ssrs barcode font download The following example rotates the curve z = x2 about the z-axis, completely and partially. in Software

Drawer QR Code 2d barcode in Software The following example rotates the curve z = x2 about the z-axis, completely and partially.

The following example rotates the curve z = x2 about the z-axis, completely and partially.
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Graphics` SurfaceOfRevolution[x2, {x, 0, 3}]; SurfaceOfRevolution[x2, {x, 0, 3}, {p, 0, 3o/2}];
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The option RevolutionAxis allows rotation about axes other than the z-axis.
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RevolutionAxis {x, z} rotates the curve about an axis formed by connecting the origin to the point (x, z) in the x-z plane. RevolutionAxis {x, y, z} rotates the curve about an axis formed by connecting the origin to the point (x, y, z) in space.
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EXAMPLE 21
Graphics` SurfaceOfRevolution[x2, {x, 0, 3}, RevolutionAxis {1, 0}, BoxRatios {1, 1, 1}, AxesLabel {"x", "y", "z"}] SurfaceOfRevolution[x2, {x, 0, 3}, RevolutionAxis {1, 1, 1}, BoxRatios {1, 1, 1}, AxesLabel {"x", "y", "z"}]
5 y 5 0
5 z 0 5
0 1 x 2 3
0 x 5
The curve z = x2 is rotated about the line connecting the points (0, 0, 0) and (1, 0, 0).
The curve z = x2 is rotated about the line connecting the points (0, 0, 0) and (1, 1, 1).
Three-Dimensional Graphics
SOLVED PROBLEMS
5.20 Construct a 3 dimensional bar chart depiction of Pascal s triangle for n = 7.
SOLUTION
Pascal s triangle is a representation of the binomial coefficients c(n, k ) =
k 0 0 1 n 2 3 4 5 6 7 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 1 3 6 10 15 21 1 4 10 20 35 1 5 15 35 1 6 21 1 7 1 1 2 3 4 5 6 7
n! . k !(n k )!
c[n_, k_] =
n! ; k!(n k)!
list = Table[c[n, k], {n, 0, 7}, {k, 0, n}];
g = BarChart3D[list, BarSpacing {.5, 2}]
5.21 Construct a scatter plot of the points on the helix x = sin 2t , y = cos 2t , z = t for t between 0 and 10 in increments of .25.
SOLUTION
list = Table[{Sin[2t], Cos[2t], t}, {t, 0, 10, .25}]; ListPointPlot3D[list, PlotStyle PointSize[.03], BoxRatios {.25, .25, 1}, Axes False]
Three-Dimensional Graphics
5.22 Construct the surface of revolution obtained by rotating the curve z = sin x, 0 x 2 , about (i) the z-axis and (ii) the x-axis.
SOLUTION
Graphics` SurfaceOfRevolution[Sin[x], {x, 0, 2 o}, Ticks False, AxesLabel {"x", "y", "z"}] SurfaceOfRevolution[Sin[x], {x, 0, 2 o}, RevolutionAxis AxesLabel {"x", "y", "z"}]
{1, 0}, Ticks False,
z y x x y
5.23 Sketch the surface obtained by rotating the curve z = x2, 0 x 1, about the line z = x.
SOLUTION
Graphics` SurfaceOfRevolution[x2, {x, 0, 1}, RevolutionAxis {1, 1}, AxesLabel {"x", "y", "z"}, Ticks False]
Three-Dimensional Graphics
5.4 Standard Shapes 3D Graphics Primitives
Graphics3D[primitives] or Graphics3D[primitives, options] creates a three-dimensional graphics object.
The standard primitives are
Cuboid[{x, y, z}] is a three-dimensional graphics primitive that represents a unit cuboid (cube) with a corner at (x, y, z) with edges parallel to the axes. , Cuboid[{x1, y1, z1}, {x2, y2, z2}] represents a cuboid (parallelepiped) whose opposite corners are (x1, y1, z1) and (x2, y2, z2). Line[{x1, y1, z1}, {x2, y2, z2},...] draws a sequence of line segments connecting the , points (x1, y1, z1), (x2, y2, z2) . . . Point[{x, y, z}] plots a single point at coordinates (x, y, z). Polygon[{x1, y1, z1}, {x2, y2, z2},...] draws a filled polygon with coordinates (x1, y1, z1), , (x2, y2, z2) . . . Text[expression, {x, y, z}]creates a graphics primitive representing the text expression, centered at position (x, y, z) .
EXAMPLE 22
Graphics3D[{Cuboid[{0, 0, 0}], Cuboid[{1, 1, 1}, {2, 3, 4}]}, Axes True, Ticks {{0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}}]
30 1 2 1 0 4 2
Three-Dimensional Graphics
EXAMPLE 23
vertices = {{0, 0, 0}, {2, 2, 0}, {0, 2, 1}, {0, 0, 2}}; Graphics3D[Polygon[vertices], Axes True, Ticks {{0, 1, 2}, {0, 1, 2}, {0, 1, 2}}]
2 1 0 2
0 0 1 2
Sphere[{x, y, z}, r] defines a sphere of radius r centered at {x, y, z}. Cylinder[{{x1, y1, z1}, {x2, y2, z2}}, r] defines a cylinder of radius r around the line from {x1, y1, z1} to {x2, y2, z2}. Cone[{{x1, y1, z1}, {x2, y2, z2}}, r] defines a cone with base radius r centered at {x1, y1, z1} and a tip at {x2, y2, z2}. Additional three-dimensional graphics commands allow for convenient drawing of other standard shapes. Only Cylinder, Cone and Sphere are available in the Mathematica kernel. DoubleHelix, Helix, OutlinePolygons, PerforatePolygons, RotateShape, ShrinkPolygons, Torus, TranslateShape, and WireFrame were available in previous versions of Mathematica and are now available either in the legacy package Graphics` or on the Web at library.wolfram.com/infocenter/MathSource/6793. If downloaded, the package Shapes.m should be placed in the folder C:\Program Files\Wolfram Research\Mathematica\x.x\AddOns\LegacyPackages\Graphics Note: A warning will be displayed when this package is loaded. It may be safely ignored. To eliminate this message, execute the following prior to loading the package: Off[General obspkg];
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