Minimalist Posters Of Great Mathematicians.

Neither do I 😀😀

Golf Ball 70,000fps 150mph. 

The straight up physics of deformation at high speeds is fascinating. Although what is also fascinating is the one thing we really take for granted. TIME. The high frames per SECOND is the only thing that makes this possible to view.

This is a visual example of what happens when you can see TIME, AND physics. I think we forget how important time is in our lives, yet it’s one of the most fascinating. Without time you have no-thing.

M-theory

Membrane theory is a relatively new theory in the world of physics. It has been backed by Stephen Hawking as being the only candidate for the complete theory of the universe.

M-theory has been growing very popular in recent years. This is because it ties together the existing string theories into one relatively simple (mathematically) depiction of the universe. The true origins start with the older string theories that came about in the 80’s. This outlined how all the different forms of energy in the universe could be constructed out of hypothetical one dimensional “strings”. The current M-theory now believes in an 11 dimensional space (this was previously 10 in earlier versions of string theories but the introduction of supergravity increased the count to 11). Now we live in a 3D space with a total of four observable dimensions meaning that there are another 5 we cannot detect. Now in string theory, it was hypothesised that depending on how the strings vibrate the might be seen in 3 dimensions as matter, light or gravity. The problem with string theory was that different equations used to describe the vibrations of the strings kept coming out and they all appeared to be correct. Then what happened was M-theory which said that it’s possible that all the equations are describing the same thing but from a different perspective.

My current understanding of M-theory is that there are lots of 2D membranes which are in an 11D space. These two dimensional branes are not fixed in this eleven dimensional space and move around. When they collide a new 2D brane is created and it is thought that when this happens it is similar to a Big Bang. So it’s entirely possible that out universe is really a 2D membrane in an 11D space.

The first image is a Calabi-Yau manifold. It’s a multi-dimensional mathematic structure and is very significant to M-theory, all they have to do is find the “right” one.

Dunno if it has happened, but it’s accurate

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!

Stack ‘em up