Skip to Main Content
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
Specific Constructions 97
If z,w are collinear with 0, circle C[z, |w|] meets L[0,z] in two points, z + w and
z w.
(2) The circle C[0,|z|] meets the line L[0, z] at z and at z.
(3) Consider the triangle T with vertices 0,1,z. Construct point p so that the triangle
with vertices 0,w, p is similar to T .
We claim that p = zw. By similarity |p|/|w| = |z|/1, so |p| = |z||w|. Further,
arg(p) = arg z + argw, where arg denotes the argument. Therefore p = zw.
(4) Let C[0,1] meet L[0, z] at p (with 0 lying between z and p). Then |p| = 1.
Construct a triangle with vertices 0, p,q similar to 0,z,1. Then |q|/1 = |p|/|z| =
1/|z|, so |q = 1/|z|.
Let C[0,q] meet L
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Galois Theory, 5th Edition

Galois Theory, 5th Edition

Ian Stewart
Number Theory and its Applications

Number Theory and its Applications

Satyabrota Kundu, Supriyo Mazumder
Classical Geometry: Euclidean, Transformational, Inversive, and Projective

Classical Geometry: Euclidean, Transformational, Inversive, and Projective

I. E. Leonard, J. E. Lewis, A. C. F. Liu, G. W. Tokarsky
Handbook of Graph Theory, 2nd Edition

Handbook of Graph Theory, 2nd Edition

Jonathan L. Gross, Jay Yellen, Ping Zhang

Publisher Resources

ISBN: 9781482245837