A Golden Ratio Activity
From Mark Wahl
2) Or, if you have been searching for any of the following keywords, a click on one will take you to an excellent book resource (A Mathematical Mystery Tour) for weeks of personal, home, or classroom learning about the Golden Ratio and Fibonacci Numbers:
3) Or you can go to Mark Wahl’s website and see a selection of his creative books, links, and information on math learning that includes but goes beyond these topics: click “Home” in the top menu.
Now, the Golden Ratio. It has fascinated layman and mathematician for centuries. It seems like magic that it turns up in such different arenas as pine cones, earth-moon and planet relationships, the Cheops Pyramid in Egypt, the Mona Lisa and even our DNA. Indeed its widespread appearance shows that there is a unifying mathematical principle that is more subtle than science has thus far been able to define.
Below the line is an activity that is two pages long, of interest to students aged 10-adult and that requires about fifth-grade math knowledge to successfully complete. To make site-loading faster the quality has been reduced. Feel free to select a page at a time and print the selection for use in a classroom or homeschooling setting though quality will be sacrificed. It is one of many from my popular book A Mathematical Mystery Tour.
A Golden Ratio Activity (found in clarity and detail in A Mathematical Mystery Tour with answers and teacher background ideas)
A GOLDEN GREEK FACE
Toolbox: Calculator; metric ruler (measures to mm)
Statues of human bodies considered most perfect by the Greeks had many Golden Ratios. It turns out that the “perfect” (to the Greeks) human face has a whole flock of Golden Ratios as well.
You’ll be measuring lengths on the face of a famous Greek statue (with a broken nose) by using the instructions on this page. Before you start, notice that near the face on the second page are names for either a location on the face or a length between two places on the face. Lines mark those lengths or locations exactly.
Using your cm/mm ruler and the face picture on the next page, find each measurement below to the nearest millimeter, that is tenth of a cm or .1cm (___._ cm). Remember, you are measuring the distance or length between the two locations mentioned. You can use the marking lines to place the ruler for your measurements. Fill in this table.
a = Top-of-head to chin = ___ . __ cm
b = Top-of-head to pupil = ___ . __ cm
c = Pupil to nosetip = ___ . __ cm
d = Pupil to lip = ___ . __ cm
e = Width of nose = ___ . __ cm
f = Outside distance between eyes = ___ . __ cm
g = Width of head = ___ . __ cm
h = Hairline to pupil = ___ . __ cm
i = Nosetip to chin = ___ . __ cm
j = Lips to chin = ___ . __ cm
k = Length of lips = ___ . __ cm
I = Nosetip to lips = ___ . __ cm
Now use these letters and go on to the image below to compute ratios with them with your calculator (a printed version of it is a must). Remember: a/g, the first one, means find measurement a divided by measurement g as a rounded-off to a 3-decimal-place value.
Go to Mark Wahl Learning Services and Books then click books to find info on the book this came from. You’ll discover an easy to use, information- packed web site. Or go directly to A Mathematical Mystery Tour. Either way, you can order a copy if you wish.