We're in the process of finishing up our algebra unit and, while I will continuously revisit these ideas with warm up problems, I am thinking about the scale factor and geometry unit that follows. I have always wondered how to engage that artistic side with the math. I found this "How To" article and think it may have some promise for my 6th graders.
What if they used this as their model and then created their own "How To"?
The "rule of three", where arrangements of triplets have a pleasing effect on the eye, makes this triangle an intriguing shape to ponder and to create. It appears frequently in the art of MC Escher. It is also known as a Penrose triangle or tribar.
- Sketch an equilateral triangle. This will be the center of your triangle.
- Lightly sketch two parallel lines outside one side of the triangle. The lines should be equally spaced. Take caution that your lines are drawn straight.
- Do this for each of the other two sides. Your sketch should look like three triangles nested together.
- Choose one side of the "center" triangle. Extend one end of that straight line until it reaches the "middle" triangle.
- Find the same side of the "middle" triangle. Extend one end of that straight line, in the same direction as before, until it reaches the "outside" triangle.
- Repeat steps for the other two sides of the triangle.
- Erase short segments so that the triangle begins to look three-dimensional rather than flat. Each edge of this "3-D" shape should look like a reverse "L".
- Add short segments at an angle in the corners. These short segments will finish off the outside points.
- Cleanup your drawing by erasing the points outside of the short segments drawn in the previous step.
- Add shading if desired.
- After you learn this basic optical illusion, you can experiment with more complex arrangements.
- How to Draw an Impossible Cube
- How to Draw an Impossible Cube with a Highlighter
- How to Draw an Impossible Cube Using a Pencil
- How to Draw the Triforce
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