Name : ________________________________
Class : _____________ Date:______________
The Golden Ratio Investigation
GOLDEN RATIO IN RECTANGLES
The golden ratio is the ratio of length to width of a rectangle that is most pleasing to the
eye. A rectangle that has sides in the golden ratio is called a golden rectangle. The ratio of length
to width in a golden rectangle is about 8: 5 or 1.6: 1.
Examples:
A rectangle that has a length of 16 cm and a width of 10 cm can be categorized as a
golden rectangle.
(*Not drawn to scale)
Many ancient buildings are said to have floors or sides which were built in the golden ratio.
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GOLDEN RATIO IN THE HUMAN BODY
Leonardo’s Conjecture:
Leonardo Da Vinci suggested the ratio of certain body measurements is close to the
golden ratio. Keeping in mind that we are all different shapes and sizes, let us see if we can find
the golden ratio using our body measurements.
What to do:
1. Take your body measurement (in mm) as indicated in the following diagrams. Record
these measurements and calculate the required ratios as shown by the example below.
Your teacher’s data:
A. Height
Height of navel
So, Height: Navel height
(1670 ÷ 990)
B. Length of hand
(fingertip to armpit)
Length of forearm
(fingertip to elbow)
So, arm : forearm
(670 ÷ 410)
=
=
=
=
1670 mm
990 mm
1670 : 990
1.7 : 1
= 670 mm
= 410 mm
= 670 : 410
= 1.7: 1
My own data:
C. Height
Height of navel
So, Height: Navel height
=
=
=
=
1430 mm
850 mm
1430 mm : 850 mm
____: 1
D. Length of arm
= ________ mm
(Fingertip to armpit)
Length of forearm
= ________ mm
(Fingertip to elbow)
So, arm: forearm
= _____ : _____
(Arm divided by forearm)
= _____: 1
1430mm
850mm
600mm
380mm
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2. Get other 9 measurements from your classmates and fill in the table below. 6A
https://binusianorgmy.sharepoint.com/personal/jhobal_sebarrotin_binus_edu/_layouts/15/guestaccess.as
px?docid=1991d06d10a3b4e0791ef1f5870ec77c4&authkey=AQgzSz3o0RUHw_baFxmgh
Mg&e=wGwRru
Height
(in mm)
Height of navel
(in mm)
Length of arm
(in mm)
Length of
forearm
(in mm)
My data
Classmate 1:
Classmate 2:
Classmate 3:
Classmate 4:
Classmate 5:
Classmate 6:
Classmate 7:
Classmate 8:
Classmate 9:
*Average
*To compute for the average, add aal numbers in each column and then divide by 10.
3. From the averages of the height and the height of navel,
Height : Height of navel =
_______ : _______
Height divided by Height of navel=
_______ : 1
4. From the averages of the length of arm and the length of forearm,
Length of arm : Length of forearm
Length of arm divided Length of forearm
=
_______ : _______
=
_______ : 1
5. What general rule can you generate from your investigation regarding the golden ratio and
Leonardo’s conjecture? (Write in words.)
From my investigation regarding the golden ratio and Leonardo’s conjecture, I can say that...
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______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. Justify the general rule that you have mentioned above by using three more data from other
classmates and comment on what you find out.
Height of
navel
(in mm)
Height
(in mm)
Length of
arm
(in mm)
Length of
forearm
(in mm)
Classmate 1:
Classmate 2:
Classmate 3:
Average
From the averages of the height and the height of navel,
Height : Height of navel
=
_______ : _______
=
_______ : 1
From the averages of the length of arm and the length of forearm,
Length of arm : Length of forearm
=
_______ : _______
=
_______ : 1
Compare and comment on the ratio of the additional three sets of data to the general rule you
suggested:
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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6A
Day/Date
Activity/ Expected Output
Feb 14
Task Introduction/ Part 1 (Taking measurements)- page 1-3
Feb 16
Questions 3-5 (answering questions on Page 3)
Feb 21
Question 6 (answering questions on Page 4)
Feb 23
Completion (individually)and uploading in ManageBac
Criterion B: Investigating Patterns
Level Indicators
Level of Achievement (LoA):_______
Task-Specific Clarification
The student does not reach a standard
described by any of the descriptors
below
The student does not reach a standard
described by any of the descriptors
below
The student applies, with some
guidance, mathematical problemsolving techniques to recognize simple
patterns similar to previously seen
examples
The student measures his/her own body
and records the results
The student applies mathematical
problem-solving techniques to recognize
simple patterns similar to previously
seen examples, and suggests
relationships or general rules
The student calculates the ratios of his
own data
LoA
0
1–2
The student collects data of his/her
friends and completes the table
The student calculates the ratios of the
averages from the tables
The student generates the general rule
The student applies mathematical
problem-solving techniques to recognize based on the data table
simple patterns similar to previously
seen examples, describes them as
relationships or general rules using
words
The student justifies the general rule
The student applies mathematical
problem-solving techniques to recognize that he/she generates by using 3 other
examples
simple patterns similar to previously
3–4
5–6
7-8
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seen examples, describes them as
relationships or general rules using
words, and justify using other examples
with guidance from the teacher
The comment that the student writes on
the ratio when justifying corresponds to
the general rule.
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