R atio By Rachel Lewis adapted from httpwwwgeomuiucedudemo5337s97bdiscoverhtm Goal Given a ruler and various rectangles found in the classroom students will measure the length and width of each rectangle ID: 297147
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Slide1
TheGoldenRatio
By Rachel Lewis
adapted from http://www.geom.uiuc.edu/~demo5337/s97b/discover.htmSlide2
GoalGiven a ruler and various rectangles found in the classroom, students will measure the length and width of each rectangleUsing a calculator, students will be able to calculate the ratio of length to width for each rectangle.Using a calculator, students will find the average of their results to estimate the Golden Ratio.
Objectives
Students will calculate the Golden Ratio and discover where it exists in the world around them.Slide3
MaterialsGolden Ratio worksheetRulerAny rectangular index cardCalculatorPencilSlide4
ProcedureFrom this picture, students are asked to measure the length and width of their favorite rectangle in centimeters and to record these values in the table in their packets.Slide5
Then measure the: length and width of the index cardlength and width of the worksheetdistance from the knuckle on the back of your hand to the next knuckle (use as length), and then from the second to knuckle to the next (use as width)Slide6
Students are then told to walk around the classroom and find various rectangles to measure. All data is to be recorded in the same table.Slide7
Sample TableMeasurements
Item
Length
Width
Ratio
Favorite Rectangle
2.8
1.2
Index Card
20.2
12.8
Worksheet
27.9
21.5
Finger
5.6
3.2
Text Book
23.9
16.6
Pencil Case
18.9
11
Notebook
29.2
25.1
Computer Screen
38.1
24.1
Slide8
Find the RatioStudents are then asked to calculate the ratio of length to width for each rectangle the measure using the formula:
Slide9
Sample RatiosIndex Card = Worksheet
=
*These values should be the same for each student
Slide10
Complete Sample TableMeasurements
Item
Length
Width
Ratio
Favorite Rectangle
2.8
1.2
2.333333
Index Card
20.2
12.8
1.578125
Worksheet
27.9
21.5
1.297674
Finger
5.6
3.2
1.75
Text Book
23.9
16.6
1.439759
Pencil Case
18.9
11
1.718181
Notebook
29.2
25.1
1.163347
Computer Screen
38.1
24.1
1.580913Slide11
QuestionsWhat do you notice about your ratios?Take the average of the 8 ratios you found. Record this number on the chart on the board.Do you think this number would change if you measured in inches instead of centimeters?Measure this worksheet in inches and find the ratio. What do you notice?Find the average of the values on the board.Slide12
The Golden RatioThe number you have calculated should be close to 1.61803. This is called the Golden Ratio. Remember the Fibonnaci sequence we studied before? Well you will notice that if we find the ratio of consecutive numbers…2/1 = 2.0 3/2 = 1.5 5/3 = 1.67
8/5 = 1.6 13/8 = 1.625 21/13
= 1.61534/21 = 1.619 55/34 = 1.618 89/55 = 1.618 the result gets closer and closer to the Golden Ratio
! The number first got its fame in Ancient
Greece
when mathematicians noticed how
frequently
it appeared in geometry. This ratio is
said
to be used in architecture from the Parthenon
in
Greece to the Great Mosque of
Kairoun
in
Tunisia
. Leonardo
DaVinci’s
famous drawing to the
left
shows a man drawn within a pentagon, suggests that the Golden Ratio exists in the human form. Slide13
Some Other Thoughts…Have students measure the distance from their shoulder to elbow and elbow to wrist.Give them a picture of the Parthenon and see if they can find Gold RectanglesResearch other places where the Golden Ratio is apparent (art, architecture, etc…)