This Is Where I Spent My Weekend. Taken On Colorado State Route 82 Between Aspen And Independence Pass.

The relationship between sine and cosine.

If you like this check out “How a Fourier series approximates a square wave.”

In the creative mathematics, the role of proof is in no way restricted to its function of carrier of conviction. Otherwise, there would be no need for Carl Friedrich Gauss to consider eight (!) different proofs of the law of quadratic reciprocity. One metaphor of proof is a route, which might be a desert track boring and unimpressive until one finally reaches the oasis of ones destination, or a foot path in green hills, exciting and energizing, opening great vistas of unexplored lands and seductive offshoots, leading far away even after the initial destination point has been reached.

Yuri Manin, Foundations as Superstructure (Reflections of a practicing mathematician)

No road is long with good company.

Turkish Proverb (via fyp-philosophy)

IIRC, this is a computer model for what's going to happen when the Milky Way (our galaxy) collides with the Andromeda galaxy in a couple billion years. So yeah, that's going to be us.

Another animation of the fractal Harriss spiral. This exploits the plastic number (1.3247…) a number whose cube is itself plus one. This number is considered by some to be the forgotten cousin of the golden ratio (whose square is itself plus one).

The planet Mars on September 25, 1977, as seen by the Viking 2 lander.

(NASA)