Sleepysneezeydopeydoc-blog - Physics Nerd

1. Take a circle and draw some points on the boundary. For every point you draw, you must also draw its antipode (point on the opposite side of the circle).

2. Draw some points in the interior wherever you want.  3. Label the points either +1, -1, +2, or -2 as you wish. The only stipulation is that antipodes must have opposite sign.

4. Draw triangles however you want without crossing lines.

Tucker’s Lemma says that you will ALWAYS end up with at least one line that has endpoints of either +1 and -1 or +2 and -2. Try it! More info and proof here.

We possess the real truth 🖖💪🤘

According to NASA, a neighboring star has 7 Earth-like planets in its orbit

Seven Earth-like planets have been found orbiting a sun not too far — in space terms, at least — from our own.

NASA announced Wednesday that the planets resemble Earth in composition and spacing from their star, which means their conditions might be favorable to liquid water and life, Time reported.

“The planets form a very compact system,” Michaël Gillon of Belgium’s University of Liège, said in a teleconference, according to Time. “They are very close to their star and are reminiscent of the system of moons that orbit Jupiter. They could have liquid water and life.”

Astronomers studied the star, Trappist-1 — which, at 39 light years away from Earth, is considered a relative neighbor — for six years, using telescopes located all over the world, plus the Spitzer Space Telescope. Read more (2/22/17 2:04 PM)

follow @the-future-now

Easy win for Tesla 🖖

Modified Leaves: Insect Traps

Carnivorous plants are plants that derive some or most of their nutrients (not energy) from trapping and consuming animals, typically insects. Carnivorous plants have adapted to grow in places where the soil is thin or poor in nutrients, especially nitrogen, such as acidic bogs and rock outcroppings. These carnivorous plants have modified leaves that help to trap and digest prey.

The carnivorous plant in the first picture is a Venus flytrap that belongs to the genus Dionaea. The Venus flytrap has small trigger hairs on the inside of its leaf that cause the trap to close around its prey. The carnivorous plant in the middle picture is a sundew that belongs to the Drosera. Sundews have small tentacles, topped with sticky secretions, that cover the leaves.  Sundews are able to move their tentacles towards the center of the leaf to bring the insect into contact with as many stalked glands as possible. The carnivorous plant in the bottom picture is a  species of North American pitcher plants that are commonly called trumpet pitchers. Insects fall into the pitcher plant and cannot climb out. Meanwhile, digestive enzymes in the pitcher leaf break down the prey.

Modified Leaves Part:   1    2     3     4     5     6

Can you flatten a sphere?

The answer is NO, you can not. This is why all map projections are innacurate and distorted, requiring some form of compromise between how accurate the angles, distances and areas in a globe are represented.

This is all due to Gauss’s Theorema Egregium, which dictates that you can only bend surfaces without distortion/stretching if you don’t change their Gaussian curvature.

The Gaussian curvature is an intrinsic and important property of a surface. Planes, cylinders and cones all have zero Gaussian curvature, and this is why you can make a tube or a party hat out of a flat piece of paper. A sphere has a positive Gaussian curvature, and a saddle shape has a negative one, so you cannot make those starting out with something flat.

If you like pizza then you are probably intimately familiar with this theorem. That universal trick of bending a pizza slice so it stiffens up is a direct result of the theorem, as the bend forces the other direction to stay flat as to maintain zero Gaussian curvature on the slice. Here’s a Numberphile video explaining it in more detail.

However, there are several ways to approximate a sphere as a collection of shapes you can flatten. For instance, you can project the surface of the sphere onto an icosahedron, a solid with 20 equal triangular faces, giving you what it is called the Dymaxion projection.

The Dymaxion map projection.

The problem with this technique is that you still have a sphere approximated by flat shapes, and not curved ones.

One of the earliest proofs of the surface area of the sphere (4πr2) came from the great Greek mathematician Archimedes. He realized that he could approximate the surface of the sphere arbitrarily close by stacks of truncated cones. The animation below shows this construction.

The great thing about cones is that not only they are curved surfaces, they also have zero curvature! This means we can flatten each of those conical strips onto a flat sheet of paper, which will then be a good approximation of a sphere.

So what does this flattened sphere approximated by conical strips look like? Check the image below.

But this is not the only way to distribute the strips. We could also align them by a corner, like this:

All of this is not exactly new, of course, but I never saw anyone assembling one of these. I wanted to try it out with paper, and that photo above is the result.

It’s really hard to put together and it doesn’t hold itself up too well, but it’s a nice little reminder that math works after all!

Here’s the PDF to print it out, if you want to try it yourself. Send me a picture if you do!

The five ingredients of a particle accelerator

Did you know there are over 30,000 particle accelerators in the world? The design of particle accelerators is a creative process. Often it starts with just one person and their concept, but they all tend to have 5 key ingredients.

1 - Particles - where do you get them, how do you make them? Accelerators might use atoms with electrons split off, called ions, or the particles inside atoms themselves: electrons or protons.

2 - Energy - you need an acceleration mechanism, some way of giving the particles a push. Typically this uses electric fields.

3 - Control - once your particles are moving, you need to control them, to move them and focus them where they’re needed. This is generally done with magnetic fields.

4 - Collision - not all particle accelerators are ‘colliders’ in the traditional sense. They don’t all collide beams together like at the LHC. But in almost every case you do need to collide your beam of accelerated particles into something - this might be a fixed target to investigate a sample, or even directly into a person’s body, such as during medical treatments.

5 - Detection - there’s normally not much point doing all of this work unless you can then detect the outcome and learn from it. You need to measure what happens to the beam of particles when they collide with their target.

Find out more in our animation about how to design a particle accelerator.