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.
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Famous quotes containing the words compass and/or theorem:
“Histories of the world omitted China; if a Chinaman invented compass or movable type or gunpowder we promptly “forgot it” and named their European inventors. In short, we regarded China as a sort of different and quite inconsequential planet.”
—W.E.B. (William Edward Burghardt)
“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)