Archimedes and Pi

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

Summary

In this Spreadsheets across the Curriculum activity, students explore the history and physical basis of the mathematical constant, pi. Using Excel, they follow the same steps that Archimedes took to determine the ratio of a circle's circumference to its diameter, including estimation of square root values and the iterative process of cascading right triangles. Finally, students build spreadsheets that allow them to approximate pi using circumscribed polygons.

Learning Goals

Students will:
• use Excel to estimate the square root of 3 using an iterative process.
• use logic functions in Excel to classify results.
• create a spreadsheet to approximate pi using a circumscribed polygon approach.
In the process students will:
• understand of the physical basis of pi.
• understand ratios and proportions.
• gain experience with estimation and iteration.
• reinforce their knowledge of basic geometry concepts, specifically the Pythagorean Theorem.

Context for Use

This module was created for use in a History of Mathematics for Teachers course.

Description and Teaching Materials

SSAC2005.QA21.EG1.1_Student Version (PowerPoint 214kB Aug2 07)
This module is a PowerPoint presentation with embedded spreadsheets. If the embedded spreadsheets are not visible, save the PowerPoint file to a disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.

Teaching Notes and Tips

The module is intended for use as a stand-alone resource. It can be used as a lab exercise or homework assignment, or as the basis of an interactive classroom activity.

Assessment

The last slide contains an end-of-module assignment that can be used to examine student understanding and learning gains.