ePub 1523 kb. | Fb2 1995 kb. | DJVU: 1538 kb.
Math

Experiments in Topology epub ebook

by Stephen Barr

Experiments in Topology epub ebook

Author: Stephen Barr
Category: Mathematics
Language: English
Publisher: Thomas Y. Crowell; 1st edition (June 1, 1964)
Pages: 220 pages
ISBN: 0690278624
ISBN13: 978-0690278620
Rating: 4.7
Votes: 243
Other formats: docx rtf mobi mbr


Stephen Barr (Author).

Stephen Barr (Author). Written for the beginner in topology but still presupposing a certain amount of mathematical maturity, this book is great fun and should be useful to high school teachers, and those who might be giving public talks on mathematics to audiences who are very interested in mathematics, but who don't have a substantial background in the subject. It is always helpful in those scenarios to have concrete examples that will illustrate some of the more difficult constructions in topology. In chapter 1, the author attempts to give an intuitive definition of topology.

Experiments in Topology - Stephen Barr.

In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Experiments in Topology - Stephen Barr. Dover books on mathematical & logical puzzles, cryptography, and word recreations.

Stephen BarrIn this lively book, the classic in its field, a master of recreational topology invites readers .

Stephen BarrIn this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip.

With this book and a square sheet of paper, the reader can make paper Klein bottles; then by intersecting or cutting the bottle, make Moebius strips

With this book and a square sheet of paper, the reader can make paper Klein bottles; then by intersecting or cutting the bottle, make Moebius strips. Conical Moebius strips, projective planes, the principle of map coloring, the classic problem of the Koenigsberg bridges and other aspects of topology are carefully and concisely illumined.

Stephen Barr’s most popular book is Go to Sleep, Little Farm. Experiments in Topology by. Stephen Barr.

Experiments in topology. urn:acs6:rr:pdf:07d-591b37b4a410 urn:acs6:rr:epub:865-47afb96a10d3 urn:oclc:record:1034667267. Columbia University Libraries.

A mathematician named KleinThought the Moebius band was divine. Said he: 'If you glueThe edges of two,You'll get a weird bottle like mine.

Stephen Barr: Experiments in Topology. 1. What Is Topology? Euler's Theorem.

In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip

In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. The text is very well written, and with support of easily reproducible graphics, is enjoyment to read

Experiments in Topology. The text is very well written, and with support of easily reproducible graphics, is enjoyment to read. Along with more traditional topics like Moebius strip construction and onesidedness, you learn of shortest (needing the least amount of paper) strip and, more importantly, learn to recognize the strip when you see one.

Defines topology, the study of continuity, and covers such topics as the shortest Moebius strip, the Klein bottle, and the projective plane
Reviews (3)
Ance
The subject of topology lends itself to many different kinds of experimentation for undergraduate students. But this book spends a disproportionate amount of space on the Mobius strip and related non-orientability issues when it could deal with more knot theory and homotopy theory than it does, and it could introduce finite topologies and Morse theory which abound in self-exploration.

Mettiarrb
Written for the beginner in topology but still presupposing a certain amount of mathematical maturity, this book is great fun and should be useful to high school teachers, and those who might be giving public talks on mathematics to audiences who are very interested in mathematics, but who don't have a substantial background in the subject. It is always helpful in those scenarios to have concrete examples that will illustrate some of the more difficult constructions in topology.
In chapter 1, the author attempts to give an intuitive definition of topology. The author uses various pictures and handwaving arguments to explain various notions in topology, such as homeomorphism ("coffee cup = donut"), simply connected (object with no holes), homology (two circles can intersect at one point only), Jordan curves, and Euler's theorem.
In chapter 2, the author uses paper models to illustrate the topology of surfaces, both orientable and nonorientable. The author gives instructions on how to make a paper model of a Klein bottle, but cautions the reader that such a model is not an exact representation of the mathematical object rigorously defined in topology, since the surface passes through itself in the paper construction.
Chapter 3 is a set of instructions on how to make a "shortest" Moebius strip. The procedures for doing this are interesting and fun, for the author constructs a Moebius strip whose length is less than its width, by a factor of 1 over the square root of 3. He devotes an appendix for an improvement due to Martin Gardner of Scientific American fame.
In chapter 4 the author constructs what he calls a "conical Moebius strip". The author asks the reader to consider an annulus with a radial slit, with which of course one can construct a Moebius strip by twisting the ends and joining them. But he asks how large the hole must be in relation to the outside diameter. The answer to this is that one does not need any hole at all in order to carry out the construction. In fact, an angular segment can be cut out instead of the radial cut, and this leads him to construct the conical Moebius strip.
The author returns to the Klein bottle in chapter 5, and shows first what happens if the usual construction of the Klein bottle is cut down the center symmetrically: two Moebius strips are obtained. But to construct this model is difficult, so he gives alternate constructions for making the Klein bottle. He then shows what happens to the various models when the pieces are cut.
But how do you make a projective plane using scissors and paper? Intuitively one can imagine this would be very difficult, but the author shows ways to do it in chapter 6. His strategy for making these models is to teach the concept of symmetry in topology, and he pulls this off very well.
The famous 4-color problem for maps, i.e. that one needs only 4 colors for a map, is considered in chapter 7. At the time of publication, the 4-color problem was still open, so the author attempts to try and explain it using various diagrams and subdivisions thereof. The 4-color problem was proved using computer algorithms by the mathematicians K. Appel and W. Haken in 1976.
Network topology is considered in chapter 8, with the famous Koenigsberg bridge problem leading off the discussion. The author also introduces the very important Betti numbers, these having far-reaching ramifications in topology. And interestingly, the author is able, via a consideration of loop-cuts and cross-cuts in paper models of the Klein bottle and projective plane, to introduce the very important concept of "duality". The theory of knots makes its appearance here, although the discussion is very short. The author is well-aware of the difficulties in finding a classification theory of knots, but more could possibly be done here in the lines of the rest of the book to illustrate some of the peculiarities of knots.
Chapter 9 is really fun, for it concerns the torus with a puncture, and how to turn it inside out. The diagrams are helpful and the intuition gained valuable. The mathematician Steven Smale found a way of turning the sphere inside out in the early 1060s, but the author does not tackle Smale's method! This is unfortunate, since it is very difficult to follow the steps in Smale's method, at least for me.
The author does not want to leave the reader with the impression that topology is all scissors, paper, and tape, so he devotes the last two chapters of the book to point-set topology. Concepts such as continuity, limit points, and neighborhoods are discussed. It is quite difficult to explain to beginning readers and students of topology what a neighborhood actually does without having the notion of a metric or distance, but the author does a fairly good job here.

Endieyab
Without wasting too much time with point-set terminology / abstractions, motivates the core subject and explains the "topological way of thinking" from the get go. It has a nice range of expository chapters on a variety of topological subjects, and helps motivate a deeper follow-up study of topology. It seems that modern proofs strive to erase every hint of the the actual insight that allowed the mathematician to arrive at the proof. This book helps remedy that. I took one start off only because the terminology is sometimes vague enough to detract from the readability of the book - it's not clear why cut & paste is allowed in certain situations and not some others, etc.

2016-2020 © www.hotellemcasadeicervia.it
All rights reserved