Week 4: Polyhedra Study

Opal’s sketch (11yrs old)

Leonardo da Vinci was an amazing mathematician, inventor and artist. His sketches in The Divine Proportion are a wonderful collection to study. Spacial awareness and being able to draw what we see is a skill that can be mastered through practice.

This week, I encourage learners to sketch polyhedra from cubes to tetrahedrons to dodecahedrons. Use charcoal, pencils or watercolors to create works of art. You can model with clay, paper, glue and sticks, or building toys and then sketch. Play with various forms of lighting and shading. Move beyond the numbers this week and look for math in the objects/polyhedra around you.

You can combine this study with history and architecture. Go out and look for polyhedra around you. Can you make a pyramid scene? What is a soccer ball? What is the shading like at different times of day for a favorite building? Are there planes of symmetry for your sketch? How many vertices are there?

Week 2: Spiral of Theodorus

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This week the Spiral of Theodorus can be used to enhance understanding of the pythagorean theorem, right triangles, pi, and more. The spiral goes by many names (square root, Pythagorean, or Einstein Spiral) and approximates the Archimedean Spiral.

Stop animation of sketching process

Instructions:

1.) Create a right isosceles triangle where the sides that are the same measure 1 unit (I used inches).

2.) Add a 1 unit line segment perpendicular to the hypotenuse of your first triangle and then connect it to create another right triangle.

3.) Add another 1 unit line segment to the hypotenuse created in step 3 and connect it to the center to create another triangle.

4.) Repeat step 3 as many times as you wish to expand your spiral.

5.) When your done, you can transform your work into a fun sketch:

Possible reflection/discussion questions:

  • How does the Pythagorean Theorem apply here? What pattern do the hypotenuses make?
  • Can you create a function that would reflect the rate of growth for the hypotenuses?
  • There are so many ways to say “right angle” – can you say it three other ways?
  • Can you create an algorithm for making these spirals?