1. Spiral of Theodorus
What inspirals you?
Mrs. Kapler

2. Spiral of Theodorus Who is Theodorus of Cyrene?
How do you draw an irrational number?
What can we learn from the Sprial of Theodorus?

3. The Spiral of Theodorus
SUPPLIES
Large sheet of paper
Pencil
Straight edge
Notecard
STEP ONE:
On the corner of your notecard, measure one unit on each side. The pictures shows one unit = one inch, however, you may use any length to = one unit. We will use the fact that the corner of an index card is a right angle formed by two perpendicular lines.

4. THE WHEEL OF THEODORUS STEP TWO:
Place the notecard in the center of your white paper. Trace the corner of your paper so you create a right angle. Draw leg a and leg b to the length of one unit.

5. The Spiral of Theodorus
STEP THREE:
Use your a straight edge and close off your right angle by drawing the hypotenuse. Draw in the right angle mark. This first triangle has both legs equal to 1 unit.

6. THE WHEEL OF THEODORUS STEP FOUR:
Now find the length of the hypotenuse using the Pythagorean Theorem. Write this length in radical form into your construction.

7. The Spiral of Theodorus
STEP FIVE:
For the next triangle:
Use a straight edge to draw in the hypotenuse.
Trace along the edge of the note card to create another right angle with a leg =1 unit.
The subsequent triangles have only one leg that equals 1 unit; it is the leg that forms the outer edge of the wheel.

8. THE WHEEL OF THEODORUS STEP SIX:
Draw in the hypotenuse. Continue to construct your Wheel of Theodorus.

9. The Spiral of Theodorus
FINISHING THE WHEEL:
Continue constructing right triangles until you have at least seventeen. When completed, label the length of each hypotenuse in radical form.
Add a title to your paper and put your name and date on it.

10. Learning from the Spiral
Required Work
Word Bank
Complete Worksheet on Spiral of Theodorus
Construct and label the Wheel of Theodorus.
Imagination
Theodorus
Plato
Pythagoras
Right Angle
Right Triangle
Hypotenuse
Legs
Pythagorean Theorem
Perfect Square
Natural Numbers
Rational Number
Irrational Number