Art-Inspired Math, by Michael Naylor
Is there a place where math and art intersect? Absolutely!
While studying art this month, don't forget to examine the geometry and mathematics in artwork. Here are some activities to get your students looking for mathematics in artwork and also creating their own artwork to show off geometric ideas.
Lines and angles (Grades K-1)
Cut many thin strips of construction paper or magazine pages. Have your students glue them on sheets of paper to make designs with intersecting strips. Ask the class to include examples of parallel lines, perpendicular lines and various angles.
Have your students then compare their artwork and challenge them to find the parallel and perpendicular lines in each others' creations. What other shapes can be found? This is a great opportunity to discuss obtuse and acute angles, different kinds of triangles and quadrilaterals and many other shapes.
Black leaf on green background (1952)
Paper cutting (Grades K-3)
Henri Matisse (1869-1954) was a French artist known for his brilliant use of colors. When he got older, he had medical problems that made it difficult for him to paint, so he turned to paper cutting.
Have your students create Matisse-like paper cuts. Supply them with a half sheet of colorful construction paper and a full sheet of black paper. They should then cut out a curvy shape from the colored paper and arrange the shape and the leftover piece on the black paper to form a double picture. Talk about how the two sides are alike and different.
With older children, have them make three smaller double images and then use them to demonstrate three transformations: translations, reflections and rotations.
Rectangular art (Grades 3-5)
Piet Mondrian (1872-1944) was a Dutch elementary school teacher who painted as a hobby and eventually became a world-famous artist. His paintings were inspired by geometry, especially parallel and perpendicular lines and rectangles.
Composition A: Composition with Black, Red, Gray, Yellow, and Blue (1920)
Ask your students to create rectangular designs. Have them use rulers and sketch the design lightly with pencil at first. They can then use black felt-tip markers to draw heavy horizontal and vertical lines. Finally, have them select a few colors of either broad markers or poster paint to fill in select rectangles.
Ask your students to then find examples of parallel and perpendicular lines in their artwork. As an extension, have them find the rectangle with the greatest area and perimeter on their page – are these two rectangles the same, or might they be two different rectangles?
Enlargements (Grades 3-8)
Renaissance artists would sometimes look at a scene through a grid they had painted onto glass. By drawing on a similar grid on a piece of paper, they could then use the grids as a guide to accurately reconstruct the scene.
For this activity, ask your students to select a picture from a magazine. Have them carefully measure with ruler and draw a 5 x 5 grid of squares (approximately 1"-2" between lines, depending on the size of the picture). They should then recreate the grid on paper (I've found that graph paper works well). You can also create a grid yourself and photocopy it for your students.
With older students, use the pictures to discuss scale factors – how many times bigger is the drawing than the original? How does this relate to the area of the picture or of elements in the picture? (If the linear dimensions change by a factor of n, the areas change by a factor of n2). Have fun!
Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.