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Examples of compass-only constructions include Napoleon's problem. It is impossible to take a square root with just a ruler, so some things that cannot be constructed with a ruler can be constructed with a compass; but (by the Poncelet–Steiner theorem) given a single circle and its center, they can be constructed.
When doing constructions in hyperbolic geometry, as long as you are using the proper ruler for the construction, the three compasses (meaning the horocompass, hypercompass, and the standard compass) can all perform the same constructions. [3] A parallel ruler can be used to draw a line through a given point A and parallel to a given ray a [3].
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. ...
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 ...
Proclus, citing Eudemus of Rhodes, credited Oenopides (c. 450 BCE) with two ruler and compass constructions, leading some authors to hypothesize that Oenopides originated the restriction. [39] The restriction to compass and straightedge is essential to the impossibility of the classic construction problems.
Pages for logged out editors learn more. Contributions; Talk; Ruler-and-compass construction