This month, Pre-Algebra Advanced and Algebra 1 Advanced students refreshed their math skills with two hands-on projects exploring the Pythagorean theorem. Pre-Algebra students constructed a Spiral of Theodorus, transforming their calculations into creative artwork and digital animations. Meanwhile, Algebra 1 Advanced students applied the same geometric principles to build more complicated Pythagoras Trees, intricate, tree-shaped fractals made from connected squares.

The Spiral of Theodorus begins with a single right triangle. To construct it, students build outward step by step, attaching each new right triangle to the previous hypotenuse. Using the Pythagorean theorem, they calculate changing side lengths to form a continuous chain of 15 connected triangles. Upper School Math Teacher Louise Lu challenged her students to transform these geometric spirals into creative artwork depicting everyday objects they feel connected to, like a sea urchin, a French horn, or a lollipop. Beyond being an engaging way for students to showcase their mathematical thinking, the project bridges the gap between rational and irrational numbers. “This is a great opportunity for them to apply what they know about square roots and irrational numbers while connecting math in a creative way to something about themselves,” notes Louise.

Similarly, Algebra 1 Advanced students built Pythagoras Trees by using the Pythagorean theorem to calculate side lengths for sequences of squares and right triangles. By repeating a single geometric rule, students observed how simple calculations yield intricate fractal patterns, noticing that as the tree branches out, the newly formed squares shrink in a mathematically precise ratio.