Mathematical Illustrations - A manual of geometry and PostScript

Shows how to use PostScript for producing mathematical graphics, at several levels of sophistication. Also includes some discussion of the mathematics involved in computer graphics as well as a few remarks about good style in mathematical illustration.

**Tag(s):**
Computer Aided Mathematics

**Publication date**: 31 Dec 1996

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
350 pages

**Views**: 20,609

Mathematical Illustrations - A manual of geometry and PostScript

Shows how to use PostScript for producing mathematical graphics, at several levels of sophistication. Also includes some discussion of the mathematics involved in computer graphics as well as a few remarks about good style in mathematical illustration.

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From the Preface:

This book will show how to use PostScript for producing mathematical graphics, at several levels of sophistication. It includes also some discussion of the mathematics involved in computer graphics as well as a few remarks about good style in mathematical illustration.

Nowadays there are many tools to help one produce mathematical graphics, of course. A partial list would include the free packages xfig, pictex, PSTricks, MetaFont and MetaPost, as well as commercial mathematical programs such as Maple and Mathematica and professional graphics design tools such as Illustrator. Which one to choose apparently involves a tradeoff between simplicity and quality, in which most go for what they perceive to be simplicity. The truth is that the tradeoff is unnecessary—once one has made a small initial investment of effort, by far the best thing to do in most situations is to write a program in the graphics programming language PostScript. There is practically no limit to the quality of the output of a PostScript program, and as one acquires experience the difficulties of using the language decrease rapidly. The apparent complexity involved in producing simple figures by programming in PostScript, as I hope this book will demonstrate, is largely an illusion. And the amount of work involved in producing more complicated figures will usually be neither more nor less than what is necessary.

Even with all its drawbacks, however, PostScript is the tool of choice for mathematical illustration. This book should therefore be of interest to a large group of people: (1) to any scientist who has to make up a fair number of technical illustrations, but who has found himself limited by what the other packages can do; (2) to any teacher, even at the level of secondary school, who would like to make mathematics a more comprehensible and better motivated subject to his students; (3) to students who want to see how even elementary mathematics that might have seemed useless when first seen can be applied to attractive real world problems; (4) even to artists who might be interested in abstract designs with a mathematical component.

Perhaps the most surprising feature of this book is that it has been used successfully as a text for a third year undergraduate course in geometry. Students found that drawing in PostScript was a definite source of pleasure, once an initial breaking in period had passed. Froman instructor’s point of view there are two great virtues to this: (1) The pleasure of producing pictures with PostScript is enough to drive students even to learning mathematics in order to do it. Drawing in PostScript forces students to become intimately familiar with coordinate systems and linear algebra. (2) Being able to draw easily on a computer makes it an intriguing process to interpret much of classical mathematics, for example Euclid’s Elements or Newton’s Principia, in graphical terms. In rendering mathematics in images, a person is forced to understand the essentials of an argument in the most intimate way, after all. This book does not deal directly with that possibility, but some references are given, and I hope that an interested instructor will easily figure out how to implement it. If I have not made projects of this kind available, it is because I like my own students to figure out things for themselves.

Bill Casselman wrote:Copyright © 2005 by Bill Casselman. Permission is granted for users of this resource to make one copy for their own personal use. Further reproduction is strictly prohibited without the express permission of the copyright holder.

From the Preface:

This book will show how to use PostScript for producing mathematical graphics, at several levels of sophistication. It includes also some discussion of the mathematics involved in computer graphics as well as a few remarks about good style in mathematical illustration.

Nowadays there are many tools to help one produce mathematical graphics, of course. A partial list would include the free packages xfig, pictex, PSTricks, MetaFont and MetaPost, as well as commercial mathematical programs such as Maple and Mathematica and professional graphics design tools such as Illustrator. Which one to choose apparently involves a tradeoff between simplicity and quality, in which most go for what they perceive to be simplicity. The truth is that the tradeoff is unnecessary—once one has made a small initial investment of effort, by far the best thing to do in most situations is to write a program in the graphics programming language PostScript. There is practically no limit to the quality of the output of a PostScript program, and as one acquires experience the difficulties of using the language decrease rapidly. The apparent complexity involved in producing simple figures by programming in PostScript, as I hope this book will demonstrate, is largely an illusion. And the amount of work involved in producing more complicated figures will usually be neither more nor less than what is necessary.

Even with all its drawbacks, however, PostScript is the tool of choice for mathematical illustration. This book should therefore be of interest to a large group of people: (1) to any scientist who has to make up a fair number of technical illustrations, but who has found himself limited by what the other packages can do; (2) to any teacher, even at the level of secondary school, who would like to make mathematics a more comprehensible and better motivated subject to his students; (3) to students who want to see how even elementary mathematics that might have seemed useless when first seen can be applied to attractive real world problems; (4) even to artists who might be interested in abstract designs with a mathematical component.

Perhaps the most surprising feature of this book is that it has been used successfully as a text for a third year undergraduate course in geometry. Students found that drawing in PostScript was a definite source of pleasure, once an initial breaking in period had passed. Froman instructor’s point of view there are two great virtues to this: (1) The pleasure of producing pictures with PostScript is enough to drive students even to learning mathematics in order to do it. Drawing in PostScript forces students to become intimately familiar with coordinate systems and linear algebra. (2) Being able to draw easily on a computer makes it an intriguing process to interpret much of classical mathematics, for example Euclid’s Elements or Newton’s Principia, in graphical terms. In rendering mathematics in images, a person is forced to understand the essentials of an argument in the most intimate way, after all. This book does not deal directly with that possibility, but some references are given, and I hope that an interested instructor will easily figure out how to implement it. If I have not made projects of this kind available, it is because I like my own students to figure out things for themselves.

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