Week 42: Perspective

Drawing with perspective is a wonderful way to play with ratios, similar triangles, transformations, and more in math. This week I encourage learners to try to draw with various perspectives. This is a fun activity for all ages and the math can either stay simple or dive into transformation matrices.

Here are some activities to start:

• One point perspective: Start with a horizon and one vanishing point. Rectangular prisms are easy objects to start with.
• Two point perspective: Start with a horizon and two vanishing points. Again, rectangular prisms are easy objects to start with.
• Three point perspective: With three points, sketch a rectangular prism.
• Distortion (try sketching through a lens, glass, or glass sphere).

After you play with some of the basic sketches:

• Look at shading and details. (Draw a city, room, fantasy land, or scene. Where is the light source? How can you show it through shading?)
• Draw shadows with perspective.
• Try a reoccurring object (power line poles, people, light posts) to see how it appears further away, yet the same height. (Look at ratios and similar triangles here.)
• Try to grid a square tile floor with perspective (hint: look at the diagonals for the squares).
• Sketch perspective using Geogebra and look at relationships in distances (some activities are here).
• Think about how perspective relates to projection on a plane – your paper. (Here is a Geogebra activity from Mathieu Blossier).
• Make skeleton objects out of dowels and use a flashlight to play with projection on a plane.
• For coders, can you create an interactive perspective drawing?
• Go out and sketch the perspective you see outside: cities, skyscrapers, looking up at trees…