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Name__________________________________ Date____________________ Section__________

Partner’s Name _____________________________

Leonardo da Vinci’s Vitruvian Man

Leonardo da Vinci’s Vitruvian Man shows how the proportions of the human body fit perfectly into a circle or a square. With these proportions, your arm span (distance from fingertip to fingertip) should be equal to your height (distance from head to heels). In this laboratory exercise, you will see if this is true! In this activity you will explore the legitimacy of Vitruvius’ theory by developing a hypothesis regarding the Vitruvian Man.

Background Information

Leonardo da Vinci, a famous Italian renaissance inventor and painter, was greatly influenced by a man named Vitruvius. Vitruvius was a Roman engineer and architect during the first century B.C. Vitruvius discovered a formula to model what he thought were ideal proportions for a man. Da Vinci used this ideal model when drawing the Vitruvian Man in about the year 1490.

The drawing shows a man standing in a square, which is inside a circle. The man has two pair of outstretched arms and two pair of outstretched legs. These are some of the proportions given for the Vitruvian Man:

• The span of the man’s arms is equal to his height.
• The width of his shoulders is one-fourth of his height.
• The distance from the top of his head to the middle of his chest is one-fourth of his height.
• The distance from the middle of his chest to the top of his leg is one-fourth of his height.
• The distance from the top of his leg to the bottom of his knee is one-fourth of his height.
• The distance from the bottom of his knee to the bottom of his foot is one-fourth of his height.

OBJECTIVE

You will learn and practice the scientific method by measuring human dimensions.

A hypothesis is a possible explanation for a set of observations or an answer to a scientific question. A hypothesis is useful only if it can be tested. Testable hypothesis are generally written in a formalized format using an if/then statement.

• If my car does not start because the battery is dead, then when I replace the old battery with a new one it will start.
• If increasing physical activity causes a person to burn calories and lose weight, then I should lose weight if I run 2 miles a day and do not increase my calorie intake.

Formalized hypothesis contain both a dependent and an independent variable. The independent variable in the one that YOU change and the dependent variable is the one you observe and measure to collect data. Using the if-then format, If I change temperature, then what will happen to movement.

Temperature is the independent variable because I change it and movement is the dependent variable because it is the one that is observed to look for change. Using the if-then format forces the scientist to think about what results are expected.

The subject of the exercise is Leonardo da Vinci’s drawing Vitruvian Man. You will focus on the primary proportion of the drawing, “The span of the man’s arms is equal to his height.” You will test a hypothesis regarding Vitruvius’ theory on human proportions.

The scientific method consists of the following steps:

1. From observations, state a question
2. Write a hypothesis
3. Design an experiment to test the hypothesis
4. Gather data by doing the experiment
5. Analyze the data
6. Write and explain your conclusion

MATERIALS

PROCEEDURE        Remember to use metric units (centimeters)

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

If the Vitruvian Man ratio/theory is                  (correct/incorrect):                  (pick one)

Then the arm span and height will be the       (same/different).                     (pick one)

1. Working with a partner, measure your arm span by standing against a flat surface and spreading your arms out as far as possible. Have your partner measure the distance from the longest finger on one hand to the tip of the longest finger on the other hand. Measure to the nearest centimeter. Record measurements in Data Table 1.

3. Repeat step two on your partner.

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. Measure to the nearest centimeter. Record measurements in Data Table 1.

5. Repeat step 4 on your partner.

6. Calculate the difference between your arm span and your height (arm span-height)

7. Go back and make a conclusion on your original hypothesis– Was it right or wrong??

Student Name: __________________________    Date: __________________

Partner’s Name: ______________________________

Lab Section: ___________________  Instructor: ________________________

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.

1. Collect foot-forearm data for yourself and your partner using a metric ruler/tape.

Measure to the nearest centimeter.

FOOT: Measure from the tipof the 1st distal phalange to the posteriorendof the calcaneus.

ARM: Measure from the styloid process of the ulnar to the olecranon process of the ulnar.

1. Collect data from all students in the class and record the measurements in Data Table 1.

1. Analyze your data by calculating the sum of the foot – forearm values for all students, males only, and females only and record in your Data Table 1.

1. Determine the correlation between foot and forearm length for all students.

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 an equation (using x, y, z) for the calculations above (foot – Forearm):

x = foot, y = forearm, z = difference

CONCLUSION QUESTIONS – Pre Lab

1. Were the results of the experiment similar for all students?

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?

1. Write a conclusion statement based on the data that you have collected for forearm and foot length.

Student Name: __________________________    Date: __________________

Partner’s Name: ________________________________

Lab Section: ___________________  Instructor: ________________________

LAB EXPERIMENT – Arm Span vs. Height

PROCEDURE

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

1. 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 TIP OF THE RIGHT 3RD DISTAL PHALANGE to the TIP OF THE LEFT 3RD DISTAL PHALANGE. The student will stand against the blackboard with their arms outstretched and a chalk mark will be placed at the tip of each finger. This distance will then be measured using the measuring ruler / tape.

Measure to the nearest centimeter. Record your measurements in Data Table 2.

1. Repeat step two for all students in the Class.

1. Remove your shoes and have your partner measure your height as you stand against the blackboard. A chalk mark will be placed at the TOP OF THE HEAD. Then measure the distance from the top of your head (chalk mark) to the floor. Measure to the nearest centimeter.

Record your measurements in Data Table 2.

1. Calculate the difference between your arm span and your height (arm span-height). Record your calculations in Data Table 2. The absolute value (no + or – sign needed) is sufficient.

Equation used: Arm Span – Height = Difference

1. Gather data from all students in the classroom. Record the student’s name, gender and data in Data Table 2. Be sure to collect data for males and females.

8.Calculate the difference between your arm span and your height (arm span-height).

Record your calculations in Data Table 2.  The absolute value (no + or – sign needed) is sufficient.

1. Analyze the data for your class, all students.

HYPOTHESIS 2– Arm length vs. Height

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DATA AND OBSERVATIONSaTable 1: Lab Partner Data

DATA TABLE 2 – Class data for arm length and height

 Group member Gender Arm Span (cm) Height (cm) Arm – Height(cm)

ANALYSIS-Show an equation (using x, y, z) for the calculations above (arm – height):

X = arm span, y = height, z = difference

GRAPHICAL ANALYSIS Scatter Plot Analysis

A scatter plot looks at the relationship between two numbers. It can indicate if there is a set proportion between two variables. If a relationship exists we will observe a pattern in our analysis. The slope on the line will give us a correlation between the variables. A positive slope (upward) indicates that as

the X variable increases so does the Y variable. A negative slope indicates that as the X variable increases, the Y variable decreases. A linear trend (straight line) indicates a proportional change.

GRAPH 1

Plot the student data that you collected on the graph paper below (each point represents 1 student). Each box represents 2 cm, begin with 140 cm for the first box and 200 cm for the last box.

Then draw a straight line (linear) through as many of the plotted points as possible.

GRAPH 1

Height (y-axis) to Arm Span (x-axis), measured in cm.

CONCLUSION QUESTIONS – Lab Project

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 graphical analysis of class height and arm span data support Vitruvius’ hypothesis?

Did you observe a linear or exponential relationship for height and arm span? Why or why not?

1. When comparing males and females, does one group fit Vitruvius’ hypothesis more closely than the other? Explain your answer.

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.

1. How useful, and relevant, is your data and conclusion to science, technology and/or society 2019 ? Was it useful in the past following Vitruvius’ life ?

Instructor’s Remarks: