Some Applications of Mathematics to Architecture: Gothic Tracery Curves
About: This article is published in American Mathematical Monthly.The article was published on 1926-08-01. It has received 2 citations till now. The article focuses on the topics: Tracery.
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01 Jan 2004
TL;DR: This chapter discusses a lot of graphical methods and examples for using Mathematica not only for symbolic calculations, but also to produce plots of measured data or sets of data produced by other programs.
Abstract: In comparison with the six chapters of the Programming volume [767] of the GuideBooks, this chapter is very long—almost one and a half times longer than the average chapter text, without the plots. The reason for this is threefold:
The reader is now familiar with the structure of Mathematica expressions, and we can make full use of this knowledge to write larger programs. Often, one of the simplest ways to check whether a calculation produces the desired result is to look at it graphically for special values of parameters or/and limiting cases.
Originally, it was not my intention to discuss a lot of graphical methods and examples. However, because of numerous requests by the students who listened to the original lectures that resulted in this book, I have now included, in my opinion, a sufficient amount of graphics. Apparently many students and colleagues wanted to use Mathematica not only for symbolic calculations, but also (sometimes, unfortunately, only) to produce plots of measured data or sets of data produced by other programs.
Visualization of mathematical knowledge is very important for teaching and “understanding” mathematics [94], [835], [597], [228], [364], [438], [649], [361], [45], [446], [428], [269], [226].
8 citations
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TL;DR: This article gives an implementation of the standard algorithm to segment a real algebraic plane curve defined implicitly and uses global information to count the number of half-branches at a critical point.
Abstract: In this article we give an implementation of the standard algorithm to segment a real algebraic plane curve defined implicitly. Our implementation is efficient and simpler than previous. We use global information to count the number of half-branches at a critical point.
Cites background from "Some Applications of Mathematics to..."
...This problem is relevant in computational vision (Fryers etal., 2001), engineering (Knudsen, 1983), architecture (Phillips, 1926) and more....
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