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#REDIRECT [[Straightedge and compass construction#Impossible constructions]] <!-- [[WP:HOT]]list redirect --> ...

[[File:Straight_edge_MET_187601.jpg|thumb|right|An ornate 18th century iron straightedge]] A '''straightedge''' or '''straight edge''' is a tool used for drawing straight lines, or che ...

'''[[Construction]]''' is the process of producing buildings and other infrastructure.<br> ** [[List of algebraic constructions|(A list of) algebraic constructions]] ...

...description|Curve which could be used to trisect an angle with compass and straightedge}} ...risected with that type of construction. There is a variety of such curves and the methods used to construct an angle trisector differ according to the cu ...

| latest release date = {{Start date and age|2022|03|21}} | latest preview date = <!-- {{Start date and age|YYYY|MM|DD}} --> ...

...ss alone. The following sections will describe solutions to three problems and [[Proof (truth)|proofs]] that they work. ...and Y. Do the same centred on Y through O, intersecting '''''C''''' at X and Z. Note that the line segments OV, OX, OY, OZ, VX, XY, YZ have the same le ...

...onstructions performed by a compass and straightedge can be performed by a compass alone}} ...t can be performed by a [[compass and straightedge]] can be performed by a compass alone. ...

...t the operations are completed on a plane (i.e. a perfect piece of paper), and that all folds are linear. These are not a minimal set of axioms but rather ...ation and Therapy'' in 1991. Axioms 1 though 5 were rediscovered by Auckly and Cleveland in 1995. Axiom 7 was rediscovered by Koshiro Hatori in 2001; [[Ro ...

{{Short description|5th-century BC Greek mathematician and astronomer}} ...to be impossible with [[Compass and straightedge constructions|compass and straightedge]]).]] ...

{{about|the drafting instrument||Compass (disambiguation)}} [[File:Zirkel.jpg|thumb|A beam compass and a regular compass]] ...

{{Short description|5th-century BCE Greek mathematician and astronomer}} ...born c. 490 BCE) was an ancient [[Greece|Greek]] [[geometer]], astronomer and mathematician, who lived around 450 [[Common Era|BCE]]. ...

A whole regular 257-gon is not visually discernible from a [[circle]], and its perimeter differs from that of the [[circumscribed circle]] by about 24 ...e all [[constructible number]]s they can be written using [[square root]]s and no higher-order roots. ...

...ment]] of given length ({{mvar|a}}) in between two given lines ({{mvar|l}} and {{mvar|m}}), in such a way that the line element, or its extension, passes ...ed the pole of the neusis, line {{mvar|l}} the directrix, or guiding line, and line {{mvar|m}} the catch line. Length {{mvar|a}} is called the ''diastema' ...

{{Short description|Ancient Greek mathematician and geometer (c. 390–320 BC)}} ...0 – c. 320 BCE) was a [[Greece|Greek]] [[mathematician]] and [[geometer]], and the brother of [[Menaechmus]]. He is known for using the [[quadratrix]] to ...

...''' is a historic term for the computation of [[area (mathematics)|area]]s and is thus used for computation of [[integral]]s. ...ysis]]; see [[numerical quadrature]]. Also, '''reduction to quadratures''' and '''solving by quadratures''' means expressing solutions of differential equ ...

{{short description|Regular polygon that can be constructed with compass and straightedge}} ...e]]. For example, a regular [[pentagon]] is constructible with compass and straightedge while a regular [[heptagon]] is not. There are infinitely many constructibl ...

[[File:Tomahawk filled.svg|thumb|right|A tomahawk, with its handle and spike thickened]] ...merica|year=2010|isbn=9780883853481|contribution=9.4 The shoemaker's knife and the salt cellar|pages=147–148}}.</ref> ...

...any straight [[line segment]] that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest [[ ...literation|grc|metron}}), "measure".<ref>{{cite web |title=Diameter—Origin and meaning of diameter by Online Etymology Dictionary |url=http://www.etymonli ...

...0px.gif|thumb|right|Creating a regular [[hexagon]] with a straightedge and compass]] ...(science philosophy)|idealized]] [[ruler]] and a [[Compass (drawing tool)|compass]]. ...

[[File:01-Würfelverdoppelung-4.svg|thumb|upright=1.3|A unit cube (side = 1) and a cube with twice the volume (side = <math>\sqrt[3]{2}</math> = 1.259921049 ...e is now known to be impossible to construct by using only a [[compass and straightedge]], but even in ancient times solutions were known that employed other metho ...