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Math + Art:

Proportion -- DaVinci's 'Vitruvian Man'


Today's Snack: On a napkin or plate, arrange washed berries in the shape of the 'Vitruvian Man' drawing. Use a strawberry for his head, blueberries for the circle around him, and raspberries to outline his arms, legs and trunk. Admire your work - and then eat, washing down your juicy berries with a well-proportioned glass of orange juice!





Measuring tape

Plain banner paper | masking tape | scissors

Large black marker | string

Paper plates


Drawing paper




Italian genius Leonardo daVinci combined art and science to advance both in a remarkable way. DaVinci (1452 - 1519) was a polymath - a person with great learning in several fields. He was a scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician and writer.


In 1487, his drawing of the "Vitruvian Man" showed the relationship between the human body and geometry that still stands today as a lesson in how closely connected are science and art.


The drawing captures "proportion" - how various dimensions of things relate to each other mathematically. DaVinci helped us see how large the human head is in relation to the entire body, how long the arms and legs are in proportion to the trunk, and so on.



The original Vitruvius was a Roman architect - a person who designs buildings and structures. He lived many centuries before DaVinci. In a book, he described the connection between the human body and math many centuries ago. DaVinci took this idea a step further by drawing it as never before. DaVinci's drawing illustrated this principle effectively because of his amazing powers of observation.


DaVinci took the study of anatomy to a new level when he obtained permission to do autopsies, or surgeries, on actual human bodies so that he could see how their muscles, bones and other parts actually connected. Many people believe that's why his art is so striking and memorable: because it is based closely on reality.


Geometry is based on shapes such as circles, squares and triangles, and how lines connect them all. The man in his drawing is within both a circle and a square, and displays two basic postures. One figure has hands at about 10 o'clock and 2 o'clock if the circle were a clockface, and feet at approximately 7 o'clock and 5 o'clock. Using the same trunk, or midsection of the body, the other figure has arms straight out, and legs straight down.


Using the measuring tape, take your shoes off, measure your height in inches, and then let's examine a few of the Vitruvian principles:


1.      First, guess: how does your height compare to your "wingspan" - your arms stretched out as wide as possible? Now measure.*


2.      Measure the distance from your hairline to the bottom of your chin. It should equal approximately 1/10th of your height.


3.      Measure your hand from the tip of your longest finger to the line on your wrist. It should equal approximately 1/10th of your height, too.


4.      Measure your shoulders at their widest point. That should equal about one-fourth of your height.


5.      Measure the length of your foot, from your heel to the tip of your big toe. That should equal about one-sixth of your height.



Now comes a fun part! You need at least one other student for this.


Assuming you are less than six feet tall, measure a six-foot length of banner paper and cut it. Now measure out two or three more six-foot lengths, and tape them together to form a large square that's about six feet wide and six feet tall. You may need to tape the corners down so the paper won't curl up.


With shoes off, one student should lay down on the paper and assume the position of the "Vitruvian Man" with arms outspread and up at an angle, and legs outspread down below. We call this position "spread-eagled."


The student should hold the end of a piece of string. The other end should be tied to a large marker. Another student should hold the marker at the edge of the paper while the "Vitruvian Man" student lays still. The student holding the marker should stretch the string fairly taut and draw a circle around the student laying down. The string acts as a simple "compass" - an instrument for drawing circles.


Once the circle is drawn, the other student should draw the outline of the "Vitruvian Man" student.


When finished, it should look like a life-size version of the real thing!


Finally, take a paper plate, trace a circle around it onto the paper, and draw yourself as a "Vitruvian Man" inside the circle.


Then practice writing in mirror-image, as Leonardo did - every letter backwards and the entire word backwards. When you hold the paper up to a mirror, the word should read correctly.


What word should you try to write in mirror-image?






* Height is approximately equal to "wingspan" except that growing children usually have longer arms until they reach their full height.


By Susan Darst Williams Math 2010




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