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Complementary Angle

If two angles are complementary, then the sum of their measures is 90 degrees.

9684

If two angles are complementary, then the sum of their measures is 90 degrees.

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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

The complex conjugate of a complex number is just the same number but with the sign in between the two terms reversed.

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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

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.

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Composite Number ▷▷▷

It is a composite number when it can be divided evenly by numbers other than 1 or itself.

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It is a composite number when it can be divided evenly by numbers other than 1 or itself.

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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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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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Dimension

The number of dimensions is how many values are needed to locate points on a shape.

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The number of dimensions is how many values are needed to locate points on a shape.

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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

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.

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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!)

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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!)

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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

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

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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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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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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 ▷▷▷

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

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

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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

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

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Logarithm

x⍻b = y ○ What is the power that I should raise this base to in order to get this number?

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x⍻b = y ○ What is the power that I should raise this base to in order to get this number?

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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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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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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

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

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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.

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(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.

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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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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.

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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.

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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.

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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.

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Prime Number ▷▷▷

It is a prime number when it can't be divided evenly by any number except 1 or itself.

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It is a prime number when it can't be divided evenly by any number except 1 or itself.

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Prime Number ▷▷▷

A prime number is a positive integer that is divisible only by itself and 1.

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A prime number is a positive integer that is divisible only by itself and 1.

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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.

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○ π(n) is asymptotically equivalent to x/log x. ○ Of the first n integers, roughly 1/log n of them would be prime.

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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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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 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.

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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.

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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

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.

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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.

9592

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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