Fibonacci golden spiral

An SVG construction of a golden rectangle tiled by Fibonacci squares (1, 1, 2, 3, 5, 8, 13, 21, 34). In each square we draw a quarter–circle so that the arcs meet at shared corners and wind smoothly. Here the spiral is mirrored relative to the usual textbook drawing (it turns the opposite way).

A checker at the end verifies that the side lengths follow the Fibonacci rule, that the squares exactly tile the rectangle (no overlap), and that the rectangle’s aspect ratio matches the golden ratio built from the last two Fibonacci numbers.

1. Start with two unit squares. Each new square is attached along the long side of the current rectangle, rotating the attachment direction by 90° each time. This produces side lengths that follow the Fibonacci sequence and a bounding rectangle of 55 by 34.
2. Inside every added square, draw a quarter–circle centered at the corner that touches the previous rectangle. Reversing the sweep direction mirrors the spiral while keeping the arcs continuous at each shared corner.