ARE YOU A GOLDENRATIO?
by:  Marilyn Harsch
Boyet Jr. High School
OVERVIEW
     This is a lesson connecting mathematics in human anatomy.  Students will work in pairs to measure specific parts of the body.  Comparison will yield ratios approximately equal to 1.618 - the golden ratio.

OBJECTIVE
     Students will find and use measurements and their relationships to discover the golden ratio in nature.

BACKGROUND INFORMATION
     Ancient Greeks believed that, for the ideal beauty of any figure (including the human form), the various parts should have the proportions of a unique ratio known as the golden ratio.  This golden ratio is an important concept in both ancient and modern artistic and architectural design.  The ancient Greeks considered rectangles whose sides form a golden ratio to be the most pleasantly proportioned of all rectangles, thus using this ratio in the design of their beautiful Parthenon.
     This ratio can also be found in nature in such places as the arrangement of the whorls on a pinecone or pineapple, petals on a sunflower, length of rows of branches on some pine trees, and the spiral in a shell.  The Audubon Institute uses in it's logo the logarithmic spiral inside a golden rectangle.

MATERIALS
     Meter stick
     Calculator

TIME FRAME
     This lesson can be completed in one class period.

PROCEDURE
     1.  Each student will measure with a partner his/her
         a.  height from head to toe
         b.  distance from floor to navel
         c.  length of face
         d.  width of face at cheek bones
     2.  Students will write ratios for
         a.  height from head to toe to distance from floor to navel
         b.  length of face to width of face
     3.  Students will change ratios above to decimals rounded to the thousandths place
     4.  Teacher will record each student's results on the board and find the class average.
     5.  Discuss the golden ratio in relation to the students' ratios

ASSESSMENT
     This can include an evaluation of students' measurements and converting fractional ratios to decimals. It can also be extended to include an outside assignment in which students identify other objects with measurements proportionally equal to the golden ratio.

EXTENSION
     Students can investigate integral measures of golden rectangles and their relationship to the Fibonacci Sequence.