EMAT 6700

by Brad Simmons

Constructing Values of Square Roots

Use geometer's sketchpad to construct values of square roots.

The diagram below shows a right isosceles triangle with two legs of length 1 unit.  By the Pythagorean Theorem, the length of the hypotenuse is the square root of 2 units.  By constructing an adjacent right triangle with legs of square root of 2 units and 1 unit, a segment of length square root of 3 can be created.

By continuing this process as shown below, a wheel of square roots can be constructed.  This wheel is called the "Wheel of Theodorus" after a Greek philosopher who lived about 400 B.C.

Please click here for a geometer's sketchpad sketch of the figure shown above.

Continue constructing the wheel until you make a segment of length square root of 18.