"How Divine Is My Proportion?"

Edwina R. Justice              Gunsaulus Scholastic Academy
10641 South Lowe Ave.          4420 South Sacramento Ave.
Chicago, Illinois 60628        Chicago, Illinois 60632
(312) 468-3376                 (312) 535-7215


Objectives (Staff):

    Demonstrate a phenomenological approach to teaching mathematics.

    Inspire others to use the approach.

Objectives (Grade 8):

    Relate the ratio of successive numbers in the Fibonacci Sequence to the
    "divine proportion".

    Compare approximate golden rectangles to human body proportions.

Materials:

Measure in advance and select items whose sides are in the approximate ratio of 
1:1.6. 

    file cards (assorted sizes)       envelopes      charge plates   photos
    greeting cards (assorted sizes)   invitations    pamphlets       books

Recommended Strategy:

    Measure items and calculate the ratio of longest side divided by shortest 
    side. 

    List quotients on the chalkboard and discuss similarities.

    Measure the height and the distance from the top of the head to the middle 
    finger tip with an arm extended to one side.  Calculate the ratio of the two 
    measurements. 

    Compare the ratio of body measurements to the results obtained from other 
    items. 

    Determine a pattern and complete a number sequence:

                 1, 1, 2, 3, 5, 8, 13, 21, ... 
              (Additional numbers are optional.)

    Calculate the ratio of two successive numbers:
     
              1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13

    (The ratio 21/13 equals 1.6154 rounded to the nearest ten-thousandth
     and represents the ratio of the sides of a golden rectangle.)

    Compare the quotient of a golden rectangle ratio to ratios of selected items 
    and body proportions. 

    Students should look for golden rectangles and divine proportion 
    measurements at school, home and other places.