Euclid’s Algorithm, Heron’s Algorithm, and the Estimation of Pi

We used Excel in an attempt to help students grasp a better understanding of Euclid’s Algorithm, Heron’s Algorithm, and the Estimation of pi.

Our group designed three Excel worksheets:  one which uses Euclid's Algorithm to find the greatest common divisor (gcd) of two numbers, one which uses Heron's Algorithm to approximate the square root of a number, and one which approximates the value of pi.

The Excel file is available from Euclid's Algorithm, etc.
Additional Versions are also available.
Please note that Excel or the Excel Viewer are required to view any Excel file (Excel viewer should be available from Microsoft).

Euclid's Algorithm-Goals

• Become more familiar with Euclid's Algorithm by programming the algorithm into an Excel spreadsheet.
• Introduce a method of calculating the greatest common divisor.
• Gain an understanding of the "IF" command in Excel.
• Become more adept at using Excel, in general.

Heron's Algorithm-Goals

• Allows students to see how Heron's Algorithm, a recursion algorithm, converges to a square root, regardless of the starting value.
• Recognize a way to approximate square roots with some ease and a high degree of precision.
• Gain a better understanding of how to use Excel as a way to manipulate recursive functions.

Approximation of pi

• Answer the question, "What IS pi?"
  • Learn the "meaning of pi."
  • Understand how pi is related to the unit circle and how we find a value for pi.
• Understand how pi was calculated by inscribing regular polygons in the unit circle and circumscribing regular polygons about the unit circle.

Instructions for using the Excel worksheets are provided within the spreadsheet itself. 

A More detailed description of our experiences with Excel.