How to Find the Geometric Mean in a Regular Pentagram

The geometric mean is like an arithmetic mean, but logarithmic instead.

The geometric mean is a measure of central tendency or average. Just as an arithmetic mean is found by calculating the sum of n numbers and dividing by n, a geometric mean is found by calculating the product of n numbers and taking the nth root of the product. It is used to find the compound annual growth rates in investments, in comparing change in social statistics and even in the aspect ratio of your television set.

Things You'll Need

• Ruler
• Graphing calculator

Instructions

1. Measure the sides of the pentagram with a ruler and record the numbers on a sheet of paper. For example, write 3,3,3,3,3,5,5,5,5,5.

2. Multiply the values of each side of the pentagram with a calculator. For example, 3 * 3 * 3 * 3 * 3 * 5 * 5 * 5 * 5 * 5 = 759,375.

3. Take the 10th root, because a pentagram has 10 sides, of the product to find the geometric mean. On a graphing calculator, input "10," press the "Square Root" button, input "759375" and press the "=" button. Your result will be 3.87.

References

• Children's Mercy Hospital: Geometric Mean
• University of Toronto: Applications of the Geometric Mean
• Buzzards Bay; Geometric Mean; Dr. Joe Costa
• Easy Calculation: Geometric Mean