Constructing With Only Ruler or Only Compass
It is possible (according to the Mohr–Mascheroni theorem) to construct anything with just a compass if it can be constructed with a ruler and compass, provided that the given data and the data to be found consist of discrete points (not lines or circles). It is impossible to take a square root with just a ruler, so some things that cannot be constructed with a ruler can be constructed with a compass; but (by the Poncelet–Steiner theorem) given a single circle and its center, they can be constructed.
Read more about this topic: Compass And Straightedge Constructions
Famous quotes containing the words constructing, ruler and/or compass:
“The very hope of experimental philosophy, its expectation of constructing the sciences into a true philosophy of nature, is based on induction, or, if you please, the a priori presumption, that physical causation is universal; that the constitution of nature is written in its actual manifestations, and needs only to be deciphered by experimental and inductive research; that it is not a latent invisible writing, to be brought out by the magic of mental anticipation or metaphysical mediation.”
—Chauncey Wright (1830–1875)
“Despots play their part in the works of thinkers. Fettered words are terrible words. The writer doubles and trebles the power of his writing when a ruler imposes silence on the people. Something emerges from that enforced silence, a mysterious fullness which filters through and becomes steely in the thought. Repression in history leads to conciseness in the historian, and the rocklike hardness of much celebrated prose is due to the tempering of the tyrant.”
—Victor Hugo (1802–1885)
“However closely people are attached to one another, their mutual horizon nonetheless includes all four compass directions, and now and again they notice it.”
—Friedrich Nietzsche (1844–1900)