- line of the ellipse, pencil, eraser.
as the original figure, use an ellipse with major axis a and minor axis b, as shown in Figure 1. If we accept the distance AB equal to 2a, and the distance DC - equal to 2b andellipse rotate around one of these axes can be obtained ellipsoid of rotation.In general, the ellipsoid obtained by deformation of the sphere along the three mutually perpendicular axes.It refers to the surfaces of the second order.The canonical equation of the figure has the form: x ^ 2 / a ^ 2 + y ^ 2 / b ^ 2 + z ^ 2 / c ^ 2 = 1.Secheniyami plane Oxz, Oxy, Oyz are ellipses.There are three types ellipsoid s: triaxial, ellipsoid of revolution and the world.In triaxial ellipsoid and all the different semi-axi
s and y ellipsoid and rotation are only two axis.In the scope of all the half-line with each other are equal.Construction of all three types of ellipsoid s maintained the same pattern.Equation ellipsoid of rotation and has the form: x ^ 2 / a ^ 2 + y ^ 2 / a ^ 2 + z ^ 2 / c ^ 2 = 1. At all the spheres of the semi-axis equal (a = b = c),and its equation looks like this: x ^ 2 + y ^ 2 + z ^ 2 = 1.Trehosny ellipsoid standard described by the equation: x ^ 2 / a ^ 2 + y ^ 2 / b ^ 2 + z ^ 2 /c ^ 2 = 1.
To build ellipsoid you the method of sections, first read the equations that characterize each of the planes: [z = 0 plane Oxy (section - ellipse with semi-axes a and b);[X ^ 2 / a ^ 2 + y ^ 2 / b ^ 2 = 1.[Y = 0 plane Oxz (section - ellipse with semi-axes a and c);[x ^ 2 / a ^ 2 + z ^ 2 / c ^ 2 = 1.[X = 0 plane Ozy (section - ellipse with semi-axes b, and c) [y ^ 2 / b ^ 2 + z ^ 2 / c ^ 2.
receiving section of different size, build in all three planes of the ellipses.We obtain a triaxial ellipsoid .Draw a three-dimensional coordinate system with center at O. initially construct an ellipse in the plane Oxy.To do this, draw an auxiliary parallelogram in which and enter the ellipse.Similarly, Draw, and the remaining two of the ellipse in the Oxz plane and Ozy.After all the ellipses are drawn, delete all auxiliary parallelograms.It now remains to outline the three ellipses around a common line to represent the surface of the ellipsoid well.Invisible lines can also delete and leave visible.The same pattern can be built ellipsoid of revolution and scope.Scope of appearance is a hollow ball.
- how to build a sphere