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Poloidal direction (red arrow) and toroidal direction (blue arrow) A torus of revolution in 3-space can be parametrized as: [2] (,) = (+ ) (,) = (+ ) (,) = . using angular coordinates , [,), representing rotation around the tube and rotation around the torus' axis of revolution, respectively, where the major radius is the distance from the center of the tube to the center of ...
Slicing with the z = 0 plane produces two concentric circles, x 2 + y 2 = 2 2 and x 2 + y 2 = 8 2, the outer and inner equator. Slicing with the x = 0 plane produces two side-by-side circles, (y − 5) 2 + z 2 = 3 2 and (y + 5) 2 + z 2 = 3 2. Two example Villarceau circles can be produced by slicing with the plane 3y = 4z. One is centered at ...
A Doyle spiral of type (8,16) printed in 1911 in Popular Science as an illustration of phyllotaxis. [1] One of its spiral arms is shaded. In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of six tangent circles.
A portion of the curve x = 2 + cos(z) rotated around the z-axis A torus as a square revolved around an axis parallel to one of its diagonals.. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints). [1]
Rotation of an object in two dimensions around a point O. Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point.
Rotating a curve. The surface formed is a surface of revolution; it encloses a solid of revolution. Solids of revolution (Matemateca Ime-Usp)In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary).
A circle (or line) is unchanged by inversion if and only if it is orthogonal to the reference circle at the points of intersection. [5] Additional properties include: If a circle q passes through two distinct points A and A' which are inverses with respect to a circle k, then the circles k and q are orthogonal.
The duocylinder is bounded by two mutually perpendicular 3-manifolds with torus-like surfaces, respectively described by the formulae: + =, + and + =, + The duocylinder is so called because these two bounding 3-manifolds may be thought of as 3-dimensional cylinders 'bent around' in 4-dimensional space such that they form closed loops in the xy - and zw-planes.