spiral in a golden rectangle
spiral
As with the sequence of Fibonacci you can draw a spiral in a golden rectangle, based on quarter circles. But now you start in reverse order: instead of creating larger squares each step you construct smaller squares in a fixed golden rectangle.
- Draw a rectangle with ratios and 1.
- Drawn within the rectangle a square with side the widt of the rectangle. Now draw a quarter circle into the square.
- The remaining part of the rectangle on its turn is again a golden rectangle. So again you can create smaller squares and golden rectangles. The result is a spiral.
- as the Fibonacci spiral this isn't a real spiral around a fixed point with a constant in(de)creasing radius. Every quater circle a new center is chosen to draw a circular arc with fixed radius.
- This spiral looks like the Fibonacci spirall, but it's not the same. The reason is the relation between the sequence of Fibonacci and the number . In the golden rectangle the ratio between consecutive sides of the squares always equals . In Fibonacci squares the ratio approaches but is always slightly different.