Fibonacci Numbers and the Golden Ratio Girls in Engineering, Math, and STEM – February 2015

Florida Gulf Coast University

You and the Golden Ratio:

Body Measure Length in centimeters

Height of Body (B)

Height of Navel (N)

Top of Head to Tip of Finger (F)

Length of Arm (A)

Length from Fingertip to Elbow (E)

Use your calculator to compute these ratios in decimal form:

Navel Ratio: B/N =

Finger Ratio: B/F =

Arm Ratio: A/E =

!

Heigh

t!of!Body!

Heigh

t!of!Navel!

Top!of!Head!to!Tip!of!Middle!Finger!

Length!of!Arm!

Fingertip!!to!Elbow!

2

The Fibonacci Sequence: Start with 1 and 1. Then add the previous two numbers in the sequence.

1+1 = 2 1, 1, 2 1+2 = 3 1, 1, 2, 3 2+3 = 5 1, 1, 2, 3, 5, 3+5 = 8 1, 1, 2, 3, 5, 8

5+8 =

…

Can you find the next three

numbers in the sequence?

How many petals do each of the following flowers have?

What do you notice about these numbers?

3

The Golden Ratio

Use your golden caliper to find things on your table that you think exhibit the Golden Ratio.

Compare part a to part b, or compare the whole length (a+b) to part a.

If you think it has the Golden Ratio, measure both parts and fill in your data in the table below! Is the ratio approximately 1.618?

Object Larger Length Smaller Length Ratio =

Larger/Smaller

Index Card

Cereal Box

Book

Painting

Building