How to Make A Spiral from the Pythagorean Theorem

This is what a finished spiral looks like.

This article will explain how to make a spiral from the Pythagorean Theorem. For those students who don't quite understand the theorem yet, this can help them start to understand. If your not a teacher making a creative lesson, this could just be a little project to get your creativity and brain stimulated.

Should you not know what the Pythagorean Theorem is or how to solve for the missing side of a triangle, this article should cover that within the instructions.

Things You'll Need

• Paper
• Pencil, pen, or other writing utensil.
• Protractor or other object that has a 90 degree angle.
• OPTIONAL: Colored pencils, markers, crayons, glitter, or other decorative materials.

Instructions

1. 

   Decide the measurements for the two *legs of the triangles. If you have a sheet of computer paper, use 2 cm for the sides. For 12" by 18" paper, use 5 cm. If you have full sized 22" by 28" poster paper, use 10 cm.

   *Legs: the two shortest sides of a triangle

2. 

   Draw a light X from corner to corner on your paper. Find the exact point they intersect. Darken that point in and erase the rest of the X. You will now have a point in the center of the paper.

3. 

   Turn your paper so that the longest end is facing you. Based upon the decided measurements from Step 1, draw a horizontal line that distance across the paper. Vertically, draw a line with the same measurements so that a right angle is created. You may want to use a protractor or a note card to create the perfect right angle. Label each side the length you used.

4. 

   Connect the two sides to form a triangle. The line you just made is called the hypotenuse, or longest side. You must now find the length of that line. Use: a squared + b squared = c squared

   If I used 5 cm, then the equation would be 5 squared + 5 squared = c squared. This translates to 25 + 25 = c squared.

   That means c = the square root of 50. Write that using the square root sign next to the hypotenuse on your paper.

5. 

   Continue to create the spiral using the steps shown. For me, the next triangle would be a right angle against the one you just made. The equation for it would be:

   5 squared + the square root of 50 squared = c squared.

   The square root of 50 squared is 50, so 25 + 50 = 75.

   If you used 5 cm like I did, the hypotenuse will increase by 25 every time.

6. 

   When the spiral is finished and you are pleased with the way it looks, it is time to pull out those coloring tools. Make a fancy design, or do something creative and make, for example, a baby carriage out of it.

   The possibilities are endless...

Tips & Warnings

• Coloring and decorating is optional.

• Great way to check and see if your students have been paying attention.

• The Pythagorean Theorem is usually taught in 5th through 8th grades. Not in these grades may find this too boring, not challenging, or if they are young, too difficult.