Number Commands

AffineRatio

AffineRatio[Point A, Point B, Point C]: Returns the affine ratio λ of three collinear points A, B, and C, where C = A + λ * AB.

Area

Area[Point A, Point B, Point C, ...]: Calculates the area of the polygon defined by the given points A, B, C,…

Area[Conic c]: Calculates the area of a conic section c (circle or ellipse).

 

Note:

·        In order to calculate the area between two function graphs, you need to use the command Integral.

·        Also see tool mode_area_32 Area

AxisStep

AxisStepX[]: Returns the current step width for the x-axis.

AxisStepY[]: Returns the current step width for the y-axis.

 

Note: Together with the Corner and Sequence commands, the AxisStep commands allow you to create custom axes (also see section Customizing Coordinate Axes and Grid).

BinomialCoefficient

BinomialCoefficient[Number n, Number r]: Calculates the binomial coefficient
n choose r.

Circumference

Circumference[Conic]: Returns the circumference of a circle or ellipse.

CrossRatio

CrossRatio[Point A, Point B, Point C, Point D]: Calculates the cross ratio λ of four collinear points A, B, C, and D, where
λ = AffineRatio[B, C, D] / AffineRatio[A, C, D].

Curvature

Curvature[Point, Function]: Calculates the curvature of the function in the given point.

Curvature[Point, Curve]: Calculates the curvature of the curve in the given point.

Distance

Distance[Point A, Point B]: Yields the distance of two points A and B.

Distance[Point, Line]: Yields the distance of the point and the line.

Distance[Line g, Line h]: Yields the distance of the parallel lines g and h.
Note: The distance of intersecting lines is 0. Thus, this command is only interesting for parallel lines.

 

Note: Also see tool mode_distance_32 Distance or Length

GCD

UK English: HCF

 

GCD[Number a, Number b]: Calculates the greatest common divisor of numbers a and b (UK-English: HCF = highest common factor).

GCD[List of Numbers]: Calculates the greatest common divisor of the list of numbers (UK-English: HCF = highest common factor).

Integer Division

Div[Number a, Number b]: Calculates the integer quotient for division of number a by number b.

Integral

Integral[Function, Number a, Number b]: Returns the definite integral of the function in the interval [a , b].
Note: This command also draws the area between the function graph of f and the x-axis.

Integral[Function f, Function g, Number a, Number b]: Yields the definite integral of the difference f(x) - g(x) in the interval [a, b].   
Note: This command also draws the area between the function graphs of f and g.

 

Note: Also see command for Indefinite Integral

Iteration

Iteration[Function, Number x0, Number n]: Iterates the function n times using the given start value x0.      
Example: After defining f(x) = x^2 the command Iteration[f, 3, 2] gives you the result (32)2 = 81.

LCM

LCM[Number a, Number b]: Calculates the least common multiple of two numbers a and b (UK English: LCM = lowest common multiple).

LCM[List of numbers]: Calculates the least common multiple of the elements of the list (UK English: LCM = lowest common multiple).

Length

Length[Vector]: Yields the length of the vector.

Length[Point A]: Yields the length of the position vector of the given point .

Length[Function, Number x1, Number x2]: Yields the length of the function graph in the interval [x1, x2].

Length[Function, Point A, Point B]: Yields the length of the function graph between the two points A and B. 
Note: If the given points do not lie on the function graph, their x-coordinates are used to determine the interval.

Length[Curve, Number t1, Number t2]: Yields the length of the curve between the parameter values t1 and t2.

Length[Curve c, Point A, Point B]: Yields the length of curve c between two points A and B that lie on the curve.

Length[List]: Yields the length of the list which is the number of elements in the list.

 

Note: Also see tool mode_distance_32 Distance or Length

LinearEccentricity

LinearEccentricity[Conic]: Calculates the linear eccentricity of the conic section.
Note: The linear eccentricity is the distance between a conic's center and its focus, or one of its two foci.

LowerSum

LowerSum[Function, Number a, Number b, Number n]: Yields the lower sum of the given function on the interval [a, b] with n rectangles.
Note: This command draws the rectangles for the lower sum as well.

Minimum and Maximum

Min[Number a, Number b]: Yields the minimum of the given numbers a and b.

Max[Number a, Number b]: Yields the maximum of the given numbers a and b.

Modulo Function

Mod[Integer a, Integer b]: Yields the remainder when integer a is divided by integer b.

Parameter

Parameter[Parabola]: Returns the parameter of the parabola, which is the distance of directrix and focus.

Perimeter

Perimeter[Polygon]: Returns the perimeter of the polygon.

Radius

Radius[Circle]: Returns the radius of the circle.

Random commands

RandomBetween[Min Integer, Max Integer]: Generates a random integer between min and max (inclusive).

RandomBinomial[Number n of Trials, Probability p]: Generates a random number from a binomial distribution with n trials and probability p.

RandomNormal[Mean, Standard Deviation]: Generates a random number from a normal distribution with given mean and standard deviation.

RandomPoisson[Mean]: Generates a random number from a Poisson distribution with given mean.

SemiMajorAxisLength

SemiMajorAxisLength[Conic]: Returns the length of the semimajor axis (half of the major axis) of the conic section.

SemiMinorAxisLength

SemiMinorAxisLength[Conic]: Returns the length of the semiminor axis (half of the minor axis) of the conic section.

Slope

Slope[Line]: Returns the slope of the given line.          
Note: This command also draws the slope triangle whose size may be changed on tab Style of the Properties Dialog.

 

Note: Also see tool mode_slope_32 Slope

TrapezoidalSum

UK English: TrapeziumSum

 

TrapezoidalSum[Function, Number a, Number b, Number n]: Calculates the trapezoidal sum of the function in the interval [a, b] using n trapezoids.    
Note: This command draws the trapezoids of the trapezoidal sum as well.

UpperSum

UpperSum[Function, Number a, Number b, Number n]: Calculates the upper sum of the function on the interval [a, b] using n rectangles.          
Note: This command draws the rectangles of the upper sum as well.


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