The compass equivalence theorem is an important statement in compass and straightedge constructions. In these constructions it is assumed that whenever a compass is lifted from a page, it collapses, so that it may not be directly used to transfer distances. While this might seem a difficult obstacle to surmount, the compass equivalence theorem states that any construction via a "fixed" compass may be attained with a collapsing compass. In other words, it is possible to construct a circle of equal radius, centered at any given point on the plane. This theorem is known as Proposition II of Book I of Euclid's Elements.
Read more about Compass Equivalence Theorem: Construction, Alternative Construction Without Straightedge
Famous quotes containing the words compass and/or theorem:
“To “give style” to one’s character—a rare and noble art! Those practice it who compass all that their natures present as strengths and weaknesses and then fit them into an artistic plan until every one appears as art and reason and even weakness enchants the eye.”
—Friedrich Nietzsche (1844–1900)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)