Olds 88… 1956 Tail Light

End to the universe ends your ideas of infinite

If the big rip or vacuum decay takes place then numbers can’t be infinite, infinity to finite

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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.

Platonic solid: In Euclidean geometry, a Platonic solid is a regular, convex polyhedron with congruent faces of regular polygons and the same number of faces meeting at each vertex. Five solids meet those criteria, and each is named after its number of faces.

An Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices . They are distinct from the Platonic soilds, which are composed of only one type of polygon meeting in identical vertices, and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices.

In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean soild. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865.

The Catalan solids are all convex. They are face-transitive but not vertex-transitive. This is because the dual Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic soilds  and Archimedean soild, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles. Additionally, two of the Catalan solids are edge-transitive: the rhombic dodecahedron and the rhombic triacontahedron. These are the duals of the two quasi-regular Archimedean solids.

Images: Polyhedral Relations by Allison Chen on Behance.

Scientists have created a fluid with negative mass – but what does it tell us?

The fluid, which defies everyday laws of motion, is a rare achievement and provides a platform to study an otherwise hypothetical form of matter

Scientists have created a fluid that exhibits the bizarre property of “negative mass” in an experiment that appears to defy the everyday laws of motion.

Push an object and Newton’s laws (and common experience) dictate that it will accelerate in the direction in which it was shoved.

“That’s what most things that we’re used to do,” said Matthew Forbes, a physicist at Washington State University and co-author of the paper, which shows that normal intuitions do not always apply to physics experiments. “With negative mass, if you push something, it accelerates toward you.”

Negative mass has previously cropped up in speculative theories, including those suggesting the existence of wormholes, a form of cosmological shortcut between two points in the universe. Just as electric charge can be either positive or negative, matter could, hypothetically, have either positive or negative mass.

For an object with negative mass, Newton’s second law of motion, in which a force is equal to the mass of an object multiplied by its acceleration (F=ma) would be experienced in reverse.

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