Two step problems:
11) 195 cm (length of ear)
12) 1.21 m (distance from nose to bottom of chin)
13) 1080 mm (length of ear)
14) 133 cm (distance from hairline to eyebrows)
15) 1730 mm (distance from nose to bottom of chin)
Exercise 5:
If we know that the ratio of hand length to height is 1:10 and the ratio of face length to height 1:8 what can we say about the ratio of hand length : face length?
What other ratios can you find using the above strategy?
The final three conjectures from Exercise 1 all compare facial features to face length. What can you deduce from these three statements?
Exercise 6:
Make one conjecture of your own and test it on the members of your group.
Exercise 7:
Design a spreadsheet that enables a person to enter their height and gives estimates of their other body part measurements.
Task 3: Perfect faces?
Let’s investigate facial measurements a bit more closely.
Exercise 1:
Take the following measurements for members of your group and present your information in a table

pupil height to nosetip AB

nosetip to lip BC

width of nose DE

outside distance between eyes FG

width of head HI

hairline to pupil JA

nosetip to chin BK

lips to chin CK

length of lips LM

nosetip to lips BC
Find the following ratios:
BK:CK BK:AB
DE:BC FG:JA
LM:DE JK:HI
If each of these were in the form a:1. What can you say about a?
Exercise 2: Golden Ratio
The golden ratio is a special number that is approximately equal to 1.618033988749. We use the greek letter Phi (Φ) to refer to this ratio. Like pi the digits of the golden ratio go on foever without repeating. This number appears in many different circumstances such as architecture, the environment, art and body proportions.
Explore: Some people have suggested that faces that fit the golden ratio are more beautiful than others. Can you find the golden ratio in any of the previous exercises?
Task 4: Exploring surface areas
Exercise 1: Surface area
Your surface area can be estimated using the fact that the area of your hand is 1% of your total body surface area.
Find the area of your hand and use it to estimate your total body surface area.
Exercise 2: Rule of 9
Doctors use the rule of 9 to estimate the amount of the body affected in cases involving the skin, for example in burn victims. The rule divides the body into 11 different areas, each of which represents approximately 9% of the total surface area of the body. Use this rule, and the total surface area for your body (calculated in Exercise 1) to calculate the surface area of each of these areas. Design your own way of testing the accuracy of this rule.
Use these 11 areas to find another way of estimating the surface area of the body.
How does your answer compare to what you got in Exercise 1?
Which do you think is more accurate and why?
Exercise 3: Children’s surface areas
Children have different proporations of surface areas than adults, as shown in the table below:
PERCENTAGE

BODY PART

6.75

Front Left Leg

18

Head and Neck

6.75

Front Right Leg

9

Chest

6.75

Back Left Leg

9

Stomach

6.75

Back Right Leg

9

Left Arm

9

Lower Back

9

Right Arm

9

Upper Back

If a child has a hand area of 12 cm^{2}, find the surface areas of the other parts of his body. You may assume that the 1% rule applies for children.
Exercise 4:
Find an estimate for the volume of your body.
Clearly communicate the strategy you have used to generate your answer.
What is your ratio of surface area to volume? Compare your ratio to those of the other members of your group. Who has the largest ratio? How can you tell?
In terms of children – would they have a larger or smaller ratio of surface area to volume than adults?
One major problem with children being left in cars is that they dehydrate very quickly compared to adults. Can you explain this in terms of the ratio of surface area to volume?
Body Ratios
Answers
Task 2
Exercise 2
1) 1:1 (2) 1:10 (3) 1:8 (4) 1:4
5) 1:5 (6) 1:8 (7) 1:3 (8) 1:3
(9) 1:3
Exercise 3