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
5079#9684 SIBLINGS CHILDREN 9684

○○○ 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
5079#9607 SIBLINGS CHILDREN 9607

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.
5079#5291 SIBLINGS CHILDREN 5291

○○○ gauge ⪢⪢
But for now you can just think of a gauge as meaning a choice of coordinate system.
5079#20854 SIBLINGS CHILDREN 20854

○○○ 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
5079#5203 SIBLINGS CHILDREN 5203

◌◌◌ 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.
5079#3658 SIBLINGS CHILDREN 3658

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.
5079#3473 SIBLINGS CHILDREN 3473

◌◌◌ 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.
5079#5177 SIBLINGS CHILDREN 5177

Linear systems
A collection of 2 or more linear equations
5079#3810 SIBLINGS CHILDREN 3810

○○○ 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
5079#3784 SIBLINGS CHILDREN COMMENT 3784

○○○ 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
5079#6085 SIBLINGS CHILDREN COMMENT 6085

○○○ logarithm ⪢⪢
Or you can say "If I raise b to the power of y, I'm going to get x." #math
5079#28242 SIBLINGS CHILDREN 28242

○○○ 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
5079#28241 SIBLINGS CHILDREN 28241

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.
5079#9716 SIBLINGS CHILDREN 9716

○○○ mold ⪢⪢
A sphere and a cube are topologically the same thing since you can just kind of mold one into the other. #math
5079#16021 SIBLINGS CHILDREN 16021

◌◌◌ 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.
5079#5031 SIBLINGS CHILDREN 5031

○○○ 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
5079#5030 SIBLINGS CHILDREN 5030

○○○ power rule ⪢⪢
(x˄n)ᐁx = n·x˄(n−1) #math
5079#9686 SIBLINGS CHILDREN 9686

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
5079#20603 SIBLINGS CHILDREN 20603

◌◌◌ 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.
5079#5178 SIBLINGS CHILDREN 5178

○○○ 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
5079#9464 SIBLINGS CHILDREN 9464

○○○ 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
5079#9592 SIBLINGS CHILDREN 9592

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