Ever seen a Riemann Sum in 3D?
Anonymous said: is there any way we could get rainbow spinners on a white background? thanks!
Signal Collection and Parabolic Reflectors
A reflector is a type of antenna that receives and focuses various types of signals. Reflectors have numerous applications, from satellite dishes and telescopes, to long-distance microphones and car headlights. One common feature of these examples is their parabolic shape, giving them the name parabolic reflectors.
It turns out that paraboloids are the perfect shape for focusing signals from distant sources. When pointed directly at the the incoming signal, a parabolic reflector (GIF 1) collects the signal to a single focal point, where a receiver, called a feed horn, is placed to collect the focused transmission.
In many applications, parabolic reflectors are too costly to produce, so spherical reflectors (GIF 2) are used instead. The disadvantage of spherical reflectors is that they have multiple focal points, and therefore produce blurry results.Mathematica code posted here.
This code is incredibly messy and I guarantee there’s a better way to calculate this. Please contact me if you have suggestions!
- for the purpose of understanding how this works we are going to imagine that something is trying pull an up quark from a proton which is made from 2 ups and 1 down quark.
- As you try to pull the up quark from the proton a tube of energy is formed between the proton and the up quark.
- eventually the tube of energy becomes enough for matter-anti-matter creation with an up and an anti-up quark.
- the up quark goes back to the proton meaning that the proton has always stayed whole and the anti-up quark joins the up quark that was separated from the proton to create a meson.
- this means that is is impossible to ever have a quark by itself.
- the quarks themselves are make up 8MeV while quark confinement generates about 930MeV meaning that most of our mass actually comes from quark confinement.
An Infinite series sequence shown in an equilateral Triangle.
it can be represented mathematically as:
The double pendulum is chaotic: the behaviour of the system is extremely sensitive even to small perturbations. Notice for instance how the two pendulums in the animation start at almost the same position, but their motion drastically drifts apart soon.
Mathematica code by fouriestseries.
“Il n’est pas certain que tout soit incertain.
(Translation: It is not certain that everything is uncertain.)”
― Blaise Pascal
Pascal’s triangle is basically my favorite thing. See what happens if you color in the prime numbers, or color different based on the numbers mod 3 or 4. So much to do!
Have you ever noticed the refraction of light in a cup of coffee?
The envelope of light rays reflected or refracted by a curved surface is called a caustic (from the Latin causticus, “burning”); more concrete a catacaustic in case of reflection, and a diacaustic in case of refraction. The caustic is a curve or surface to which each of the light rays is tangent. In case of a circle, the resulting shape is a cardioid.
Wolfram MathWorld provides a list of famous catacaustics.
Rainbows are familiar examples of caustics as well!