In this Instructable you will learn how to make a perfect hexagon. It is very easy and can be done in about 5 - 10 minutes. You will only need a few supplies:

### Supplies:

1. Blank white piece of paper(I used 8.5 x 11)

2. Compass(the kind used to draw circles)

3. Pencil

4. Ruler

5. Scissors

### Teacher Notes

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## Step 1: Draw the Circle

1. Open the compass so that when you hold it up to the paper it measures a little less than half of the paper.

2. Hold the compass by the part that sticks up on the top. Take the pointed side of the compass and rest it at the center of the paper

3. Rest the pencil side of the compass at any point in the circle radius.

4. Keeping the point and the pencil on the paper, turn the pencil around the metal tip, creating a circle.

## Step 2: Draw the Curves to Form the Points

1. Place the metal point part of the compass at any point along the circle line. Turn the metal point of the compass so that the pencil it rests on the line of the circle.

2. Starting at the part of the circle the pencil part of the compass falls on, draw inward until the line gets to the part of the circle opposite to where you started. Because this can be hard to understand, see the pictures above.

3. Rest the metal tip at the point where the curved line you just drew touches the outer circle. Now, draw a line in a similar manner as you did in step 1 draw a curve starting at the point where the pencil tip of the compass meets the circle and draw inward until you get to the edge of the circle opposite to where you started.

4. Rest the metal tip at the point where the curved line you just drew touches the outer circle. Now, draw a line in the same manner as you did in step 3 draw a curve starting at the point where the pencil tip of the compass meets the circle and draw inward until you get to the edge of the circle opposite to where you started.

5. Repeat step 4 until you reach the point at where you started in step 1

## Step 3: Draw the Hexagon

1. Place one end of the ruler at the point where any one of the petal-shaped lines meet the circle. Place the other end on another petal-shaped line that is touching the circle. Trace the ruler from the first petal to the second petal.

2. Repeat this on all the petals.

You should now have a hexagon outline around all the petals. You can either erase all the petals and use the hexagon for whatever you want or you can cut out the hexagon and either flip it and glue it to something or you can use it to trace on other things. Have fun making!

## Step 4: The Math Behind It

The hexagon looks cool, right? But how does it work? To start, you have to know that the inside angles of triangles add up to 180°. Knowing this, we divide the hexagon into triangles, and we get 6 equilateral triangles. Then, we divide the triangles by 3 to find each of their angle measures, and we get 60°. Looking at the drawing above, you can see that for every angle of the hexagon, there are 2 60° angles that are part of the triangle. This tells us that each interior angle on the hexagon is 60° + 60° which equals 120°. So that means if you were to take a ruler and draw a straight line, let's say 2 inches, then take a protractor and measure 120° then repeat that 5 more times, you would end up with a perfect hexagon.

This is an entry in the

Made with Math Contest

## 7 Discussions

15 days ago

This will make it much easier to make paper snowflakes in December. Thanks for posting this.

Reply 15 days ago

Your welcome :)

4 weeks ago

technically it's not a "perfect" hexagon, because, as everybody learn in maths school, the circumference is egal to 2*pi*radius, so as you keep your radius in your compass, you got 6.28 and not exactly 6 ...but that will do the job :) (but not a "perfect" hexagon...only an awesome hexagone)

Reply 4 weeks ago

I'm afraid you have it wrong, the side of the "perfect" hexagon inscribed in a circle is equal to the circle's radius. The value of 2*pi*radius is the length of the circumference, not the sides of the hexagon. JustMakeStuff's explanation is correct.

Reply 4 weeks ago

my bad ... sorry, when i sa your answer i was "... he may not be wrong..." i was about to check myself, and then I saw that JutMakeStuff already made an update to prove it :D, thanks for the correction and thanks to JustMakeStuff for the update

Reply 4 weeks ago

Thank you

Reply 4 weeks ago

I understand that it is impossible to create a perfect circle but it is possible to create a perfect hexagon. This may not be possible with drawing it by hand on paper because you cannot line up the ruler and draw the curves perfectly but it is possible on a computer.