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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:BROWN UNIVERSITY IN PROVIDENCE IN THE STATE OF RHODE ISLAND AND PROVIDENCE PLANTATIONS
Doing Business As Name:Brown University
PD/PI:
  • Richard Schwartz
  • (401) 863-1135
  • res@math.brown.edu
Award Date:05/04/2021
Estimated Total Award Amount: $ 352,324
Funds Obligated to Date: $ 93,050
  • FY 2021=$93,050
Start Date:07/01/2021
End Date:06/30/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Geometric optimization and polygonal geometry
Federal Award ID Number:2102802
DUNS ID:001785542
Parent DUNS ID:001785542
Program:GEOMETRIC ANALYSIS
Program Officer:
  • Krishnan Shankar
  • (703) 292-4703
  • kshankar@nsf.gov

Awardee Location

Street:BOX 1929
City:Providence
State:RI
ZIP:02912-9002
County:Providence
Country:US
Awardee Cong. District:01

Primary Place of Performance

Organization Name:Brown University
Street:151 Thayer Street
City:Providence
State:RI
ZIP:02912-9002
County:Providence
Country:US
Cong. District:01

Abstract at Time of Award

This project involves the use of computer experimentation and graphical user interfaces to study simple but unsolved geometric problems. The PI is currently studying the paths taken by a superball as it bounces around the inside of a tetrahedral shaped room. The project will use computer experimentation to figure out how the patterns change as the room gradually changes shape. As another example, the PI is studying how bugs will crawl around the surface of a dodecahedron in order to move as far away from each other as possible. These simply defined problems exhibit a fascinating and sometimes unexpected complexity. These types of problems fall under the general rubric of geometric optimization and polygonal geometry. The project also involves training and mentoring of students, as well as dissemination via outreach and the creation of applets and computer programs to aid geometric visualization. In this project the PI will work on questions in geometry and dynamics which fall into two categories: geometric optimization and polygon geometry. The three main optimization topics that will be studied in this project are point configurations, paper Moebius bands, and the Lie group Sol. The three main polygon problems that will be investigated are polygonal outer billiards, symplectic polygonal billiards, and inscribed triangles and rectangles. Additionally, the PI plans to continue writing graphical user interfaces which help with research for the project, and the PI also plans to continue to write and illustrate children's math books. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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