Golden Spiral Builder
The Golden Spiral is a famous mathematical curve admired for its geometric elegance and aesthetic appeal. It has been of interest not just to mathematicians, but also artists, architects, and other creative types. While claims about its prevalence in nature are often exaggerated, we can all agree that it looks quite nice regardless!
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The Golden Spiral is formally defined as: a logarithmic spiral that expands outward by a factor of the golden ratio (φ ≈ 1.618) for every quarter turn it makes.
We can create a very close approximation of a Golden Spiral by first subdividing a Golden Rectangle (a rectangle whose ratio of its long to its short side is φ) into a square and another Golden Rectangle, ad infinitum. Then, we simply use a compass or computer to draw a quarter-circle arc through each of the squares, creating the spiral.
Use the left and right arrow keys, or the 'Next' and 'Back' buttons, to subdivide the rectangles. Then press the 'Show Spiral' button (or 's' on your keyboard) to reveal the Golden Spiral.
If you'd like to see a TRUE Golden Spiral drawn in Desmos, click here.