By Rudenskaya O.G.

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Dividing an angle in radians by Degree converts the angle from radians to degrees. 4 Line Segments 13 We may want to construct lines with certain relationships to another line. For example, the following commands construct lines parallel and perpendicular to a given line through a given point. 4 -4 -2 0 2 4 Line Segments Perhaps it is more familiar to us that a line has a definite start point and end point. Such a line is called a line segment and is represented in Descarta2D as Segment2D[{x0, y0 }, {x1 , y1 }] where (x0 , y0 ) and (x1 , y1 ) are the coordinates of the start and end points, respectively, of the line segment.

If there is but one value of y for a given value of x, y is said to be a single-valued function. If, for a given value of x, y has more than one value, y is said to be multiple-valued. The function f (x) is periodic if f (x + P ) ≡ f (x) for some period, P . Usually it is assumed that P is the least number for which this identity is true. 2 Polynomials A mathematical expression consisting of a sum of various positive integer powers of a variable is called a polynomial. The largest exponent that appears in a polynomial is called the degree of the polynomial.

Nb C b a d A B m AB = c D n Show that for any ABC as shown in the figure above the relationship between the lengths of the labeled line segments is given by a2 m + b2 n = c(d2 + mn). —– Collinear Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . nb Show that the points P1 (r1 , θ1 ), P2 (r2 , θ2 ) and P3 (r3 , θ3 ) in polar coordinates are collinear if and only if −r1 r2 sin(θ1 − θ2 ) + r1 r3 sin(θ1 − θ3 ) − r2 r3 sin(θ2 − θ3 ) = 0. —– Hypotenuse Midpoint Distance.

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4-Quasiperiodic Functions on Graphs and Hypergraphs by Rudenskaya O.G.


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