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
Pick’s Theorem
Math Circles: MTC Network
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.
Activity Guide
This guide looks at the activity in detail and goes into the underlying math.
Digital App
Online geoboard from MathLearningCenter.org
