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)
“Who made you a ruler and judge over us?”
—Bible: Hebrew, Exodus 2:14.
Hebrews to Moses.
“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)