This document provides instructions for drawing the Wheel of Theodorus, which involves constructing a series of right triangles to form a spiral shape. It discusses Theodorus of Cyrene, who developed this construction to represent irrational numbers. The document guides the reader through each step of constructing the wheel using a notecard, ruler, and pencil. It then prompts analyzing the area of triangles in the sequence and representing it with an equation. Finally, it asks how understanding spirals can help us understand the world.

1. Wheel ofWheel of
TheodorusTheodorus
What inspirals you?What inspirals you?

2. How do you drawHow do you draw
an irrational number?an irrational number?
• Who isTheodorus of Cyrene?Who isTheodorus of Cyrene?
• Drawing the Wheel ofDrawing the Wheel of
TheodorusTheodorus
• Math into ArtMath into Art
• What can we learn from theWhat can we learn from the
Wheel ofTheodorus?Wheel ofTheodorus?

3. SUPPLIESSUPPLIES
 Blank white paperBlank white paper
 PencilPencil
 RulerRuler
 NotecardNotecard
THE WHEEL
OF
THEODORUS
STEP ONE:
On the corner of your notecard,
measure one inch on each side.

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.

5. THE WHEEL
OF
THEODORUS
STEP THREE:
Use your note card as a straight
edge and close off your right angle
by drawing the hypotenuse.

6. THE WHEEL
OF
THEODORUS
STEP FOUR:
Now find the length of the
hypotenuse using the Pythagorean
Theorem. Make sure to show your
work on a separate sheet of paper.

7. THE WHEEL
OF
THEODORUS
STEP FIVE:
Line up your note card along the
hypotenuse. Trace only the
bottom of the note card to create
another right angle.

8. THE WHEEL
OF
THEODORUS
STEP SIX:
Draw in the hypotenuse. You are
on your way to drawing the Wheel
of Theodorus.

9. FINISHING THE WHEEL:
Continue making right triangles
until you have AT LEAST ten. For
each of these ten triangles make
sure that you continue to show
your work for finding each new
hypotenuse. You may make more
triangles, but you only need
calculations for the first ten.
THE WHEEL
OF
THEODORUS

10. Math into ArtMath into Art

11. My student’s workMy student’s work

19. Phi Vortex in Galaxy

20. After finding the area of several ofAfter finding the area of several of
the triangles on your “wheel,”the triangles on your “wheel,”
can you write an equation to helpcan you write an equation to help
find the area of the n triangle infind the area of the n triangle in
the sequence?the sequence?
What would it look like on aWhat would it look like on a
graph?graph?

22. http://cosmometry.net/vortex-and-double-spirals-in-nature

23. Learning from the WheelLearning from the Wheel
 Answer the questions aboutAnswer the questions about
Pythagoras,Theodorus, andPythagoras,Theodorus, and
the Wheel you constructedthe Wheel you constructed
 Include picture, calculationsInclude picture, calculations
 Graded on:Graded on:
 IB Rubric B – InvestigatingIB Rubric B – Investigating
PatternsPatterns
 IB Rubric D – Reflection inIB Rubric D – Reflection in
MathematicsMathematics
 PresentationPresentation
 CalculationsCalculations
Word BankWord Bank
 PythagorasPythagoras
 TheodorusTheodorus
 Right triangleRight triangle
 HypotenuseHypotenuse
 LegsLegs
 Right angleRight angle
 Irrational numberIrrational number

24. How can understanding spiralsHow can understanding spirals
help us understand the worldhelp us understand the world
around us?around us?