Draw an Impossible Triangle
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 Penrose tribar.
Contents
Steps
Starting with an Inverted Triangle
- Sketch an inverted 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.
Extending a Triangle
- Draw a triangle and extend the ends of the lines past where they join.
- Draw lines from these tips, extending them beyond the corners of the inner triangle.
- Draw in the 'corners'.
- Draw in the final long lines to connect the corners.
- Finished.
Starting from an Irregular Hexagon
- Draw a hexagon. Three sides should be long and three short, alternating short and long sides. This can easily be done by constructing an equilateral triangle and "chopping" off the corners.
- Put a smaller, equilateral triangle in the middle of the hexagon.
- Draw a line from a corner of the triangle to a corner of the hexagon, as seen in the above picture.
- Repeat this process for the other two sides.
- Finished. Shade or colour if desired.
Tips
- After you learn this basic optical illusion, you can experiment with more complex arrangements.
- Try to outline it with a sharpie to make it look sharp.
- Practice shading techniques. Shading is a technique to provide depth in two-dimensional images.
- Always sketch first because you might get it wrong. Also do it on an old scrap piece of paper first so you don't waste new paper.
- Practice before you make your final copy.
- Make sure the shading is well done to give it the "Wow!" effect.
- A protractor might be a good idea as well.
