Example with a = b = c = 1 Illustration of the wedge as a control surface described by a line item.
The wig of Wales is an object with a separate shape. The special thing is that it fits through all three openings, circle, square and triangle. The form is named after the mathematician John Wallis. The wig of Wales is an example of a control surface. This wedge is formed from a circle with diameter d and a line piece of length d, the center of which is perpendicular to the center of the circle, at height d. The wig descriptions are all parallel to the centerline plane of the line piece and connect a point of the line piece with a point of the circle. The cross-sections of the wedge with a plane parallel to a plane of the circle are ellipses.
The wedge is used to show that a spatial figure in the direction of each of the three dimensions can look totally different.
The surface can be analytically described with the parametric equations: x = v cos u , Y = v without u , from = c a 2 & # x2212; b 2 cos 2 u . {\displaystyle x=v\cos u,\quad y=v\sin u,\quad z=c{\sqrt {a^{2}-b^{2}\cos ^{2}u}}.\,}
where a, b and c represent constants, u and v the variable parameters and x, y and z are the cartesian coordinates.
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