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Inversive Geometry
This introduction to algebraic geometry makes particular reference to the operation of inversion and is suitable for advanced undergraduates and graduate students of mathematics. One of the major contributions to the relatively small literature on inversive geometry, the text illustrates the field's applications to comparatively elementary and practical questions and offers a solid foundation for more advanced courses.
The two-part treatment begins with the applications of numbers to Euclid's planar geometry, covering inversions; quadratics; the inversive group of the plane; finite inversive groups; parabolic, hyperbolic, and elliptic geometries; the celestial sphere; flow; and differential geometry. The second part addresses the line and the circle; regular polygons; motions; the triangle; invariants under homologies; rational curves; conics; the cardioid and the deltoid; Cremona transformations; and the n- line.
The two-part treatment begins with the applications of numbers to Euclid's planar geometry, covering inversions; quadratics; the inversive group of the plane; finite inversive groups; parabolic, hyperbolic, and elliptic geometries; the celestial sphere; flow; and differential geometry. The second part addresses the line and the circle; regular polygons; motions; the triangle; invariants under homologies; rational curves; conics; the cardioid and the deltoid; Cremona transformations; and the n- line.
288 pages, Paperback
First published January 1, 2013
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Displaying 1 of 1 review
November 30, 2021
Browsing this book as a freebie, I find the introduction a little clunky and confusingly written.
For instance, there is the statement 'We thus get the idea by isolating a point on a sphere (which point we call infinity) we get the Euclidean plane' right in the preface, but a point by itself does not make a plane. Perhaps the author meant 'add' instead of isolate?
It's hard to find freebie texts on the subject, so I'm not about to give it no stars, but... I'm not really impressed with the writing here. To be fair, most mathematical texts aren't exactly well written, but usually their preface is at least comprehensible.
The first chapter is fairly simple, starting off with talking about Euclid and what you can do with a mere card on the table, and this is not so bad, although it has the usual mathematical habit of replacing simple words with identical fancier ones (outright stating they will use 'reflexion' for overturning the card).
'The method of integration is the same for numbers and reals' more weirdness of language, reals ARE numbers.
This will probably be a DNF for me, although I'm still browsing it soo, I guess it's not a bad skim if you're bored and you get it free.
For instance, there is the statement 'We thus get the idea by isolating a point on a sphere (which point we call infinity) we get the Euclidean plane' right in the preface, but a point by itself does not make a plane. Perhaps the author meant 'add' instead of isolate?
It's hard to find freebie texts on the subject, so I'm not about to give it no stars, but... I'm not really impressed with the writing here. To be fair, most mathematical texts aren't exactly well written, but usually their preface is at least comprehensible.
The first chapter is fairly simple, starting off with talking about Euclid and what you can do with a mere card on the table, and this is not so bad, although it has the usual mathematical habit of replacing simple words with identical fancier ones (outright stating they will use 'reflexion' for overturning the card).
'The method of integration is the same for numbers and reals' more weirdness of language, reals ARE numbers.
This will probably be a DNF for me, although I'm still browsing it soo, I guess it's not a bad skim if you're bored and you get it free.
Displaying 1 of 1 review