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Geometry 183
arcLen
Returns the length of the arc of a curve between two points on
the curve. The curve is an expression, the independent
variable is declared, and the two points are defined by values
of the independent variable.
This command can also accept a parametric definition of a
curve. In this case, the expression is a list of 2 expressions (the
first for x and the second for y) in terms of a third independent
variable.
arcLen(expr, real1, real2)
Examples:
arcLen(x^2, x, –2, 2) returns 9.29….
arcLen({sin(t), cos(t)}, t, 0, π/2) returns
1. 57…
area
Returns the area of a circle or polygon.
area(circle) or area(polygon)
This command can also return the area under a curve
between two points.
area(expr, x=value1..value2)
Examples:
If GA is defined to be the unit circle, then area(GA) returns
.
area(4-x^2/4, x=-4..4) returns 14.666…
coordinates
Given a vector of points, returns a matrix containing the x- and
y-coordinates of those points. Each row of the matrix defines
one point; the first column gives the x-coordinates and the
second column contains the y-coordinates.
coordinates([point1, point2, …, pointn]))
distance
Returns the distance between two points or between a point
and a curve.
distance(point1, point2) or distance(point,
curve)