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In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.
C.a.R.– Compass and Ruler (also known as Z.u.L., which stands for the German "Zirkel und Lineal") — is a free and open source interactive geometry app that can do geometrical constructions in Euclidean and non-Euclidean geometry. The software is Java based. The author is René Grothmann of the Catholic University of Eichstätt-Ingolstadt.
Ruler and compass. The process of geometric drawing is based on constructions with a ruler and compass, which in turn are based on the first three postulates of Euclid's Elements . The historical importance of rulers and compasses as instruments in solving geometric problems leads many authors to limit Geometric Drawing to the representation ...
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 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.
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.
The compass equivalency theorem shows that in all the constructions mentioned above, the familiar modern compass with its fixable aperture, which can be used to transfer distances, may be replaced with a "collapsible compass", a compass that collapses whenever it is lifted from a page, so that it may not be directly used to transfer distances ...
Trisection, like many constructions impossible by ruler and compass, can easily be accomplished by the operations of paper folding, or origami. Huzita's axioms (types of folding operations) can construct cubic extensions (cube roots) of given lengths, whereas ruler-and-compass can construct only quadratic extensions (square roots).