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2. Solid of revolution - Wikipedia

   en.wikipedia.org/wiki/Solid_of_revolution

   Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration.To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness δx, or a cylindrical shell of width δx; and then ...

3. Spheroid - Wikipedia

   en.wikipedia.org/wiki/Spheroid

   The oblate spheroid is the approximate shape of rotating planets and other celestial bodies, including Earth, Saturn, Jupiter, and the quickly spinning star Altair. Saturn is the most oblate planet in the Solar System , with a flattening of 0.09796. [ 5 ]

4. Rotational symmetry - Wikipedia

   en.wikipedia.org/wiki/Rotational_symmetry

   Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

5. Catenoid - Wikipedia

   en.wikipedia.org/wiki/Catenoid

   A catenoid A catenoid obtained from the rotation of a catenary. In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). [1] It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. [2]

6. Orientation (geometry) - Wikipedia

   en.wikipedia.org/wiki/Orientation_(geometry)

   Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it.. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]

7. Einstein problem - Wikipedia

   en.wikipedia.org/wiki/Einstein_problem

   The tiles are colored according to their rotational orientation modulo 60 degrees. [1] (Smith, Myers, Kaplan, and Goodman-Strauss) In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way.