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Pythagorean Spiral Compass Instructions

In mathematical equations, the length of the hypotenuse, which is the long side of a right triangle, can be determined using the Pythagorean theorem. Although performing the calculation is not necessary to draw a Pythagorean spiral, the design that is drawn provides physical evidence of the rule. While the drawing of the spiral is used in schools to teach the theorem, the design can also be created as an art project.

Things You'll Need

  • Poster board
  • Compass
  • Pencil
  • Colored pencils
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Instructions

    • 1

      Place the poster board in the landscape orientation. Use a ruler and pencil to mark a point that is 27 1/2 cm to the right and 20 1/2 cm down from the top-left corner. This is the starting point for the design.

    • 2

      Use the ruler to create a horizontal segment that is 10 cm across, beginning at the starting point and heading towards the center of the poster board. Use the compass to measure a 90-degree angle, then use the ruler to draw a segment of equal length that is perpendicular to the original. Connect the end points of the two segments to create a right triangle. The long line that is drawn to close the triangle is called the hypotenuse.

    • 3

      Using the hypotenuse of the first triangle, use the compass and ruler to create another right triangle on top of the previous hypotenuse. Then use the old hypotenuse as the base for a new triangle that is created by drawing additional 10 cm lengths. Connect the two new segments to form a new hypotenuse.

    • 4

      Continue connecting and constructing new triangles with a side length of 10 cm, using the previous hypotenuse as the base, until you have formed a full spiral. The design is called a Pythagorean spiral.

    • 5

      Use colored pencils to detail each triangle of your spiral with creative colors or patterns.

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