Category

# Mathematics

54 items

### Angular Frequency

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Angular frequency (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency and pulsatance) is a scalar measure of rotation rate.

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### Angle Subtended

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The angle formed between the bottom and top of an object at a distance from the observer.

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### Arc Length on a Circle

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The arc length on a circle is the length of arc, or segment, of the circle.

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### Area of a Regular n-Gon

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A regular n-gon is a plane figure that is bounded by a chain of n straight line segments of equal length closing in a loop to form a closed polygonal chain.

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### Birthday Problem Approximation

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The birthday problem, or birthday paradox, concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.

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### Cartesian-to-Polar-Coordinates Equations

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The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. These can be directly trans...

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### Circle Chord Length by Angle and Radius

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A circle chord is a line segment whose endpoints lie on the circle.

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### Circle Chord Length by Apothem and Sagitta

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A circle chord is a line segment whose endpoints lie on the circle. The sagitta is the distance from the center of the arc bridged by the chord to the center of the chord. The apothem is the distance from the center o...

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### Circle Sector Area

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The area of a sector of a circle depends on the size of that circle and the size of the arc for that sector.

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### Circumference Formula

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A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the center.

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### Cohen's d

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Cohen's d is defined as the difference between two means divided by a standard deviation for the data.

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### Complement Probability

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In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur.

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### Cuboid Volume

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The volume of a cuboid is the quantity of three-dimensional space enclosed by it.

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### Cylinder Total Surface Area

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A cylinder is the surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder. Surface area refers to the area covered by all sides of the cylinder.

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### Cylinder Lateral Surface Area

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A cylinder is the surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder. Lateral surface area refers to the area covered by the curved side of the cylinder.

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### Cylinder Volume

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A cylinder is the surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder. The volume is the space enclosed by the cylinder.

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### Eccentricity of an Ellipse

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An ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. The shape of an ellipse (how \"elongated\" it is) is r...

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### Ellipsoid Volume

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An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

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### Euler Characteristic

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The Euler characteristic is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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### Gambling Winnings Using American Odds

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The American odds indicate how much money will be won on a $100 wager.

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### Gambling Winnings Using Fractional Odds

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Fractional odds quote the net total that will be paid out to the bettor, should he or she win, relative to the bet.

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### Gambling Winnings Using Decimal Odds

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Decimal odds quote the ratio of the payout amount, including the original bet, to the bet itself.

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### Glass's δ

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Glass's δ is an estimator of the population effect size that uses only the standard deviation of the second group. An effect size is a quantitative measure of the strength of a phenomenon. A population effect size bas...

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### Golden Ratio

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Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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### Heron's Formula

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Heron's formula (sometimes called Hero's formula) gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin.

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### Law of Cosines

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The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

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### Law of Haversines

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The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.

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### Law of Sines

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The law of sines is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.

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### Law of Tangents

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The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.

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### Logistic Equation

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The logistic equation is used to calculate population growth—the increase in the number of individuals in a population.

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### Log Odds Ratio

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The log odds ratio is a way to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population.

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### Odds Ratio

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The odds ratio is a way to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population.

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### Pooled Standard Deviation

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Pooled standard deviation is the square root of the pooled variance. Pooled variance is a method for estimating the variance of several different populations when the mean of each population may be different, but one ...

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### Pooled Variance

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Pooled variance is a method for estimating the variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.

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### Probability of the Union of Two Events

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The probability of the union of two events depends on the probability of either event and the probability of only one of the events occuring.

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### Pythagorean Theorem

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The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of...

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### Quadratic Equation

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A quadratic equation is any equation having the form a x^2 + b x + c = 0.

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### Rectangle Area

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A rectangle is a quadrilateral with four right angles. Its area is the space within its borders.

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### Rise and Run of Slopes

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The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal.

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### Sample Size for Estimating a Population Mean

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Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.

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### Sample Size for Estimating a Binomial Parameter

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The sample size for estimaitng a binomial parameter estimates the minimum sample size to estimate the binomial parameter.

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### Slope of a Line

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The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

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### Spherical Law of Cosines Using Sides

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The spherical law of cosines is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.

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### Spherical Law of Sines

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The spherical law of sines is an equation relating the angular lengths of the sides of a triangle (any shape) to the sines of its angles.

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### Spherical Law of Tangents

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The spherical law of tangents is a statement about the relationship between the tangents of two angles of a triangle on a sphere and the angular lengths of the opposing sides.

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### Spherical Law of Cosines Using Angles

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The spherical law of cosines is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.

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### Spheroid Volume

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A spheroid is a solid generated by a half-revolution of an ellipse about its major axis (prolate spheroid) or minor axis.

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### Torus Volume

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A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. The volume is the space contained within the resulting surface.

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### Trapezoid Area

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A convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs or the lateral sides...

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### Triangle Area Using Base and Height

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A triangle is a polygon with three edges and three vertices. The area is the space enclosed by the triangle.

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### Vector Projection

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The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolution of a in the direction of b) is the orthogonal projection of a onto a straight line parallel ...

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### Volume of a Solid Sphere

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The volume of a solid sphere is the measure of the space enclosed by it.