Democratic Sentinel, Volume 18, Number 23, Rensselaer, Jasper County, 22 June 1894 — “THE FOURTH POWER.” [ARTICLE+ILLUSTRATION]

“THE FOURTH POWER.”

An Attempt to Indicate What It Looks Like. In a recent number of St Nicholas the above question was asked, more as an amusing puzzle than as a seri-

ous mathematical problem. Two clever correspondents, however, have sent answers. Paul R. Heyl, of Philadelphia, incloses a model in wire open work and writes: “When we wish to represent the fourth power (which, being of four dimensions, we may call a hypercube), we may do so in solid perspective by placing a cube diagonally above another and a little behind It, and joining the corresponding corners.” He refers inqdirers to a book, “Scientific Romances. ” A younger correspondent, Arthur Howe Carpenter, of Deadwood, 8. D., also defines the properties of the fourth power figure: “It is a figure bounded by eight cubes, just as a cube is bounded by six squares; it has sixteen corners, twenty-four squares, and thirty-two edges.” One of the correspondents says that this model shows as nearly as possible “what the fourth power looks like;” what it really looks like cannot be shown. This figure has many of its qualities, but the thing itself is only a theory of geometry.

“THE FOURTH POWER.”