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22 Cards in this Set
- Front
- Back
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O
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1
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OO
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-x^2 -x^-2
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OOO
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x^4 + 2 + x^-4
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Jones Polynomial Formula
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(x^3)^-write < >
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computing linking number
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RH's + LH's = X/2 = [x] = x
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when should mirror images be equal?
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when both images have a crossing number which is even
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tricolorability
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1) can't be all one color
2) each crossing must have 3 different colors 3) each strand must be one solid color |
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knot diagram and its mirror image relation
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a knot diagram and it mirror image have the same c#, but opposite crossings
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equilateral triangle
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r1m1 = m1r1^2
m1^2 = 1 r1^3 = 1 |
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translation
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points/figure slide in direction up/down or left/right equally distanced
no fixed points |
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rotation
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points/figure rotates or turns around a fixed point (rotocenter) with equally distanced points
fixed point: rotocenter |
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reflection
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points/figure reflect or are flipped to show the mirror image along the fixed mirror line with equally distanced points
fixed point: mirror line |
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rot. + rot.
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rot. or trans.
angle 1 + angle 2 = 0 --> translation angle 1 + angle 2 doesn't equal 0 --> rotation |
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rigid motion
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preserves the distances and relationships between points
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only rigid motion with a single fixed point
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rotation
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changing the order in which you combine two rotations (r then s vs. s then r)
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changes the center of the resulting rotation as well as the angle
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which point can be fixed by all the symmetries of the square?
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none
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# of basic symmetries of shape n
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2n
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transl. + transl.
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transl.
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transl. + rot.
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rot.
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refl. + refl.
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transl. or rot.
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fibonacci sequence
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need 2 starting terms
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