# 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 he drew the 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. 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 is valid today?

## Problem

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

## Plan

Before you begin your investigation, what answer do you predict? Why?

Now test your prediction using your class data from Census at School.

## Data

Fill in the data table below, using the Census at School results for all the students in your class. (If you need more rows, create your own larger table.)

 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. What do you notice from the table of data?

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

3. What helpedyou decide that a student fits this theory?

4. Check your prediction by plotting four graphs on pages 4 to 7.

Graph 1: Create your own graph from the data table above and give it a title.

Graph 2: Graph one measurement against the other in a scatterplot. Use only data for the girls.

Graph 3: Graph one measurement against the other in a scatterplot. Use only data for the boys.

Graph 4: Graph one measurement against the other in a scatterplot. Use data for all students.

Answer the questions written below each graph after you have plotted the data.

5. Compare the distribution shape, middle range and spread for boys and girls.

Are boys different from girls?

What evidence do you have to support your claim?

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

7. Do you think the results would be the same for babies or seniors?

Babies    Yes/No  Why?

Seniors    Yes/No  Why?

## Conclusion

You are now ready to answer the question we asked at the beginning.

Remember to give reasons based on what you found out in your investigation. Include things you wish you had more information about or were wondering about when you drew your graphs.

You might like to use some statistical language in your conclusion. Here are some phrases that might be useful:

For scatterplots: outlier, slope of the graph, trend

For all analysis: This sample suggests, probably, most, spread, shape, relative proportions, ratios, middle range.

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

Who would be interested in your conclusion?

## Graphs:

### Graph 1 – Title:

What is the shape of the plotted data?

What is the spread of the plotted data?

Is there anything interesting you notice about the graph (middle range, outliers, clusters)?

### Graph 2 – Height versus arm span, girls

Draw a line of best fit.

What is the shape of the plotted data?

What is the spread of the plotted data?

Is there anything interesting you notice about the graph (middle range, outliers, clusters)?

### Graph 3 – Height versus arm span, boys

Draw a line of best fit.

What is the shape of the plotted data?

What is the spread of the plotted data?

Is there anything interesting you notice about the graph (middle range, outliers, clusters)?

### Graph 4 – Height versus arm span, all students

Draw a line of best fit.

What is the shape of the plotted data?

What is the spread of the plotted data?

Is there anything interesting you notice about the graph (middle range, outliers, clusters)?

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