A convex regular polyhedron.

Their beauty is a classification type result as stated at classification of regular polytopes.

Agriculture is not the official definition of the age. But it is good enough. Likely related to the official end of glaciations thing.

Full set of all possible special relativity symmetries:

In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.

There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.

The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.

The first working one in 1947 by John Bardeen and walter Brattain in Bell Labs Murray Hill.

People had already patented a lot of stuff before without being able to make them work. Nonsense.

As the name suggests, this is not very sturdy, and was quickly replaced by bipolar junction transistor.

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This section discusses the pre-photon understanding of the polarization of light. For the photon one see: photon polarization.

polarization.com/history/history.html is a good page.

People were a bit confused when experiments started to show that light might be polarized. How could a wave that propages through a 3D homgenous material like luminiferous aether have polarization?? Light would presumably be understood to be analogous to a sound wave in 3D medium, which cannot have polarization. This was before Maxwell's equations, in the early 19th century, so there was no way to know.

A device that modifies photon polarization.

As mentioned at Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)", it can be modelled as a bra.

The science that studies cell.

Discovered by Marie Curie, published July 1999.

TODO definition. Appears to be isomers

Example:

By default, we think of polynomials over the real numbers or complex numbers.

However, a polynomial can be defined over any other field just as well, the most notable example being that of a polynomial over a finite field.

For example, given the finite field of order 9, $GP(3)$ and with elements $\{0,1,2\}$, we can denote polynomials over that ring aswhere $x$ is the variable name.

For example, one such polynomial could be:and another one:Note how all the coefficients are members of the finite field we chose.

Given this, we could evaluate the polynomial for any element of the field, e.g.:and so on.

We can also add polynomials as usual over the field:and multiplication works analogously.

The dot product is a positive definite matrix, and so we see that those will have an important link to familiar geometry.

TODO understand this stuff: