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Geometry
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Geometric constructions
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The notion of geometric constructions go back at least to Greek antiquity. The classical constructions are called Euclidean constructions, but they certainly were known prior to Euclid. The only instruments allowed to be used in these constructions are compass and straightedge. The compass is used to establishes the equidistance, and the straightedge establishes the collinearity. Thus Euclidean geometric constructions are based on these two procedures:
Constructions are understood as a theoretical exercise, whether for instance a line has zero width, and various physical imperfections of the drawing instruments are neglected.
Marked straightedges and protractors are not allowed in the classical Euclidean constructions. Even if the marked straightedge is not used in Euclid’s Elements, other Greek geometers used it, for instance Hippocrates of Chios (ca. 430 BC). Pappus reports that Applonius of Perga (ca. 262-190 BC) wrote two books on constructions using marked straightedge.
The constructions using marked straightedge were called neusis constructions by ancient Greeks. [1]
When the straightedge and compass constructions did not offer a solution then also other types of construction instruments were accepted, for instance
[1] | Hartshorne, R. (2000). Geometry: Euclid and Beyond. Springer. |
Cite this web-page as:
Štefan Porubský: Geometric Constructions.