cubes and pyramids built out of polygons on the outside. Using the Zome pieces, we can show why there are only 5 polyhedra whose faces are all the same shape, and also why in the fourth dimension there are only 6 shapes with the same kind of property. We explored the geometry of shapes we can build using Zome, such as angles, counting faces of solid shapes, symmetries, knots, and/or many other possibilities.