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Galois Theory, 4th Edition
book

Galois Theory, 4th Edition

by Ian Nicholas Stewart
March 2015
Intermediate to advanced content levelIntermediate to advanced
344 pages
10h 18m
English
Chapman and Hall/CRC
Content preview from Galois Theory, 4th Edition
102 Ruler-and-Compass Constructions
EXERCISES
7.1 Express in the language of this chapter methods of constructing, by ruler and
compasses:
(a) The perpendicular bisector of a line.
(b) The points trisecting a line.
(c) Division of a line into n equal parts.
(d) The tangent to a circle at a given point.
(e) Common tangents to two circles.
7.2 Estimate the degrees of the field extensions corresponding to the constructions
in Exercise 7.1, by giving reasonably good upper bounds.
7.3 Prove using Euclidean geometry that the ‘marked ruler’ construction of Fig-
ure 11 does indeed trisect the given angle AOB.
7.4 Can the angle 2π/5 be trisected using ruler and compasses? ...
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Publisher Resources

ISBN: 9781482245837