Students Learn About Perspective in Geometry

Students in Middle School math class recently learned about the geometry concept of dilation and applied it to a drawing in teacher Karen Seder’s class. The students discovered how to increase or decrease the size of a shape keeping its perspective the same.

To create a dilation, you start with a given point, called the center point, and a shape. From the center point, you draw rays that go through key points on your shape. Then using a compass or ruler you can enlarge your shape by moving all your points by a certain factor (say 2x or 3x) further from the center along the ray. When you connect these new points, you have a larger version of your shape where the lengths have all changed by the same factor and the angles have all stayed the same. To decrease the size, you just do the opposite by moving a fractional distance from the center point. 

“It’s fun to notice that this mathematical idea is related to perspective drawing and vanishing points in art,” said Seder. “We learned about this concept, and then I asked the students to apply it to a drawing on big pieces of butcher paper. We studied this fairly quickly and then the students had fun, making these drawings in 35 or 40 minutes. And now that we’ve studied this, we will look at similarity and ratios and more proportional relationships.”