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Steinmetz solids are named after mathematician Charles Proteus Steinmetz, [2] who solved the problem of determining the volume of the intersection. However, the same problem had been solved earlier, by Archimedes in the ancient Greek world, [ 3 ] [ 4 ] Zu Chongzhi in ancient China, [ 5 ] and Piero della Francesca in the early Italian ...
A Steinmetz curve is the curve of intersection of two right circular cylinders of radii and , whose axes intersect perpendicularly. In case of a = b {\displaystyle a=b} the Steimetz curves are the edges of a Steinmetz solid .
Steinmetz's equation, derived from his experiments, defines the approximate heat energy due to magnetic hysteresis released, per cycle per unit volume of magnetic material. A Steinmetz solid is the solid body generated by the intersection of two or three cylinders of equal radius at right angles.
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 ...
Any horizontal cross-section of a cloister vault is a square. This fact may be used to find the volume of the vault using Cavalieri's principle.Finding the volume in this way is often an exercise for first-year calculus students, [4] and was solved long ago by Archimedes in Greece, Zu Chongzhi in China, and Piero della Francesca in Renaissance Italy; [5] for more, see Steinmetz solid.
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).
Steinmetz's equation, sometimes called the power equation, [1] is an empirical equation used to calculate the total power loss (core losses) per unit volume in magnetic materials when subjected to external sinusoidally varying magnetic flux.
The Charles Proteus Steinmetz Memorial Lecture is a series of academic lectures initiated in 1925 [1] in honor of celebrated mathematician and electrical engineer Charles Proteus Steinmetz. To date seventy four addresses have been given on subjects ranging from peace [2] and educational reform [3] to nanotechnology [4] and solar photovoltaics. [5]