Vitruvian Man Meets the Scientific Method

BACKGROUND INFORMATION

Leonardo da Vinici’s drawing Vitruvian Man shows how the proportions of the adult human body fit perfectly into a circle or a square. This diagram by Leonardo da Vinci is an illustration of Vitruvius’ theory. According to Vitruvius’s theory the distance from fingertip to fingertip (arm span) should be equal to the distance from head to heel (height). In this activity you will explore the legitimacy of Vitruvius’ theory by developing a hypothesis regarding the Vitruvian Man.

PURPOSE

In the pre-lab activity, you will be guided through the processes of developing a hypothesis, testing a hypothesis, collecting data, analyzing data, and drawing conclusions. We will be investigating the relationship between foot and arm span lengths.

In Part I, you will test Vitruvius’ theory and draw conclusions based upon the data you collect.

MATERIALS

1 – 8’ length of string1 – meter stick1 – metric ruler

Pre-lab Activity

1. Some people have observed that the length of their foot is the same as the length of their forearm. Others disagree saying there is no relationship between the two. You have been assigned to investigate this phenomenon. Write an if-then hypothesis for the relationship between foot length and forearm length on the student answer page in the space below.

2. Collect foot-forearm data for yourself using a metric ruler. Measure to the nearest centimeter.

3. Collect data from nine other people and record the measurements in Data Table 1. Be sure to collect data for 5 males and 5 females.

4. Analyze your data by calculating the sum of the foot – forearm values for all students, males only, and females only.

5. Determine the correlation between foot and forearm length for all three groups.

6. Answer the conclusion questions.

HYPOTHESIS – Foot vs. Forearm length

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Data table 1 – Data for foot and forearm length

Student Name / Gender / Foot length (cm) / Forearm length (cm) / Foot – Forearm (cm)

ANALYSIS (Show work for calculations for all three groups in the space below)

CONCLUSION QUESTIONS

  1. Were the results of the experiment similar for all three groups? Describe the results you obtained.
  1. Based on the data that you have collected, is there a correlation between the length of the forearm and the length of the foot? Explain your answer.
  1. Write a conclusion statement based on the data that you have collected for forearm and foot length.

PROCEDURE

PART I

1. Write an if-then hypothesis based on Vitruvius’ theory relating arm span and height. Record your hypothesis on the student answer page.

2. Working in groups of four, measure your arm span by standing against a flat surface and spreading your arms out as far as possible. Have your partners measure the distance from the longest finger on one hand to the tip of the longest finger on the other hand by passing the string behind your back. Measure the string using the meter stick. Record your measurements in Data Table 1.

3. Repeat step two for each person in the group.

4. Remove your shoes and have your partner measure your height as you stand against a flat surface. Measure the distance from the top of your head to the floor. Record your measurements in DataTable 1.

5. Repeat step 4 for each person in your group.

6. Calculate the difference between your arm span and your height (arm span-height). Record yourcalculations in Data Table 1. (Be sure to indicate positive or negative differences).

7. Gather data from 12 additional students in the classroom. Record the student’s name, sex and datain Data Table 2. Be sure to collect data for 8 males and 8 females.

8. Calculate the difference between your arm span and your height (arm span-height). Record your calculations in Data Table 1. (Be sure to indicate positive or negative differences).

9. Analyze the data for your group only, all 16 students, males only, and females only.

Vitruvian Man Meets the Scientific Method

HYPOTHESIS #1 – Arm length vs. Height

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DATA AND OBSERVATIONSa Table 1: Lab Partner Data

Data Table 1 – Group data for arm length and height.

Group member / Gender / Arm length (cm) / Height (cm) / Arm span – Height (cm)

Data table 2 – Class data for arm length and height

Group member / Gender / Arm length (cm) / Height (cm) / Arm span – Height (cm)

ANALYSIS (Show work for calculations for all four groups in the space below)

CONCLUSION QUESTIONS

  1. Does your individual group’s data for height and arm span lead you to accept or reject Vitruvius’ hypothesis? Why or why not?
  1. Does the class height and arm span data support Vitruvius’ hypothesis? Why or why not?
  1. When comparing males and females, does one group fit Vitruvius’ hypothesis more closely than theother? Explain your answer.
  1. Write a conclusion statement based on the data that you have collected.
  1. An experimental procedure that implements good experimental design will be much more likely to yield results that can be duplicated in future experiments. Describe three factors that would improve the experimental design for this activity.