Using an orange to illustrate an Euler spiral.

quantumaniac:

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).

quantumaniac:

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).

Reblogged from Quantumaniac

isomorphismes:

All right, Φ is straight-up crazy.

  • Φ² = Φ + 1
  •  ⅟Φ = Φ − 1

Not sure which is more awesome - his words or his hair.

Reblogged from Proof
seanivins:

A curve intersecting an asymptote infinitely many times.

seanivins:

A curve intersecting an asymptote infinitely many times.

Reblogged from smoot
onemagnificentfailure:

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?

onemagnificentfailure:

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?