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:
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.
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:
MATERIALS
Measuring Tape Masking tape Chalk
PROCEEDURE Remember to use metric units (centimeters)
If the Vitruvian Man ratio/theory is (correct/incorrect): (pick one)
Then the arm span and height will be the (same/different). (pick one)
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
Measure to the nearest centimeter.
FOOT: Measure from the tipof the 1^{st} distal phalange to the posteriorendof the calcaneus.
ARM: Measure from the styloid process of the ulnar to the olecranon process of the ulnar.
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
Describe the results you obtained.
Explain your answer.
Student Name: __________________________ Date: __________________
Partner’s Name: ________________________________
Lab Section: ___________________ Instructor: ________________________
LAB EXPERIMENT – Arm Span vs. Height
PROCEDURE
Measure to the nearest centimeter. Record your measurements in Data Table 2.
Record your measurements in Data Table 2.
Equation used: Arm Span – Height = Difference
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.
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.
This represents your slope.
GRAPH 1
Height (y-axis) to Arm Span (x-axis), measured in cm.
CONCLUSION QUESTIONS – Lab Project
Did you observe a linear or exponential relationship for height and arm span? Why or why not?
Explain your answer.
Instructor’s Remarks: