Wheel of Theodorus

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

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

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

Continue the pattern…

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

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 2 + 1 𝑢𝑛𝑖𝑡 2 = 𝑐 2 2 𝑢𝑛𝑖𝑡𝑠 2 = 𝑐 2 2 𝑢𝑛𝑖𝑡𝑠 2 = 𝑐 2 𝑐= 2 𝑢𝑛𝑖𝑡𝑠 2 𝑢𝑛𝑖𝑡𝑠 1 unit 1 unit

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

Showing your work – the third triangle 1 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

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