Articles on plane curves appear throughout math journals. Here is a compilation of over literatures on plane curves. The following books are mostly advanced undergraduate level text books that deal with plane curves directly or indirectly.
For example, topics like differential geometry, algebraic geometry, and projective geometry. Most of them I haven't read. I've only read prefaces, intros, and scaned chapters.
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Because I learn math mostly on my own, I often select books that's suitable for self study, which basically means well-written self-contained undergraduate texts. I believe the following are good books, and my comments may serve as a guide for those of you amateur mathematicians to-be. For the following books, one should at least be comfortable in calculus. In general, the following books assume that you have some familiarity with basic modern math concepts like sets, vector spaces, differentiation; someone who are familiar with math courses offered in the first 2 years of US colleges, which often means multi-variable calculus, linear algebra, and differential equations.
Though, don't let these requirements scare you. If you have never heard of the terms, then you might be concerned about the book's suitability. I've listed the books roughly in order of difficulty. This book is a undergraduate introduction to differential treatment of plane curves. You should know your calculus well to read this book. Also, you shoud have some understanding of complex numbers.
This book isn't particularly easy to read or friendly, despite the author might want to claim otherwise. It is written by a English mathematician. Written by a English mathematician of University of Liverpool, England. The writing style is a bit pompous, and because of that it reads funny. If you had abstract algebra, you'll get along with this book fine. If you never had abstract algebra, it'll be problematic for a self-study. These text books are not exactly curve related, but on modern geometries. These are carefully picked text books on advanced undergraduate level, usually that means you have had some basic linear algebra and multi-variable calculus.
This is a great book. However it is not my personal favorite. I didn't like it because the English writing style is very informal and sloppy. It particular, it treats math as physicists do, and i hate that. Tristan's writing style is chatty and is in fact one of its selling point. Nevertheless, if you are looking for self-study on complex numbers, especially the geometric aspect, this is perhaps the only and best book.
These text books are geometry at graduate level.
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I selected them based on amazon. I think they are great books, but i do not know for certain. Curves and their Properties Buy at amazon Author: Robert C Yates Publisher: Written at beginning college math level, this book gather most of the interesting properties of curves with a brief account of their history. If you read plane curves for fun, this is the book to get.
Most information on this site is from this book. As of , it is not in print, but should be available at most university libraries. This book is now available on CD. The Trisection Problem Buy at amazon Author: Well written with many quality illustrations. As of , it's not in print.
The Trisectors Buy at amazon Author: Mathematical Association of America Date: Exposition of the many angle-trisectors in history. This is a very well written fascinating book. The author takes us thru the many trisetors that he personally had been contacted or visited. He tells us who they are, what they do, and what kind of ilk are they, if any.
One'd be surprised the numerousness of them besiege unisersities's math department, even today. It is interesting to note, that I myself have actually been contacted by a angle-trisector in , and asked by him to do some illustration for him. I tried to convince him that it is not possible, and during the first meeting, realized that this persuasion is impossible. It is with this incident when I found this book by Underwood, and in fact, this trisector in particular is accounted in the book.
I contacted Underwood and confirmed the identity. I did, in fact, actually agreed to do drawing for the trisector and got paid for it. A Book of Curves Buy at amazon Author: E H Lockwood Publisher: This book teachs practical methods of drawing curves. It even indicates the appropriate paper size to carry out the drawing. The methods of constructions rely on curve's properties, and many proofs, formulas, and bits of history are given along the way. You'll have fun figuring it out. Includes bibliography of 20 items. This book is reprinted in J D Lawrence Publisher: This book is a good reference on curve's mathematical formulas.
It contains formulas of curve's Cartesian, parametric, polar, bipolar, and other intrinsic equations. Information on a curve's intercept, extrema, extent, discontinuity, symmetry, asymptote, loop, node, volume and surface of revolution are also given. However, proofs are not given. A chronological bibliography of 95 items is included. This is a dry but worthy references. The bad points about this book are: It's a bit outdated.
Most formulas given in the book can be generated by computer algebra systems such as Mathematica or Maple. The techniques used in the book is not modern.
Plane Curves Books
The illustrations look very primitive with respect to today's plotting softwares. Encyclopedia Britannica has a chapter on plane curves. The 11th edition , published in , is now in public domain. Encyclopedic Dictionary of Mathematics Buy at amazon Author: If you are looking for a printed version of the most comprehensive encyclopedia of math, this is it. This is a 2 volume set. The writing is aimed at professional mathematicians, in a extremely condensed, summarized fashion.
First published in , so it's slightly dated, but still is far above all other printed math references in scope and depth. It has a entry on plane curves 7-pages , as well entries on coordinate systems, differential geometry, algebraic geometry, projective geometry, their subfields and concepts, … and so on. Let's say you just want to own 5 math books in your life, this should be one of them.
Oxford University Press Date: Perhaps the most ambitious history of mathematics book that is aimed at general math reader. Contents are as accurate as historians can claim. Easy reading but not trivial. This is a acclaimed book. An Introduction to the History of Mathematics; 6th ed. Buy at amazon Author: This book is in the form of a typical modern text book, complete with photographs of mathematicians, artifacts, and old writings, some ancient geographic maps, illustrations on math, and one quarter of the book is devoted to annotated exercises that lets the student get a feeling of how math in different periods are like.
Each chapter covers a period, followed by a fairly complete bibliography. A History of Mathematics, 2nd ed.
Conics and Cubics - A Concrete Introduction to Algebraic Curves (Hardcover, 2nd ed. 2006)
John Wiley and Sons, Inc. Mathematics and its History Buy at amazon Author: Two major strengths of the book are its historical perspective, in the form of informative introductions to the chapters which give the main developments in non-technical language, and its exercises, which are numerous and interesting.
But could it, or at least some of it, be presented, at the undergraduate level? This book attempts to do that. At the beginning of each of the four chapters, the author provides a synopsis of the historical development of the subject. And within each section many exercises are provided for further discussion and illumination.
And the author manages to keep things concrete. Vestal, MathDL ' online, October, Harry Potter Years by J. Rowling , Hardcover Harry Potter and the Sorcerer's Stone 1 by J. Harry Potter Boxset Books by J. Pete the Cat I Can Read! The Elf on the Shelf-a Christmas Tradition: Revised Edition Hardcover Textbooks.
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