Leonardo

da Vinci

Are His Body Proportion Theories Still Valid Today?

A WebQuest for 6th through 8th
Grade Math Students

Introduction

Leonardo da Vinci (1452-1519) had theories on bodily proportions and how one section of the body would usually compare with another. He theorized that if you put your arms out to the side measuring from one finger tip to the other, it would equal your height. People come in all shapes and sizes. But here are some general rules that Leonardo da Vinci thought about proportions that you can follow:

arm span equals height

Another theory proposed that the hips are halfway between your head and your toes.

hands fall halfway between hips and knees

Also, that the arms
and hands at the
sides fall halfway
between the hips
and knees                            Mona Lisa

                Many artists study the proportion
                of the human body to make
                figures look real. Artists often                         make quick sketches or "studies"                 of models to learn about anatomy.

Task

First, as an introduction to scatter plots, students will record a number of human examples and will study what these examples have in common. Second, with that new understanding, students will demonstrate their understanding by creating a scatter plot and looking for what kind of correlation there might be (positive, negative, or none).

In this assignment, students will show whether da Vinci's ratios are still valid today. Initially, we will compare the height of a person and their wingspan. Leonardo's theory was that they were very nearly the same in length. Then we will explore some of his other proportions theories (hips in the middle of the body, hands between hip and knee, foot length tequalinghe distance between the waist and elbow).

Process

Working in groups of three, students will measure each other's height and wingspan from fingertip to fingertip. Use this form .
These measurements will be posted on the board and into the computer designated for this task, by student ID number and period.
Students will use these measurements on a scatter plot. Use this form .
Each student group will create a product (Power Point, chart, plot) that demonstrates their understanding by creating a scatter plot and looking for what kind of correlation there might be (positive, negative, or none). If needed, information on how to make scatter plots are on this site: Scatter Plot
For a look at da Vinci's Vitruvian Man and the proportions of the human body, try this site: Vitruvian Man
Here is a site to see human body proportions: Standard Visual Human Body Proportions
For a look at da Vinci's head proportions, check out this site: Head proportions
Look at these sites for an idea of what can happen with proportions that Fibonacci did with two of da Vinci's drawings. Fibonacci and da Vinci
A class discussion debriefing the analysis and consolidating any discrepancies in analyses from possible outliers, and the correlations of the scatter plots.
Student groups will try to find other proportions on the body that have positive correlations on a minimum of three other students outside their own group.
Finally, the students will come up with a business that sells shirts and shorts. The use of the scatter plot information on all the above will dictate why they are selling which sizes of both.

Evaluation of Presentation

The collaborative group work and the presentation to the class will be assessed according to the rubric. See the chart below to guide your performance and reach your goal.

	Beginning 1	Developing 2	Accomplished 3	Exemplary 4
Time - use of class time and the computer lab	Group does not use class and lab time to prepare for scatter plot presentation.	Group uses a small portion of class time and lab time to prepare for the scatter plot presentation.	Group uses almost all of the available class and lab time to research, prepare, and practice the scatter plot presentation.	Group uses all of the available class and lab time to discuss, prepare, and practice the presentation.
Organization of Presentation	Organization is not evident. Students do not know what each individual's responsibilities are.	Organization is somewhat evident. Students have some understanding of their responsibilities.	Organization is visible. Students know most of their roles. Notes or other forms or organizational aides are used.	Organization is very visible. Students know their exact role and how to perform their select tasks.
Voice and Intonation	Voices are inaudible. Students do not use intonation.	Voices are somewhat audible. Students use a small amount of intonation	Voices are audible. Some intonation is utilized.	Voices are very clear and audible. Intonation is utilized and makes the presentation interesting.
Audience Participation	No effort is made to involve the audience in the participation. The audience is very passive.	Some effort is made to involve the audience in the presentation. The audience is somewhat engaged.	Visible effort is made to involve the audience. Group uses a question, handout, or discussion to involve the audience.	Group effectively uses a variety of questions, handouts, or writing activities to involve the audience. Group responds to reactions appropriately.
scatter plot Exhibit	Group does not show a physical or electronic model of its scatterpplot	Group shows a rough and /or incomplete physical or electronic model of its scatter plot exhibit.	Group shows a complete model of its scatter plot exhibit.	Group thoughtfully displays a carefully designed and constructed exhibit.
Attitude and Effort	The group's attitude is poor. Students complain about project, group or other items. Group may appear listless during the presentation.	Little energy is spent within the group during class and lab time. Teacher must intervene during group conflicts.	Group works together with interest. They solve disagreements with few problems.	All members actively participate, demonstrate excitement, and work as a supportive team. Problems are solved quickly.

Conclusion

Students should have found positive correlations between the heights and wingspans of themselves and their peers.

Here are some other possible bodily correlations given by Leonardo da Vinci.

The average adult is seven and a half heads tall.

Shoulders are wide enough for three heads.

Facial Correlations: da Vinci Facial Proportions

Other possible proportions to attempt to verify as to whether the correlations are still valid are

Other Proportions

Leonardo writing right to left: Backwards writing

Credits & Reference

I wish to thank Judy and Jerry Headley, Kay Butler-Nalin, Kris White, Mike Williams, and Jill Proudfoot for all their patience, support, and assistance in the development and maintenance of this WebQuest. Without their encouragement and expertise this educational opportunity for students would not be possible.

I also wish to thank the Santa Barbara County Office of Education the use of their facilities during the development of this project.

In creating this lesson I consulted the Mathematics Framework for California Public Schools.

"We all benefit by being generous with our work. Permission is hereby granted for other educators to copy this WebQuest, update or otherwise modify it, and post it elsewhere provided that the original author's name is retained along with a link back to the original URL of this WebQuest. On the line after the original author's name, you may add Modified by (your name) on (date) . If you do modify it, please let me know and provide the new URL."

List any books and other analog media that you used as information sources as well.

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Last updated on June 26, 2002. Based on a template from The WebQuest Page