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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
Thus one only has to find a compass and straightedge construction for n-gons where n is a Fermat prime. The construction for an equilateral triangle is simple and has been known since antiquity; see Equilateral triangle. Constructions for the regular pentagon were described both by Euclid (Elements, ca. 300 BC), and by Ptolemy (Almagest, ca ...
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 final three chapters go beyond the straightedge and compass to other construction tools. A highly restricted form of construction, the "match-stick geometry" of Thomas Rayner Dawson from the 1930s, uses only unit line segments, which can be placed along each other, intersected, or pivoted around one of their endpoints; despite its limited ...
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.
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.
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]
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.