# The Vitruvian theory-does it apply to you?

## Student worksheet

Downloadable versions of this activity are available in the following formats: (RTF format,PDF format)

Note: Teachers, see Teacher’s lesson plan

Leonardo da Vinci (1452-1519) was a scientist and an artist, one of the greatest painters of the Italian Renaissance. He left only a handful of completed paintings, one of which is the Mona Lisa. He was so secretive that he wrote backwards to disguise his ideas.

In 1492, Leonardo drew a picture of a man standing inside a circle and a square. This is known as the ‘Vitruvian Man’. It was a study of the proportions of the human body as described by Vitruvius, a Roman architect from the first century B.C. Based on his observations of European people of his day, Leonardo believed that arm span was equal to height in a perfectly proportioned body.

Why do you think he was interested in working out body proportions?

Do you think the Vitruvian theory illustrated by Leonardo would work today?

## Problem

Is the Vitruvian theory that height is equal to arm span true for Canadian students today?

## Data

Enter the data for 10 students from your class in this table.

How will you select the students for your sample?

Do not simplify the fraction for the arm span / height ratio.

 Student Gender Arm span Height Ratio: arm span / height M or F cm fraction decimal Student A Student B Student C Student D Student E Student F Student G Student H Student I Student J

## Analysis

1. Have a look at the table of data. What does each row represent? What do you notice about the data?

2. Which students most closely fit Leonardo’s theory?

3. How do you know that a student fits this theory?

4. Graph the information from the table, using graph paper. You might have to draw different kinds of graphs to show all the information.

5. Look at the graphs you have drawn. What words could you use to describe the shapes, range and spread of the information?

6. Not everybody has an arm span / height ratio that is equal to 1. Why do you think this is?

## Conclusion

Is the Vitruvian theory that height is equal to arm span true for Canadian students today?

Using some of the words below, give reasons based on what you found in your investigation:

 analysis gradient ratio arm span height row biased investigate sample bivariate justify scatterplot cluster measure selection conclusion middle skew data outlier slope distribution predict spread equal problem systematic frequent random table

Adapted and reproduced with permission from CensusAtSchool New Zealand.

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