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A related concept is a ”’sectrix”’, which is a curve which can be used to divide an arbitrary angle by any integer.<ref>{{citation|url=https://www.mathcurve.com/courbes2d.gb/sectrice/sectrice.shtml|title=Sectrix curve|first=Robert|last=Ferréol|year=2017|work=Encyclopédie des formes mathématiques remarquables|access-date=2025-10-20}}</ref> Examples include: |
A related concept is a ”’sectrix”’, which is a curve which can be used to divide an arbitrary angle by any integer.<ref>{{citation|url=https://www.mathcurve.com/courbes2d.gb/sectrice/sectrice.shtml|title=Sectrix curve|first=Robert|last=Ferréol|year=2017|work=Encyclopédie des formes mathématiques remarquables|access-date=2025-10-20}}</ref> Examples include: |
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* [[Archimedean |
* [[Archimedean ]]<ref>{{cite book |first1=Uta B.|last1=Merzbach|author1-link=Uta Merzbach| first2=Carl B. | last2=Boyer | author2-link=Carl Benjamin Boyer | title=A History of Mathematics | pages = 113–114 | edition=Third | publisher=John Wiley & Sons | year=2011|isbn=978-0470525487|pages=90–108}}</ref> |
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* [[Quadratrix of Hippias]] |
* [[Quadratrix of Hippias]] |
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* [[Sectrix of Maclaurin]] |
* [[Sectrix of Maclaurin]] |
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Latest revision as of 06:06, 21 October 2025
Curve which could be used to trisect an angle with compass and straightedge
In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool. Such a method falls outside those allowed by compass and straightedge constructions, so they do not contradict the well known theorem which states that an arbitrary angle cannot be trisected 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 curve. Examples include:
A related concept is a sectrix, which is a curve which can be used to divide an arbitrary angle by any integer.[4] Examples include:
- ^ Chisholm, Hugh, ed. (1911), “Trisectrix“, Encyclopædia Britannica, vol. 27 (11th ed.), Cambridge University Press
- ^ Dudley, Underwood (1994), The Trisectors, Cambridge University Press, pp. 6–8, ISBN 0883855143; excerpt, p. 12, at Google Books
- ^ Farouki, Rida T. (2008), Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Geometry and Computing, vol. 1, Springer, pp. 398–399, doi:10.1007/978-3-540-73398-0, ISBN 978-3-540-73397-3, MR 2365013
- ^ Ferréol, Robert (2017), “Sectrix curve”, Encyclopédie des formes mathématiques remarquables, retrieved 2025-10-20
- ^ Merzbach, Uta B.; Boyer, Carl B. (2011), A History of Mathematics (Third ed.), John Wiley & Sons, pp. 90–108, ISBN 978-0470525487
