1. Wheel of Theodorus

2. Wheel of Theodorus aka…
Spiral of Theodorus
Square root spiral
Einstein spiral
Pythagorean spiral

3. How do I form this wheel? Starts with a right angle triangle where:
Legs = 1 unit
Hypotenuse = 2 units

4. Next step
Draw another 1 unit leg that is perpendicular (at a 90 degree angle) to the hypotenuse of the first triangle
Then add the new hypotenuse

5. Continue the pattern…

6. Eventually, you’ll start to see a spiral forming.

7. Showing your work 2 𝑢𝑛𝑖𝑡𝑠 1 unit 1 unit Use the Pythagorean Theorem
𝑎 2 + 𝑏 2 = 𝑐 2
(1 𝑢𝑛𝑖𝑡) 2 + (1 𝑢𝑛𝑖𝑡) 2 = 𝑐 2
1 𝑢𝑛𝑖𝑡 𝑢𝑛𝑖𝑡 2 = 𝑐 2
2 𝑢𝑛𝑖𝑡𝑠 2 = 𝑐 2
2 𝑢𝑛𝑖𝑡𝑠 2 = 𝑐 2
𝑐= 2 𝑢𝑛𝑖𝑡𝑠
2 𝑢𝑛𝑖𝑡𝑠
1 unit
1 unit

8. Showing your work – the second triangle
𝑎 2 + 𝑏 2 = 𝑐 2 (1) 2 + ( 2 ) 2 = 𝑐 2 1+2= 𝑐 2 3= 𝑐 2 3 = 𝑐 2 𝑐= 3 1 3 2 1 1

9. Showing your work – the third triangle1
𝑎 2 + 𝑏 2 = 𝑐 2 (1) 2 + ( 3 ) 2 = 𝑐 2 1+3= 𝑐 2 4= 𝑐 2 4 = 𝑐 2 𝑐= 4 1 3 4 2 1 1

10. It’s the spiral that never ends, yes it goes on and on my friend…