real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special...

Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space...

shows the intersection of a sphere and a cylinder, which consists of two circles. If the cylinder radius were that of the sphere, the intersection would be...

etc.) or a quadric (sphere, cylinder, hyperboloid, etc.) lead to quadratic equations that can be easily solved. Intersections between quadrics lead...

versus sphere surface)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces...

the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of the cone and...

intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case...

It is the intersection of a sphere with a cylinder that is tangent to the sphere and passes through two poles (a diameter) of the sphere (see diagram)...

swept sphere and the segment that the sphere is swept across). It has traits similar to a cylinder, but is easier to use, because the intersection test...

a second sphere is also a circle, and the sphere's intersection with a concentric right circular cylinder or right circular cone is a pair of antipodal...

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions around a main axis (a chosen directed line) and...

r^{3}} It is the intersection between a plane containing the axis of the cylinder and the cylinder. In the case of the right circular cylinder, the meridian...

Cavalieri's principle, was able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the...

quadric, as this circle is the intersection with the quadric of the plane containing the circle. Any plane section of a sphere is a circular section, if it...

shrinking is called a developable surface. The cylinder, cone and the plane are all developable surfaces. The sphere and ellipsoid do not have developable surfaces...

obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves of the intersection of two cylinders is an ellipse...

etc.) or a quadric (sphere, cylinder, hyperboloid, etc.) lead to quadratic equations that can be easily solved. Intersections between quadrics lead...

Any plane passing through O, inverts to a sphere touching at O. A circle, that is, the intersection of a sphere with a secant plane, inverts into a circle...

accompanying figure of the balanced sphere, cone, and cylinder be engraved upon his tombstone. To find the surface area of the sphere, Archimedes argued that just...

(apex) the point of intersection. However, if the generatrix and axis are parallel, then the surface of revolution is a circular cylinder. In analogy with...

rest of the sphere. The plane z = 0 {\displaystyle z=0} runs through the center of the sphere; the "equator" is the intersection of the sphere with this...

Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The...

dimension Spherical code Soddy's hexlet Cylinder sphere packing Conway, John H.; Neil J.A. Sloane (1999). Sphere Packings, Lattices and Groups (3rd ed.)...

surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional...

cylinder. To glue the ends of the cylinder together so that the arrows on the circles match, one would pass one end through the side of the cylinder....

_{1}\kappa _{2}.} For example, a sphere of radius r has Gaussian curvature ⁠1/r2⁠ everywhere, and a flat plane and a cylinder have Gaussian curvature zero...

of the k-sphere X = Sk, let A and B be two hemispheres of X with intersection homotopy equivalent to a (k − 1)-dimensional equatorial sphere. Since the...

global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. Examples of Riemann surfaces...

In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through the center. In the intrinsic approach,...

circular cylinder or a right circular double cone or a torus of revolution by an inversion (reflection at a sphere). The inversion at the sphere with equation...