EngliSea > M > math > Litionary
◎◎◎ complement ⪢⪢
When two angles are complementary, we say that one angle is the _____ of the other. #math
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◎◎◎ complementary ⪢⪢
If two angles are _____ , then the sum of their measures is 90 degrees. → measure #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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◎◎◎ congruent ⪢⪢
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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.
5079#20854 SIBLINGS CHILDREN 20854
Songs in Easy English
○○○ 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
5079#1780 SIBLINGS CHILDREN 1780
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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intereststart off
irrational number
Irrational numbers can't be expressed as the ratio of two integers. #math
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◌◌◌ Limit
The limit of f of x as x approaches a is L.
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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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Linear systems
A collection of 2 or more linear equations
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○○○ linearize ⪢⪢
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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
○○○ logarithm ⪢⪢
When we say "log base b of x equals y", we are saying that b to the y equals x. ┆ x⍻b = y ➔ b˄y = x #math
○○○ logarithm ⪢⪢
Or you can say "If I raise b to the power of y, I'm going to get x." #math
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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
5079#28240 SIBLINGS CHILDREN 28240
○○○ 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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◌◌◌ loop
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○○○ Lorenz Gauge ⪢⪢
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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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mathematical notation
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◌◌◌ matrix
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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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Pascal's Triangle
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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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○○○ power rule ⪢⪢
(x˄n)ᐁx = n·x˄(n−1) #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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◌◌◌ Quadrilateral
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○○○ quadrilateral ⪢⪢
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○○○ rational number ⪢⪢
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○○○ rectangle ⪢⪢
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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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Taylor and Maclaurin Series
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trianglestrianglesacuteequilateral triangleisoscelese triangleobtuse triangleright trianglescalene triangle
○○○ β ⪢⪢
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bubonicChristoph GrienbergerFrancois VieteLudolph van Ceulenπ
○○○ 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° ⪢⪢
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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
5079#28243 SIBLINGS CHILDREN 28243
√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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