## Introduction: Draw a Penrose Triangle

A Penrose triangle is an "impossible object" - that is, a 2-d image that represents a 3-d object that would be impossible to actually construct as shown. This instructable will show you how to draw one using two methods - one freehand and the other using a compass and straightedge (for the perfectionists out there).

If you'd like to skip right to the beginning of the compass and straightedge process, go directly to step five. Do not pass "go" and do not collect $200. ;-)

(Note: I am aware that instructions for drawing a Penrose triangle have already been uploaded, but I chose to upload this anyway because I included compass and straightedge instructions.

## Step 1: What You'll Need.

The supply list is pretty straight forward:

*Pencil and eraser

*Paper

*Ruler

*Compass

If you don't already have a compass, you can pick one up at your nearest Michael's craft shop.

## Step 2: Step 1 (freehand)

The first thing you'll need to do is draw an L-shape with an angle of about 60 degrees. Close the bottom end with a line that is parallel to the first side, as shown, but don't close off the top of the L just yet.

## Step 3: Step 2 (freehand)

Draw a second L shape like the first. Place the bottom edge of this L on the inside edge of the first. Close the top end of the L as shown.

## Step 4: Step 3 (freehand)

Draw the third and final L shape with its bottom edge on the inside edge of the second L. Close this third L with a line that connects with the corner of the first L. Extend the lines of the first L shape as long as you need to reach the edge of the second L.

## Step 5: Step 1 (Compass)

Start the construction by drawing a single line of any length. Then set your compass to the length of that line.

Placing the stylus of the compass on one end of the line, draw an arc over the vicinity of the lines middle. Draw a second arc intersecting the first arc by placing the stylus on the opposite end. Then draw two lines from the original line's endpoints to the point where the arcs intersect. The result is an equilateral triangle.

## Step 6: Step 2 (Compass)

Set your compass to a much smaller width and draw one circle on each of the triangle's points. The radius of the circle will be about equal to the width of the sides of your Penrose triangle.

After that, extend the lines of your triangle so that they touch the circle. For convenience in later steps, we will label the points where the lines touch the circle like so:

1.) The points on the top circle will be labeled A, B, C, and D.

2.) The points on the bottom-right circle will be labeled E, F, G, and H.

3.) The points on the bottom-left circle will be labeled I, J, K, and L.

## Step 7: Step 3 (Compass)

Now we will begin drawing the L shapes for this triangle. Make the first by drawing a lines:

*from point D to point K

*from point L to point I

*from point I to point F

*from point F to point E

Then erase as shown. It should end up like the second picture.

## Step 8: Step 4 (Compass)

The second L shape is made by drawing lines:

*from point L to point G

*from point E to point B

*from D to A

*from A to B

Again, erase so it looks like the second picture. (Forgive me for making this so repetitive!)

## Step 9: Step 5 (Compass)

The last L shape goes like this:

*a line from A to J

*a line from J to I

*a line from H to C

Once more, erase the lines as shown so that you end up with what's shown in the second picture. You can then get rid of all other unnecessary lines and labels to get the final result, shown in the third picture. Shade as you wish.

It's done! Hope you've enjoyed this 'Ible, despite its repetition. Please comment!

## 3 Comments

12 years ago on Step 2

wow this is a great penrose triangle 5 stars

12 years ago on Introduction

Wow! Impressed. The more work you put into it, the finer it looks. Good job!

Reply 12 years ago on Introduction

Thank you very much!