Wheel of Wheel of TheodorusTheodorus

What inspirals you?What inspirals you?

How do you draw How do you draw an irrational number?an irrational number?

• Who is Theodorus of Who is Theodorus of Cyrene?Cyrene?

• Drawing the Wheel of Drawing the Wheel of TheodorusTheodorus

• Math into ArtMath into Art

• What can we learn What can we learn from the Wheel of from the Wheel of Theodorus?Theodorus?

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.

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.

THE WHEEL OF THEODORUS

STEP THREE:

Use your note card as a straight edge and close off your right angle by drawing the hypotenuse.

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.

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.

THE WHEEL OF THEODORUS

STEP SIX:

Draw in the hypotenuse. You are on your way to drawing the Wheel of Theodorus.

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

Math into ArtMath into Art

My student’s workMy student’s work

Phi Vortex in Galaxy 

After finding the area of After finding the area of several of the triangles several of the triangles on your “wheel,” can on your “wheel,” can

you write an equation to you write an equation to help find the area of the help find the area of the

n triangle in the n triangle in the sequence? sequence?

What would it look like What would it look like on a graph?on a graph?

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

Learning from the Learning from the WheelWheel

Answer the questions Answer the questions about Pythagoras, about Pythagoras, Theodorus, and the Theodorus, and the Wheel you constructedWheel you constructed

Include picture, Include picture, calculationscalculations

Graded on:Graded on: IB Rubric B – IB Rubric B –

Investigating PatternsInvestigating Patterns IB Rubric D – Reflection IB Rubric D – Reflection

in Mathematicsin Mathematics PresentationPresentation CalculationsCalculations

Word BankWord Bank PythagorasPythagoras TheodorusTheodorus Right triangleRight triangle HypotenuseHypotenuse LegsLegs Right angleRight angle Irrational numberIrrational number

How can understanding How can understanding spirals help us spirals help us

understand the world understand the world around us? around us?