Owen Biesel

If you’re like me, you like to doodle fun patterns. One of my favorite things to doodle is an “impossible triangle” that looks like three straight bars meeting in right angles, which can’t exist in real life:

But I had trouble drawing an impossible triangle from memory, until through trial and error I came up with this 7-step method—now it turns out great every time:

1. Start by drawing an equilateral triangle. (It doesn’t have to be exact.) This will be the “window” in the center of the impossible triangle, so leave some space on all sides for the three bars.
2. Extend the right-hand side an arbitrary amount toward the top left. The longer the extension, the thicker will be the bars of your triangle, but don’t make it too long: the top edge of the finished triangle will be about three times as far from the center window as the length of this extension, so keep the edges of your doodle area in mind.
3. Extend the left and bottom sides the same amount, making a small pinwheel.
4. Now draw a line from the right end of the bottom extension to a point directly above the top end of the right-side extension, keeping it parallel to the right-hand side of the triangle.
5. Draw lines of the same lengths from the ends of the other two extensions, parallel to the other two sides. (Reader suggestion: Try turning the paper so you can use the same visual rule as in Step 4.)
6. Draw a line from the new bottom-right point, parallel to the right side of the triangle, until it reaches the same height as the top of your shape. Connect it to that top point with a short horizontal line.
7. Repeat with new lines of the same lengths for the other two sides. (Again, turning the paper might be helpful.)

There you have it! By varying how big you make the original triangle and how long you make the original side extensions, you can make your impossible triangle light and open or thick and chunky.

You can even shrink the starting triangle to a point and get an impossible shape with no window in the middle.

Happy doodles!