Overview
Italian genius Leonardo daVinci combined art and science to advance both in a remarkable way. DaVinci
(1452-1519) was a polymath – a person with great learning in several fields. He was a scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician, and writer.
In 1487, his drawing of the “Vitruvian Man” showed the relationship between the human body and geometry that still stands today as a lesson in the close relationship between science and art. The drawing captures “proportion” – how various dimensions of things relate to each other mathematically. DaVinci helped us see how large the human head is in relation to the entire body, how long the arms and legs are in proportion to the trunk, and so on.
The original Vitruvius was a Roman architect who lived many centuries before daVinci. He described a relationship between the human body and math. daVinci took it a step further by drawing the relationship.
Geometry is a math based on shapes such as circles, squares, and triangles, and the lines that connect them all. DaVinci’s Vitruvian Man is drawn within both a circle and a square, with his legs and hands in two different positions. This is meant to illustrate some of the mathematical proportions that exist in the human body.
Your skeleton provides the shape of your body. And, while people come in “all shapes and sizes”, daVinci was correct in his proportions. Most adult humans will have the same ratios and proportions as found in the
Vetruvian Man.
(
Children and growing teens do not always fit the same proportions.
)
In today’s activity, we will take body measurements and see how close we are to the Vetruvian Man.

Activity 1: Arm Span
According to the “Vitruvian Man”, your arm span (the length of your arms, spread out, from fingertip to fingertip) should equal your height. Scientific studies have found this to be generally true – most people will have an arm span that is within a couple of centimeters of their height.
Part 1: Working with a partner, each of you will measure your arm span and your height, to determine if your arm span is longer than, the same as, or shorter than your height. Then, you and your partner will measure the arm span and height of two adults.
Record all data in the data table.
Part 2: Add your student and adult data to the class results. Then, use the class results to create a double bar graph (one bar for students, one bar for adults). The 3 categories are:

Arm span is shorter than height (more than 2 cm difference)

Arm span is equal to height (within 2 cm)

Arm span is longer than height (more than 2 cm difference)
Part 3: Analyze results. Write and answer the following questions:
1.
Do most people fit the “Vitruvian Man” formula (arm span equal to height)?
2.
Was there a difference between students and adults? If there was a difference, why do you think that might be?
Activity 2: Other Vitruvian Man measurements
Take the following measurements to see if you fit the Vitruvian Man pattern. Record all data in your data table.

Measure the distance from your hairline to the bottom of your chin. This measurement should equal about 1/10 of your height. Record and analyze the data – are you a “match”?

Measure your hand, from the tip of your longest finger to the line on your wrist. This measurement should equal about 1/10 of your height. Record/analyze the data – are you a “match”?

Measure your shoulders at their widest point. This measurement should equal about
1/4 of your height. Record and analyze the data – are you a “match”?

Measure your foot, from your heel to the end of your big toe. This measurement should equal about
1/6 of your height. Record and analyze the data – are you a “match”?

Part 3: Other Human Proportions
DaVinci was not the only one to recognize ratios in the human body. Here are some more.
Please write your data and results in your notebook.
Femur Length
The femur (thigh bone), is about
¼
the length of an adult human. Measure your femur and compare it to your height. Is it
¼
the length?
In growing kids, the femur length is usually longer than total height. Most kids and teens have longer femurs and shorter torsos. During the last stages of growth, the torso gets longer and adds to the total height. Take your femur length and multiply it by 4. Will this be your adult height? (Check back in a few years!)
Head Circumference
Another interesting body proportion is that of head circumference compared to height. Measure and cut a piece of string that is the same as your height. Now, predict how many times you can wrap the string around your head. Then give it a try and record the actual results.
RESULTS: In most adults, the height is about 3 times the circumference of the head. So, you should have been able to wrap the string around your head about 3 times.
Head Height
The ancient Greeks and Romans believed that the “perfect person” was “7 heads tall”. Measure the height of your head, from your chin to the top. Then, multiply your head height by 7. Is this equal to your height?
Are you a “perfect person” (according to the Greeks and Romans)?