Wednesday, April 1, 2020

Pythagorean Theorem Spiral of Theodorus

Pythagorean theorem is maybe my all time favorite thing for students to learn! It is also close to my heart from growing up on a construction site with my daddy. Pythagorean theorem was the thing that made me want to teach math and want to teach it in real ways. This is because my daddy would argue all day about how he did NOT use this fancy formula to calculate the pitch of the roof on the house he was building. Even though he would measure and use Pythagorean triples, he would never concede! I also love Pythagorean theorem because of the scandalous stories there are about Pythagoras! I love celebrity gossip and Pythagoras provides us with that. 

I like this math art because it helps students visualize a segment length with the square root of two. This is one of the first times students use irrational numbers so I want them to see the amazement in them. I have students use notecards that I have pre-cut to a one inch square for a template. I have them measure the bottom and side to be sure it is one inch. Then I have them measure the diagonal and get as close as they can to an estimate. Then we work it using the Pythagorean theorem to show how precise we can get. 

Students then use the notecard template to draw only half of the square, two adjacent sides of the square, creating a right angle in the lower left side of their big paper. Next, they create a triangle from the half and label all the sides with their lengths. 

Now the fun begins! Add a new right-angled, one-inch leg to the base of the hypotenuse of the first right triangle then add the new hypotenuse and label. Calculate the length of the new hypotenuse using the Pythagorean theorem then measure and change to decimal form. Is it close?!

Continue to add on one inch legs at right angles {this is super important} to your last hypotenuse and label all the new triangle's sides using the Pythagorean theorem. This is where the template square comes in handy!

Once you have the wheel, students can decide what it will become! Have them rotate it and think big about what it reminds them of. As you can see, some students put a LOT of detail into their design and others transformed their wheel into other shapes. 

Create a huge display of their wheels because they will be so super proud of their art! Get creative and peak their curiosity about Theodorus!

1 comment

  1. Amazing! If I taught this, I would definitely use your project!


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