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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
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.
Martin originally intended his book to be a graduate-level textbook for students planning to become mathematics teachers. [2] However, as well as this use, it can also be read by anyone who is interested in the history of geometry and has an undergraduate-level background in abstract algebra, or used as a reference work on the topic of geometric constructions.
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.
Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid , who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of ...
As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19. [1] This proof represented the first progress in regular polygon construction in over 2000 years. [1]
Jørgen Mohr (Latinised Georg(ius) Mohr; 1 April 1640 – 26 January 1697) [1] was a Danish mathematician, known for being the first to prove the Mohr–Mascheroni theorem, which states that any geometric construction which can be done with compass and straightedge can also be done with compasses alone.