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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. Pappus's centroid theorem - Wikipedia

   en.wikipedia.org/wiki/Pappus's_centroid_theorem

   The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation.. In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of ...

4. Catenoid - Wikipedia

   en.wikipedia.org/wiki/Catenoid

   The catenoid was the first non-trivial minimal surface in 3-dimensional Euclidean space to be discovered apart from the plane. The catenoid is obtained by rotating a catenary about its directrix. [2] It was found and proved to be minimal by Leonhard Euler in 1744. [3] [4] Early work on the subject was published also by Jean Baptiste Meusnier.

5. Spheroid - Wikipedia

   en.wikipedia.org/wiki/Spheroid

   Deformed nuclear shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects. Spheroids are common in 3D cell cultures. Rotating equilibrium spheroids include the Maclaurin spheroid and the Jacobi ellipsoid. Spheroid is also a shape of archaeological artifacts.

6. Rotation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotation_(mathematics)

   The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...

7. NYT ‘Connections’ Hints and Answers Today, Tuesday, January 7

   www.aol.com/nyt-connections-hints-answers-today...

   If you've been having trouble with any of the connections or words in Tuesday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down ...