The CW releases 12 photos from season 3 episode 4 of The Flash, set to air on October 25, 2016!
You can read the official synopsis for this episode of The Flash below. Episode 304, “The New Rogues” is directed by Stefan Pleszczynski and written by Benjamin Raab & Deric A. Hughes. The episode is set to air on Tuesday, Oct 25, 2016 at 8/7c, only on the CW network.
WENTWORTH MILLER RETURNS AS CAPTAIN COLD; MIRROR MASTER AND THE TOP BATTLE WITH THE FLASH — Barry (Grant Gustin) continues to train Jesse (guest star Violett Beane) and when a new meta human, Mirror Master (guest star Grey Damon), appears on the scene he lets her tag along. Mirror Master has teamed up with his old partner, Top (guest star Ashley Rickards), and is looking for Snart (Wentworth Miller) to even a score. Jesse is quick to join the chase but defies one of Barry’s orders which results in disastrous consequences.
In math, a group is a particular collection of elements. That might be a set of integers, the face of a Rubik’s cube–which we’ll simplify to a 2x2 square for now– or anything, so long as they follow 4 specific rules, or axioms.
Axiom 1: All group operations must be closed, or restricted, to only group elements. So in our square, for any operation you do—like turn it one way or the other—you’ll still wind up with an element of the group. Or for integers, if we add 3 and 2, that gives us 1—4 and 5 aren’t members of the group, so we roll around back to 0, similar to how 2 hours past 11 is 1 o’clock.
Axiom 2: If we regroup the order of the elements in an operation, we get the same result. In other words, if we turn our square right two times, then right once, that’s the same as once, then twice. Or for numbers, 1+(1+1) is the same as (1+1)+1.
Axiom 3: For every operation, there’s an element of our ground called the identity. When we apply it to any other element in our group, we still get that element. So for both turning the square and adding integers, our identity here is 0. Not very exciting.
Axiom 4: Every group element has an element called its inverse, also in the group. When thetwo are brought together using group’s addition operation, they result in the identity element, 0. So they can be thought of as cancelling each other out. Here 3 and 1 are each other’s inverses, while 2 and 0 are their own worst enemies.
So that’s all well and good, but what’s the point of any of it? Well, when we get beyond these basic rules, some interesting properties emerge. For example, let’s expand our square back into a full-fledged Rubik’s cube. This is still a group that satisfies all of our axioms, though now with considerably more elements, and more operations—we can turn each row and column of each face.
Each position is called a permutation, and the more elements a group has, the more possible permutations there are. A Rubik’s cube has more than 43 quintillion permutations, so trying to solve it randomly isn’t going to work so well. However, using group theory we can analyze the cube and determine a sequence of permutations that will result in a solution. And, in fact, that’s exactly what most solvers do, even using a group theory notation indicating turns.
From the TED-Ed Lesson Group theory 101: How to play a Rubik’s Cube like a piano - Michael Staff
The Trapentrix is a strange little Rubik’s-style puzzle designed and 3D printed by Timur Evbatyrov. It’s irregularly shaped and has only 2 moves (120-degree turns of the yellow or white triangular faces). Despite this, the shape is always preserved and both turns are always possible.
Like other twisty puzzles, one can analyze the underlying group structure. Brandon Enright over at the TwistyPuzzles.com forum has done just that
(link to his post here)
and discovered something rather odd. The 18 star point pieces form 2 non-intersecting orbits of 9 pieces each (i.e. some pieces can never exchange places with some others). That itself is not unusual. What is unusual is that one of these orbits has a subgroup structure of the Ree(3) group - an incredibly complicated group of order 1512. Brandon notes:
One orbit of the points forms a group so crazy one of Wikipedia’s descriptions of it is “exceptionally hard to characterize” and “a simplified construction of the […] groups, as the automorphisms of a 7-dimensional vector space over the field with […] elements preserving a bilinear form, a trilinear form, and a bilinear product"”
There is frankly no reasonable explanation for why this subgroup should appear. Subgroups of twisty puzzles groups are typically fairly simple, such as permutation groups, alternating groups, or cyclical groups (note: simple here does not refer to “simple groups” but rather “easy to comprehend”). For example, the orbits of the Helicopter Cube are just the permutation group on 6 elements. The appearance of such a strange and complicated subgroup within the Trapentrix is puzzling indeed!
I was finally able to draw my demon guardian once again!And i also finally gave him a surname!And oh my,now that i see the first drawing of him and this one,side by side,there are visible changes haha I really love my bby! <3
If you are curious,here was my first reference sheet of him! [Click here]
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