An -digit number that is the sum of the th powers of its digits is called an -narcissistic number. It is also sometimes known as an Armstrong number, perfect digital invariant (Madachy 1979), or plus perfect number. Hardy (1993) wrote, "There are just four numbers, after unity, which are the sums of the cubes of their digits: , , , and . These are odd facts, very suitable for puzzle columns and li
Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term derives from the Greek (brachistos) "the shortest" and (chronos) "time, delay." The brachistochrone problem was one of the earliest problems posed in the calculus of variations. Newton was challenged to solve the problem in 16
The (complete) gamma function is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by a slightly unfortunate notation due to Legendre which is now universally used instead of Gauss's simpler (Gauss 1812; Edwards 2001, p. 8). It is analytic everywhere except at , , , ..., and the residue at is There are no points at which . The gamma fu
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