Have you ever tried to draw a Pentagram? You know, this five-point star that is always seen in stuff connected to magic. Well, have you? Sure you have. It's a basic doodle thing. But what you probably hadn't done, is make a REGULAR pentagram- a pentagram with all sides equal. It's not as easy as you may think!

So, here are a few methods for accomplishing this task.

Basic Ingredients

1. Pen/Pencil/Quill
2. Paper/Parchment/Papyrus
3. Ruler

The Easy Method

For this method you'll need a special ingredient- a protractor. All you need to do is draw a line at the desired length, then use the protractor to measure 36 degrees from it's tip and draw another line of the same length. Repeat with the rest of the tips until you close the pentagram.


This method is nice and simple, but who walks around with a protractor? (or even knows what this word means?)

The Ratio Method

The following method is based on a specific ratio that exists between the sides of the regular pentagon that form the base of the pentagram and the sides of the triangles that make it's shpitses(points). This ratio is (1+√5)/2:1, which is approximately 1.61803398874989484820458683436564:1 (1 is the side of the pentagon and the other number of the triangles). So for this method, one should use a calculator, or just round the number into 1.618 and use his head. Here this ration (called also the "golden ratio" will be referred as P.

Work Process

1. Draw a line of desired length (X will be used here for demonstration) and mark it's ends.
2. Add to this line (from both ends) lines at the length of P*X (no need to be extremely accurate), so if you had a line at the length of 1 cm now you have a line at the length of 3.236 cm (2*P*1).
3. Mark the center of the first line and draw a weak guideline vertical to it. This guideline should be nearly at length P*X.
4. Draw lines from the marks you made at step 1 to the guideline. These lines should be at length X*P and should meet at the same point. You can now vanish (erase) the guideline.
5. Continue the lines you made on step 4 with lines at the length X+X*P from the point where they meet the first line.
6. Connect the ends of the lines- left with right and vise versa, and there you have it! A regular pentagram!

The Method of Many Circles

Ok, so not everyone likes to calculate. The following method requires no calculation or protractor, but you will need compasses.

Work Process

1. Draw a circle with two lines at 90 degrees to each other crossing in the center. Looking at an analog clock one line goes from 12 to 6 and the other from 9 to 3, and that is how they will be referred here.
2. Divide the line from center to 3 in half. This can be easily done by setting the compasses at over half the distance and then drawing an arc from both the center and 3 points. A line between the two crossings of the arcs, above and below the center-3 line, will divide it in half.
3. Draw an arc with the center at the half way point of the center-3 line and the radius set at 12. Draw this arc through the 9-center line.
4. Draw one more arc with the center at 12 and the radius set at the point were the last arc intersects the 9-center line. Draw this arc through the initial circle. This radius is 1/5 of the circle.
5. Use the above intersections as center to find the other two points on the initial circle(the fifth is at 12).
6. Connect the five points, each one with a point not neighboring it, and there you're done!