Introduction: Fibonacci Triangle Spiral

Using right triangles, Pythagorean theorem a^2 + b^2 = c^2, and a few supplies, you will learn to construct a Fibonacci spiral. This one differs from the typical square, but it is elegant and simple.

When the hypotenuse is created, it will be presented as the square root of the original Fibonacci sequence!


Recommended but not required : 90° triangle, compass (circle craft), ruler (straight edge), graph paper

Required : pen or pencil, paper (larger = better), squared corner (2x folded paper works great!)

Step 1: Create an Isosceles-right Triangle

This is your initial unit of measure, the two same legs count for 1. The hypotenuse is the square root of 2.

Step 2: Second Triangle

Perpendicular to the hypotenuse, and opposite what will become the common origin, a leg with length of 1 unit. Will create a hypotenuse of the square root of 3.

Step 3: Continue Building

Using the squared paper straight edge, continue building. The third triangle will be the square root of 2, adjacent to the square root of 3. The hypotenuse meets the origin, with a length of the square root of 5.

Step 4: Fibonacci Continued All in the Square Root Of

3+5=8, 5+8=13, 8+13=21,...

Step 5: Limited Paper Size....

Missed proportion, resumed on other side of the paper. Until limited space, then went digital.

Step 6: Digital Rendered

Thinking outside the box. Challenge someone to construct one with 20 triangles on one paper! Cut them out! Be creative!
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