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‎geolab/index.md‎

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‎geolab/application.md‎ renamed to ‎mathexlab/application.md‎

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title: Apply Now
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<h2 class="mb-3">Apply Now</h2>

‎mathexlab/contact.md‎

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title: Contact
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---
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<h2 class="mb-3">Contact Information</h2>
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For questions about the Math Experimental Lab, please contact:
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[Sara Maloni](https://math.virginia.edu/people/sm4cw/)
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Associate Professor
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Department of Mathematics
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University of Virginia

‎geolab/contact.md‎ renamed to ‎mathexlab/current_projects.md‎

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title: Mentors and Faculty Advisors
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<h2 class="mb-3">Current mentors and projects</h2>
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### Projects Spring 2025:
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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.
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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.
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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 will explor the geometry of shapes we can build using Zome, such as angles, counting faces of solid shapes, symmetries, knots, and/or many other possibilities.
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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.
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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 will explor the geometry of shapes we can build using Zome, such as angles, counting faces of solid shapes, symmetries, knots, and/or many other possibilities.

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title: FAQ
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<h2 class="mb-3">Frequently Asked Questions</h2>
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+ Am I eligible to participate in the Geometry Lab?
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- Any undergraduate student can apply to participate. You do not need to be a math major, but you need to be curious and enthusiastic about exploring some new mathematical ideas and making real life models of these ideas in a chosen medium. There are projects at all levels. You do not need to have any specific prior mathematical background: you will learn it here! You can apply to participate <a href="{{site.url}}/geolab/application/">here</a>.
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+ Why should I apply to participate in the Geometry Lab?
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- Participation in the Geometry Lab is a great opportunity to learn some advanced math topics in a very experimental way, join a welcoming and inclusive community of people curious and enthusiastic about math, and get a little glimpse of what math research is about. You can apply to participate <a href="{{site.url}}/geolab/application/">here</a>.
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+ Am I eligible to participate in the Math Experimental Lab?
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- Any undergraduate student can apply to participate. You do not need to be a math major, but you need to be curious and enthusiastic about exploring some new mathematical ideas and making real life models of these ideas in a chosen medium. There are projects at all levels. You do not need to have any specific prior mathematical background: you will learn it here! You can apply to participate <a href="{{site.url}}/mathexlab/application/">here</a>.
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+ Why should I apply to participate in the Math Experimental Lab?
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- Participation in the Math Experimental Lab is a great opportunity to learn some advanced math topics in a very experimental way, join a welcoming and inclusive community of people curious and enthusiastic about math, and get a little glimpse of what math research is about. You can apply to participate <a href="{{site.url}}/mathexlab/application/">here</a>.
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+ What kinds of things will I learn about?
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- Generally speaking, the projects will explore geometric concepts beyond what one might see in traditional lower-level math courses. (But note that you do not need any specific mathematical background to participate!) See <a href="{{site.url}}/geolab/projects/">past projects</a> for examples of projects we have run in the past.
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+ How is the Geometry Lab structured? How will the groups be assigned?
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- Generally speaking, the projects will explore geometric concepts beyond what one might see in traditional lower-level math courses. (But note that you do not need any specific mathematical background to participate!) See <a href="{{site.url}}/mathexlab/projects/">past projects</a> for examples of projects we have run in the past.
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+ How is the Math Experimental Lab structured? How will the groups be assigned?
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- Each group will consist of two graduate student or postdoc mentors, and roughly three to five undergraduate students. When filling out the registration form, you will be asked to rank which groups you would most like to join. We will try our best to sort everyone into one of their top-ranked groups, depending on scheduling constraints.
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+ What is the time commitment to participate in the Geometry Lab?
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+ What is the time commitment to participate in the Math Experimental Lab?
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- Students will meet in groups with their project mentors for 1.5 hours per semester, and are expected to spend about 2 hours each week working on their own and preparing for the group meetings. Each student will be asked to create a “blog” where they can share their progress, things they did, where they are stuck, etc. There will also be three common meetings between all groups throughout the semester where students from all the groups will meet, discuss their project and learn about other projects, and improve in other related important skills.
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+ What will happen during group meetings?
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- Each weekly 1.5 hour meeting will consist of a mix of mini lectures from the mentors introducing new mathematical concepts, discussion amongst students about what they explored in the past week, further hands-on exploration as a group, and possibly more! The meetings will be guided by the questions and interests of the students, and are meant to operate more like a hands-on lab than a traditional classroom experience.
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+ Can I get course credit? Do I have to get course credit?
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- Yes, students will sign up for one course credit. Generally this is mandatory, although it may be possible to make exceptions in special cases. Please <a href="{{site.url}}/geolab/contact/">contact us</a>.
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- Yes, students will sign up for one course credit. Generally this is mandatory, although it may be possible to make exceptions in special cases. Please <a href="{{site.url}}/mathexlab/contact/">contact us</a>.
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For current participants:
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+ Where can my team present the results of our project?

‎mathexlab/index.md‎

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---
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title: Math Experimental Lab
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nav_parent: Undergraduate
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---
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<img src="{{site.url}}/mathexlab/images/Group3.jpeg" class="centerImage" style="cermax-width:100%;max-height:300px;height:auto;width:auto" class="mb-3" alt="Group Math Experimental Lab">
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<h2 class="mb-3">Math Experimental Lab</h2>
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The Math Experimental Lab is a mentoring and research opportunity for students interested in experiencing Mathematics in a more hands-on way. Undergraduate students are paired with graduate students or postdocs for a semester-long project. See the <a href="{{site.url}}/mathexlab/projects/">projects page</a> for examples of projects which have run in the past. During the semesters there are various opportunities for the different groups to interact and for presenting the ideas behind the project to a wider community, like high school students from the <a href="https://www.virginiaequitycenter.org/starr-hill-pathways">Starr Hill Pathways</a> program, other undergraduate students from the <a href="{{site.url}}/awm/">AWM Student Chapter</a> or <a href="{{site.url}}/undergraduate/mathclub_redirect/">Math Club</a>, and also the Charlottesville community at the local Farmers Market. The mentors suggest general projects or media to use, but the details of the work will be decided together with the students.
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This program allows students to learn and understand subjects not usually covered in the classes currently offered by the department. In addition, the students learn how to use hands-on activities to learn how to ask questions and start answering those questions which is exactly what research in mathematics is about, so for students interested in pursuing undergraduate research this is a great first step, together with the <a href="{{site.url}}/drp/">Directed Reading Program</a>. This program is also a great way to see if a math major is right for you.
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**Current projects**: Click <a href="{{site.url}}/mathexlab/current_projects/">here</a>
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<h2 class="mb-3">Requirements</h2>
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The students are required to meet with their group and their mentor(s) once a week for an hour and a half to discuss their progress and plan for future work. Additionally, two hours of independent work are required each week. We will also have monthly common meetings (three total) between the different groups. You can see the <a href="{{site.url}}/mathexlab/schedule/">schedule</a> for a more detailed discussion of the type of meetings, where students will have the opportunity to discuss their project with other students and wider communities.
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<h2 class="mb-3">Apply</h2>
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Applications to participate in the Math Experimental Lab open at the start of each semester. Click <a href="{{site.url}}/mathexlab/application/">here</a> for more information about applying.
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<h2 class="mb-3">Got Questions?</h2>
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See the <a href="{{site.url}}/mathexlab/faq/">FAQ page</a> for more details about the lab. If your question is not answered there, please feel free to contact [Sara Maloni](https://math.virginia.edu/people/sm4cw/).
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<h2 class="mb-3">Other experimental labs</h2>
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* [https://geometrylabs.net/](https://geometrylabs.net/)
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<img src="{{site.url}}/mathexlab/images/Group2.JPG" class="centerImage" style="cermax-width:100%;max-height:300px;height:auto;width:auto" class="mb-3" alt="Group2 Math Experimental Lab">

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<h2 class="mb-3">Schedule</h2>

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