Wheel of Theodorus

“The Wheel of Theodorus begins with a triangle with legs one unit long and winds around. Each triangle is drawn using the hypotenuse of the previous triangle as one leg and a segment one unit long as the other leg. To make The Wheel of Theodorus, you only need to know how to draw right angles

and segments one unit long”.

HistoryTheodorus of Cyrene lived in the 5th century BC. He was known as a philosopher, a musician, and as an astronomer, as well as a mathematician. In mathematics, he is chiefly known for his work with irrational numbers.Theodorus was a Pythagorean, a member of the devoted followers of Pythagoras, a pupil of Pythagoras and Protagoras, also a teacher and tutor of mathematics to Plato and Theatus.Little is known about Theodorus; however, Plato gave him credit for proving that the square roots of 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, and 17 are irrational.  

What do you see?

Original Isosceles

right triangle

DuplicateIsosceles

right triangle

New hypotenuse for the next right

triangle

The Wheel Of Theodorus is a rather simple geometric construction based on the Pythagorean Theorem that allows you to construct line segments

with length of the square root of any integer, i.e. irrational numbers.

Start with an

isosceles, right

triangle...

(or a 45-45-90 Δ)

Project requirements:•Complete the Wheel of Theodorus. The wheel you make will have at least 18 right triangles. •Complete the Wheel of Theodorus Calculations Table and the Project Questions worksheets.•All wheels must be hand drawn.•Please read the rubric carefully before beginning your project•All 90° angles drawn accurately.•Label all triangle legs and hypotenuse with appropriate lengths.•Write your labels using radicals unless they can be simplified to rational numbers. (ex. = 2)•All lines are straight and drawn precisely with a straightedge•First and last name, class period and teacher name is clearly written on the back of the wheel.•Overall appearance of the wheel is pleasing to the eye. It looks neat and carefully crafted.

Wheel of Theodorus Project