Using an orange to illustrate an Euler spiral.
A collection of mathematical fascinations, not strictly limited to the subject itself but also people's interactions and interpretations. My curiosity for the subject is infinite, but I try to stay away from the sciences. The thrill lies in the purity, not the application.
Info on my icon can be found here.
Using an orange to illustrate an Euler spiral.
Spiral of Theodorus
First constructed by Theodorus of Cyrene, the spiral (also called the square root spiral, Einstein spiral or Pythagorean spiral) is composed of contiguous right triangles. It is begun with an isosceles right triangle with each leg having a length of 1 - then another right triangle is formed next to it with one leg being the hypotenuse of the prior triangle and the other leg having a length of 1.Thus, each successive nth triangle has side lengths √n and 1, with a hypotenuse of √(n + 1).
All right, Φ is straight-up crazy.
- Φ² = Φ + 1
- ⅟Φ = Φ − 1
Not sure which is more awesome - his words or his hair.
GOLDEN RATIO
I’ve been going through some old school notebook entries about the Golden Ratio which I hope to finish “touching up” soon to post here. In the interim you may have noticed I’ve been posting artwork which illustrates the principle in situ. The Ratio is essentially the DNA formula for the structure of the Universe. As an artist, scientist, mathematician, even knitter, the Ratio, “Spiral”, or “Rule” (just a few ways it’s referenced) features heavily in life and the way in which it is experienced. Fibonacci anyone?