Fibonacci Activities

By Elizabeth Debban, Rebecca Stewart, and Erin Obrock

Golden Ratios

The golden ratio is made up of three points on a line. 

The first point is A, the second point is B, and the third point is C.

Segment AB divided by segment BC is equal to segment BC divided by segment AC.

AB/BC=BC/AC

Are You A Golden Proportion?

See the above section on Golden Ratios to further understand how this works.

Measure:                                                                                      Calculate:

a. Navel to Chin_____              b. Length of Head_____                  a/b_____

m. Navel to ground_____          n. Navel to Top-of-Head____          m/n_____

d. Knee to Sternum_____          e. Sternum to Top-of-Head_____    d/e_____

a. Navel to Chin_____               k. Top of leg to navel_____            a/k_____

g. Top of leg to sternum_____    h. Sternum to Chin_____               g/h_____

*Any unit of measurement will work for this*

If the number in the Calculate column is between 1.6-1.64 you are a golden proportion!

Fibonacci Squares

You start off with a box that has a length and width of 1. You then draw a box that has the same length and width as that box. For the rest of the boxes you make their length and width the same as the previous two boxes' combined. What are the next three numbers?

Fibonacci Bee Line

How many different ways can the bee reach the different numbers on the bee line?

Rules:

• The bee MUST start at either the 1 or 2.
• The bee can only go to higher numbers with each move. 
• The bee can only move to the right. 

Examples: To reach cell 1 the bee can only take one route. To reach cell 2 the bee can go directly to two or he can go from one to two. 

Fibonacci Brick Wall Patterns

The point of this activity is to see how many ways you can build a brick wall using the given amount of bricks. 

• Each wall needs to be two units tall.
• Each brick standing on end is two units tall.
• Each brick laying on it's side is one unit tall.
• You are first given one, then two, three, etc.
• For one brick there is only one method of building a wall. Two methods for two, and three methods for three.
• How many ways are there to build a wall with four bricks, five, six?

!!!Answers!!!

(NO cheating!!!)

Fibonacci Squares

The next three numbers are:13, 21, 34.

Fibonacci Bee Line

These are the answers in numerical order starting with cell three:3,5,8,13,21.

Fibonacci Brick Wall Patterns

Same answers as the bee line.

THE ANSWERS ARE FIBONACCI NUMBERS!!!

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