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complement ⪢⪢
When two angles are complementary, we say that one angle is the _____ of the other.
#math
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complex number ⪢⪢
A _____ is a number that can be expressed in the form a + bi where a and b are real numbers and i is the square root of -1.
#math
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Cross Product
Given two nonzero vectors in two or three dimensions, their cross product is a vector with magnitude equal to the product of the magnitudes of the vectors times the sine of the angle between the vectors and direction perpendicular to the vectors.
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gauge ⪢⪢
But for now you can just think of a gauge as meaning a choice of coordinate system.
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Golden Section ⪢⪢
A length is devided into two parts in such a way that the smaller part is to the larger part in the same proportion as the larger one is to the whole.
#math
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Greek alphabet
Α α
Β β
Γ γ
Δ δ
Ε ε
Ζ ζ
Η η
Θ θ
Ι ι
Κ κ
Λ λ
Μ μ
Ν ν
Ξ ξ
Ο ο
Π π
Ρ ρ ϱ
Σ σ/ς
Τ τ
Υ υ
Φ φ
Χ χ
Ψ ψ
Ω ω
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Integration
With the sum of f of x i times delta x from i equals one to infinity in the limit of n approaching infinity.
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Line
From here, we can construct a one- dimensional object by stringing an infinite number of points along a particular dimension. This object is called a line.
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logarithm ⪢⪢
So if you want to find log base b of x, you're asking "what power you have to raise b to in oder to get x?".
#math
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COMMENT
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logarithm ⪢⪢
With logs, the base of the log raised to the power of what's on the other side of the equal sign will equal the number that the log is operating on. ┆ x⍻b = y ➔ b˄y = x
#math
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logarithm ⪢⪢
By definition, when we say "log base b of x equals y", that's the same thing as saying "b to the y equals x".
#math
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Mathematical Induction
Let P(n) be a statement for each natural number n. If
(a) P(1) is true, and
(b) P(k) true ⇒ P(k+1) true for every natural number k∈ℕ
then P(n) is true for all n∈ℕ.
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mold ⪢⪢
A sphere and a cube are topologically the same thing since you can just kind of mold one into the other. #math
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Plane
By stringing an infinite number of lines along a dimension perpendicular to the line, a two-dimensional object called a plane can be obtained. And then if we string an infinite number of planes in either direction, we get three dimensional space.
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Point ⪢⪢
First we look at a point. This is nothing more than a location in space. It is zero-dimensional, meaning that it has no dimensions of any kind. #math
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prime number theorem
○ π(n) is asymptotically equivalent to x/log x.
○ Of the first n integers, roughly 1/log n of them would be prime. #math
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rhombus ⪢⪢
If all four sides are the same length, we call the shape a _____.
#math #bookmark
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Space
By stringing an infinite number of lines along a dimension perpendicular to the line, a two-dimensional object called a plane can be obtained. And then if we string an infinite number of planes in either direction, we get three dimensional space.
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Φ ≈ 1.618 ⪢⪢
Keplar observed that the relationship between a number in the Fibonacci sequence and the previous number more and more closely approaches the irrational number Φ, the longer the sequence is continued. #math
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ψ ≈ 137.5° ⪢⪢
As angles smaller than 180° proved to be more handy in practice, the smaller of the resultant angles is usually called golden angle. #math
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√2 ≈ 1.414
According to Pythagoras theorem the diagonal length of a square with each side measuring one unit would be square root of two.
The assumption that square root of two could be expressed as a ratio of two integers deduces a contradiction. #math
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