Euclids Algorithm, Herons Algorithm, and
the Estimation of Pi
Mark Moore, Allison Kyte, and Heather
Excel Project Summary
We used Excel in an attempt to help students grasp
a better understanding of Euclids Algorithm, Herons
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
The Excel file is available from Euclid's
Versions are also available.
Please note that Excel or the Excel Viewer are
required to view any Excel file (Excel viewer should be available
- Become more familiar with
Euclid's Algorithm by programming the algorithm into an Excel
- Introduce a method of calculating the greatest
- Gain an understanding of the
"IF" command in Excel.
- Become more adept at using
Excel, in general.
- 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
- Gain a better understanding of
how to use Excel as a way to manipulate recursive
Approximation of pi
- Answer the question, "What IS
- Learn the "meaning of
- Understand how pi is
related to the unit circle and how we find a value for
- 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
detailed description of our experiences with Excel.