Math + Art:
Proportion -- DaVinci's
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!
Plain banner paper | masking tape | scissors
Large black marker | string
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
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
Using the measuring tape, take your shoes off,
measure your height in inches, and then let's examine a few of the Vitruvian
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
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?
is approximately equal to "wingspan" except that growing children usually have
longer arms until they reach their full height.