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The "straightedge" and "compass" of straightedge-and-compass constructions are idealized versions of real-world rulers and compasses. The straightedge is an infinitely long edge with no markings on it. It can only be used to draw a line segment between two points, or to extend an existing line segment.
The concept of constructibility as discussed in this article applies specifically to compass and straightedge constructions. More constructions become possible if other tools are allowed. The so-called neusis constructions, for example, make use of a marked ruler. The constructions are a mathematical idealization and are assumed to be done exactly.
Pages in category "Compass and straightedge constructions" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes .
The next four chapters study what happens when the use of the compass or straightedge is restricted: by the Mohr–Mascheroni theorem there is no loss in constructibility if one uses only a compass, but a straightedge without a compass has significantly less power, unless an auxiliary circle is provided (the Poncelet–Steiner theorem).
Compass and straightedge constructions. Squaring the circle; Complex geometry; Conic section. Focus; Circle. List of circle topics; Thales' theorem; Circumcircle; Concyclic; Incircle and excircles of a triangle; Orthocentric system; Monge's theorem; Power center; Nine-point circle; Circle points segments proof; Mrs. Miniver's problem ...
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
This can be done with a compass alone. A straightedge is not required for this. #5 - Intersection of two circles. This construction can also be done directly with a compass. #3, #4 - The other constructions. Thus, to prove the theorem, only compass-only constructions for #3 and #4 need to be given.
In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions.The tool advocated by Plato in these constructions is a divider or collapsing compass, that is, a compass that "collapses" whenever it is lifted from a page, so that it may not be directly used to transfer distances.