Leonardo da Vinci Activity

## Student Page

Teacher Lesson Plan

Vitruvius, a Roman engineer of the first century B.C., influenced Leonardo da Vinci's work in architecture and also his drawing of the human figure. One of Leonardo's drawings is called the Vitruvian Man. It is based on a model of ideal proportions which Vitruvius established.

The drawing shows a square inscribed inside a circle. There is a man with outstretched arms and legs, in fact two pairs of each, which touch both the circumference of the circle and the vertices of the square. Upon viewing the drawing the conclusion can be made that the length of a man's arm span is equal to the height of the man. In other words the ratio of the Vitruvian Man's arm span to his height equals 1.

How can we trust a drawing? The following activity will investigate if this is true or not. After data have been gathered from all of the students in the class, you will be asked:
1. Explain the conclusion to the question - Is your arm span equal to your height?
2. Do men (boys) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
3. Do women (girls) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
4. Are taller men (boys) more likely to have Vitruvian Man proportions than shorter men (boys)?
5. Are taller women (girls) more likely to have Vitruvian Man proportions than shorter women (girls)?
6. Generalize for all of the students in the class using the class data.
7. Explain what your graphs showed.
Question: Is the ratio of our arm span to our height really equal to 1?

 Gathering the Data

Using measuring devices work in pairs and measure both your height and your arm span. As you measure cut a piece of string equal to the two measurements. This can be accomplished by measuring first and then measuring out the string OR by using the string as the measuring device, cut it and then find the length of the string. Either method should result in two pieces of string per person and noted measurements per person.

As you and your partner are waiting for the class to complete their measurements and record them on the data sheet provided by your teacher, look at the difference between the lengths of string. As you work with the data and calculate the ratios, remember what you noticed about the two string lengths.

Method 1 -- Graph Paper
Using the class data graph the two columns of data using either the given grid or standard graph paper. Here is a sample.

Using the class data instruct students to graph the third column of data using either the given grid or standard graph paper.
Using the class data instruct students to graph the two columns of data using a spreadsheet program.

Using the class data instruct students to graph the third column of data using a spreadsheet program
Discussion Questions:
• Do men (boys) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
• Do women (girls) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
• Are taller men (boys) more likely to have Vitruvian Man proportions than shorter men (boys)?
• Are taller women (girls) more likely to have Vitruvian Man proportions than shorter women (girls)?
• Does the arm span increase linearly with height, i.e. is there a sort of best-fit line through the data points or does the taller you are mean the wider your arm span is?
 Processing the Data

Respond to the following journal prompts:
• Explain the conclusion to the question - Is your arm span equal to your height?
• Generalize for all of the students in the class using the class data
• Explain what your graphs showed.
 Extensions/Resources

Leonardo da Vinci Resources