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)
“Can anything be more ridiculous than that a man should have the right to kill me because he lives on the other side of the water, and because his ruler has a quarrel with mine, though I have none with him?”
—Blaise Pascal (1623–1662)
“be a while our guests:
For stars, gaze on our eyes.
The compass love shall hourly sing,
And as he goes about the ring,
We will not miss
To tell each point he nameth with a kiss.”
—William Browne (1591–1643)