 EngliSea > math > Litionary

••• Circle
○ Radius, Diameter, Chord, Circumference, Sector
3796 Complementary Angle
If two angles are complementary, then the sum of their measures is 90 degrees.
9684

complex conjugate ▷▷▷
The complex conjugate of a complex number is just the same number but with the sign in between the two terms reversed.
13421 Complex Number ▷▷▷
A complex number 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.
9607 Composite Number ▷▷▷
It is a composite number when it can be divided evenly by numbers other than 1 or itself.
9580 Convergence and Divergence
The Return of Sequences and Series
5172 Converse
Switching the hypothesis and conclusion of a conditional statement.
3732 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.
5291 Dimension
The number of dimensions is how many values are needed to locate points on a shape.
5047 Dot Product
Given two nonzero vectors in two or three dimensions, their dot product is the product of the magnitudes times cosine of the angle between the two vectors.
5288 Factorial, Permutation and Combination (Choose)
Factorial n! = ｢k Πk=1,n｣ Permute ｢nPr｣ = n!/(n−r)! = ｢k Πk=(n−r+1),n｣ Choose ｢nCr｣ = ｢nPr｣/r! = n!/((n−r)!·r!)
3735 FOIL
Firsts, Outers, Inners, Lasts
9442

genus ▷▷▷
16023 Golden Section ▷▷▷
It was the Greek mathematician Euclid who produced the first precise description of the 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.
1780 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.
3658 Interest
Simple & Compound Interest
5156 Irrational Number
Irrational numbers can't be expressed as the ratio of two integers.
9591 Limit
The limit of f of x as x approaches a is L.
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.
5177 Linear systems
A collection of 2 or more linear equations
3810 Logarithm ▷▷▷
What power do you have to raise b to in oder to get x? ❶ b˄y = x ❷ x˅y = b ❸ x⍻b = y
3784 COMMENT

Logarithm ▷▷▷
x⍻b = y ○ 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.
6085 COMMENT

Logarithm
x⍻b = y ○ What is the power that I should raise this base to in order to get this number?
9636 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.
9716 Matrix
A rectangular array of numbers
3811

mold ▷▷▷
16021 Number, Numeral and Digit
A number is account or measurement. It is really an idea in our minds. A numeral is a symbol or a name that stands for a number. A digit is a single symbol used to make numerals. Digits make up numerals and numerals stand for an idea of a number just ...
8945 Partial derivative
(1) partial derivative of f with respect to x, f sub x, partial f over partial x. (2) f sub xx, partial squared f over partial x squared. (3) f sub xy, partial squared f over partial y partial x.
5077 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.
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.
5030

Point
We represent points with little dots and some capital letter, making sure to realize that the dot we draw is infinitely larger than the point it is meant to represent.
6290 Power Rule
(x˄n)ᐁx = n·x˄(n−1)
9686 Prime Number ▷▷▷
It is a prime number when it can't be divided evenly by any number except 1 or itself.
9581

Prime Number ▷▷▷
A prime number is a positive integer that is divisible only by itself and 1.
9582 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.
9583 Quadrilateral
A four-sided polygon ○ Rhombus, Rectangle, Square, Trapezoid, Parallelogram
5167 Rational Number
Any number that can be expressed as the ratio of two integers.
9590 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.
5178 Trigonometric Functions
Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent
3457 Vector
A mathematical construct that has both magnitude and direction
3815 π ≈ 3.14
The ratio of a circle's circumference to its diameter
9593 π(n)
π(n) is the number of primes less than or equal to n.
9466 Φ ≈ 1.618
Keplar observed that the relationship between a number in Fibonacci sequence and the previous number more and more closely approaches the irrational number Φ the longer the sequence is continued and Φ describes nothing other than the golden section.
9464 ψ ≈ 137.5°
Divides the angle of 360° in the proportions of the golden section. As angles smaller than 180° proved more handy in practice, the smaller of the resultant angles is usually called golden angle.
9465 √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.
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