Skip to content # Pick’s Theorem

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

## Digital App

# Online geoboard from MathLearningCenter.org

## More Resources

# J. E. Reeve, On the Volume of Lattice Polyhedra, Proceedings of the London Mathematical Society, s37(1):378395

# Pick, Georg (1899). Geometrisches zur Zahlenlehre. Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines fr Bhmen ”Lotos” in Prag. (Neue Folge) 19: 311-319

Johnston, Aimee. Sabloff, Joshua. (2022). Pick’s Theorem. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/picks-theorem

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter pegs, and the number of interior pegs.
This session is also suitable for student circles or the classroom.

MP1 - Make sense of problems and persevere in solving them.

MP2 - Reason abstractly and quantitatively.

MP3 - Construct viable arguments and critique others' reasoning.

MP4 - Model with mathematics.

MP5 - Use appropriate tools strategically.

MP6 - Attend to precision.

MP7 - Look for and make use of structure.

MP8 - Look for and express regularity in repeated reasoning.

MP2 - Reason abstractly and quantitatively.

MP3 - Construct viable arguments and critique others' reasoning.

MP4 - Model with mathematics.

MP5 - Use appropriate tools strategically.

MP6 - Attend to precision.

MP7 - Look for and make use of structure.

MP8 - Look for and express regularity in repeated reasoning.