| 释义 |
construction with ruler and compass Ancient Greek geometers, in particular, were interested in what geometrical constructions were possible using a ruler (strictly a straight edge, so no increments on the edge) and a pair of compasses. Many constructions were known classically, such as bisecting an angle, reflecting a point in a line, drawing the circle through three non-collinear points, but famously they were unable to resolve the (im)possibility of the following: (i) given a square base of a cube, drawing a second square, a cube on which would have twice the volume; (ii) trisecting a general angle; (iii) given a circle, drawing a square with the same area as the circle. All these are now known to be possible, though the solutions lay more in algebra and analysis than in geometry. See constructible number.
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