Hyperbolic parabolic shape of mathematical graphics

The hyperbolic parabolic dish is also called the Saddle Surface. Its Equation in the Cartesian coordinate system is:

X, Y, and Z are the variables in the direction of the three coordinate axes of the Cartesian coordinate system, and A and B are constants.

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(1)

vertices = dimension1:64 dimension2:64x = from (-4) to (4) dimension1z = from (-4) to (4) dimension2y = x*x - z*z

 

(2) parameter equation representation

#y = x*x/a/a - z*z/b/bvertices = dimension1:64 dimension2:64u = from (-3) to (3) dimension1v = from (-3) to (3) dimension2a = rand2(0.5, 2)b = rand2(0.5, 2)x = a*(u + v)z = b*(u - v)y = 2*u*v

(3) trigonometric function representation

vertices = D1:64 D2:64u = from (0) to (2*PI) D1v = from (0) to (3) D2a = rand2(0.5, 1)x = v*sin(u)z = v*cos(u)y = a*v*v*sin(u*2)

 

(4) Multiplication

If the hyperbolic parabolic

Follow +ZThe equation is:

If so, it is simplified:

.

Finally, let's see the hyperbolic parabolic

.

It is equal to the following surface:

Therefore, it can be regarded as the geometric representation of the multiplication table.

vertices = dimension1:64 dimension2:64x = from (-4) to (4) dimension1z = from (-4) to (4) dimension2y = x*z