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The basic constructions. All straightedge-and-compass constructions consist of repeated application of five basic constructions using the points, lines and circles that have already been constructed. These are: Creating the line through two points; Creating the circle that contains one point and has a center at another point
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.
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.
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 .
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Classically, the only instruments used in most geometric constructions are the compass and straightedge. [c] Also, every construction had to be complete in a finite number of steps. However, some problems turned out to be difficult or impossible to solve by these means alone, and ingenious constructions using neusis, parabolas and other curves ...
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.