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The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
In their calculation, Zu used the concept that two solids with equal cross-sectional areas at equal heights must also have equal volumes to find the volume of a Steinmetz solid. And further multiplied the volume of the Steinmetz solid with π/4, therefore found the volume of a sphere as πd^3/6 (d is the diameter of the sphere).
It was a popular problem in the 1920s going back to an anecdote, that Steinmetz had solved the problem of finding the volumes of two intersecting cylinders in very short time but without giving hints to his method (Richard Sutton The Steinmetz problem and school arithmetic, Mathematics Teacher, 50, 1957, 434, reference after Martin Gardner ...
Steinmetz curves for various cases Steinmetz solid (intersection of two cylinders) involving Steinmetz curves (purple) A Steinmetz curve is the curve of intersection of two right circular cylinders of radii a {\displaystyle a} and b , {\displaystyle b,} whose axes intersect perpendicularly.
Charles Proteus Steinmetz (born Karl August Rudolph Steinmetz; April 9, 1865 – October 26, 1923) was an American mathematician and electrical engineer and professor at Union College. He fostered the development of alternating current that made possible the expansion of the electric power industry in the United States, formulating mathematical ...
123Movies, GoMovies, GoStream, MeMovies or 123movieshub was a network of file streaming websites operating from Vietnam which allowed users to watch films for free. It was called the world's "most popular illegal site" by the Motion Picture Association of America (MPAA) in March 2018, [3] [6] before being shut down a few weeks later on foot of a criminal investigation by the Vietnamese ...
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Since the values for the cylinder were already known, he obtained, for the first time, the corresponding values for the sphere. The volume of a sphere of radius r is 4 / 3 π r 3 = 2 / 3 (2 π r 3). The surface area of this sphere is 4 π r 2 = 2 / 3 (6 π r 2). A sculpted sphere and cylinder were placed on the tomb of ...