Fibonacci Numbers - Math (Page 4 of 4) in pdf

Fibonacci Numbers - Math Page 4

Fibonacci Numbers and the

1. Collect boxes and cans from home, or use some

Golden Ratio

that are in the classroom. For boxes, measure the

Lesson 4 of 4

height and width of the boxes, and for cans,

measure the height and diameter. Make a table of

Look at the answer to Question 3 of Lesson 3

what you measured.

before you read further.

Description

Height

Width

longer one ÷

in cm

shorter one

If you keep doing divisions of consecutive (one

Cereal box

30.0

19.4

1.546

right after the other) Fibonacci numbers, like you

did in Lesson 3, you will get closer and closer to a

special number called the golden ratio. The

Answers will vary

golden ratio shows up in art, architecture, music,

and nature. The ancient Greeks thought that

rectangles whose sides form a golden ratio were

pleasing to look at.

The golden ratio is often symbolized by the

Examine

Is the quotient close to the golden

Greek letter phi, which looks like this: ��. It is the

ratio ��? It probably will never exactly equal ��,

number �� = 1.6180339887… (and so on). When

but many of the items are probably close. Which

you write out the decimal, it continues on forever

ones are closest?

without repeating or making a pattern.

Answers will vary.

Explain

Why do you think that the common

household items show the golden ratio?

Fibonacci Numbers - Math Page 4