Physics in the Mathematics Curriculum Summary

Tuesday, July 9, 2002

Area of Unusual Shapes via Uniform Density of Paper

Cut out some irregular shape form card stock paper. Cut out a square from the same paper; this becomes the unit of area measurement.
Weigh the unit square on an electronic balance.
Weigh the irregular shape.
Calculate the area of the irregular shape in terms of the unit circle.


Why do we measure area in unite squares? Unit triangles? Unit hexagons? Why wouldnÕt unit circles be practical for unit area measurement?

At this point, we have explored with the following activities:

  • Beans in the classroom
  • Blowgun
  • Bouncing Ball
  • Magnetic Field Deflection
  • Singing Tubes
  • Addition of Vector Force
  • Temperature Conversion
  • Area of Irregular Shapes

Format of Web Site Activities

  • Use links for extensions, background, other web sites, etc. to keep format clean and brief.
  • Notes to the teacher: what to do so the activity works, misconception
  • Equipment list
  • Objective (mathematics/physics)
  • Setup (photos)
  • Time required
  • Procedure
  • Extensions

Home page of Physics and Math Website

  • Mission statement
  • Activity Matrix

Here is an example of Microsoft Word with embedded mathematics expressions through its equation editor. The first equation is: (missing graphic) Now we try another (missing graphic).

Mathematics through Physics Activities


Objective (include mathematics and physics concepts addressed)


Setup (include photos and/or diagrams)

Procedure (include time required)


Notes to the Teacher (include hints in setup, safety concerns, student misconceptions to watch for, background information on physics, etc.)

Use hyperlinks where possible to keep presentation clean and brief.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.