- 查看更多
前往 Wikipedia 查看全部内容Angle trisection - Wikipedia
Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass. In 1837, Pierre Wantzel proved that the problem, as stated, is … 展开
Using only an unmarked straightedge and a compass, Greek mathematicians found means to divide a line into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct 展开
The general problem of angle trisection is solvable by using additional tools, and thus going outside of the original Greek framework of compass and straightedge.
Many incorrect methods of … 展开Pierre Wantzel published a proof of the impossibility of classically trisecting an arbitrary angle in 1837. Wantzel's proof, restated in modern terminology, uses the concept of 展开
However, some angles can be trisected. For example, for any constructible angle θ, an angle of measure 3θ can be trivially trisected by ignoring the given angle and directly constructing an angle of measure θ. There are angles that are not constructible but are … 展开
A cubic equation with real coefficients can be solved geometrically with compass, straightedge, and an angle trisector if and only if it has three 展开
• Courant, Richard, Herbert Robbins, Ian Stewart, What is mathematics?: an elementary approach to ideas and methods, Oxford … 展开
CC-BY-SA 许可证中的维基百科文本 Trisecting the Angle: Archimedes’ Method | Archimedes, Geometry ...
Archimedes (c. 285–212/211 bc) made use of neusis (the sliding and maneuvering of a measured length, or marked straightedge) to solve one of the great problems of ancient geometry: …
Why Trisecting the Angle is Impossible - Princeton University
在cs.princeton.edu上查看更多信息I will respond to questions and comments as time permits, but if you want to take issuewith any position expressed here, you first have to answer this question: What evidence would it take to prove your beliefs wrong? I simply will not reply to challenges that do not address this question. Refutabilityis one of the classic dete…Demonstration of the Archimedes' solution to the Trisection …
However, one illicit solution that has been found in the works of Archimedes is demonstrated below. (This is Proposition 8 from his Book of Lemmas.) The Java applet has two control rings. …
The Problem of Angle Trisection in Antiquity - Rutgers …
The spiral discovered by Archimedes was used for angle trisection and more generally to solve the problem of cutting an angle contained by straight lines in a given ratio. Archimedes used these spirals in most of his works, not just to …
Trisecting the Angle/Archimedean Spiral - ProofWiki
2024年11月4日 · Use of the Archimedean spiral to trisect an angle was a standard technique for mathematicians following Archimedes. Retrieved from " …
- 其他用户还问了以下问题
geometry - Archimedes trisection of equilateral …
I applied this method to my triangle ABC by using a compass to measure length AI. Pivoting about point I, the arc intersects AB and here I mark origin O. From origin O, I add a line parallel to AC that intersects AB at origin point O. I then …
of the required trisection angle (∠E’MG or ∠E’MA = 1/3∠E’CG), formed by the connecting rod E’M and the horizontal slot to comply with the Archimedes’ Construction [2].
Angle Trisection - University of Illinois Urbana-Champaign
The first method, Archimedes' trisection of an angle using a marked straightedge has been described on the Geometry Forum before by John Conway. First take the angle to be …
Archimedes’ Construction is doubly interesting. First, it accomplishes the trisection quickly with simple tools. Second, it illuminates an aspect of mathematics that annoys many people: …
Archimedes Trisection 的相关搜索
