17May 2015 by Vincent Summers 2 Comments

Discrete Mathematics: What is a Point and What a Line?

Mathematics
[caption id="attachment_7234" align="alignright" width="440"] Discrete points? An abstract.[/caption] Most technically minded people will probably take me to task over what I am going to say in this article. That is OK, though. I’m used to it. Not only are my writings quirky—I am quirky. Hey! This is QuirkyScience. I want to talk about points and lines in the real world—in other words, discrete mathematics. What is Reality, What Fantasy? To a mathematician, the point may be a dimensionless object in 3D space, a mathematical object with an x, y, z coordinate in Euclidean space. A line would be a collection of such dimensionless points lined up all in a row. But that is in the world of the mathematician. In the real world, there can be no such thing. Rather,…
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14Nov 2014 by Vincent Summers No Comments

Introduction to Cylindrical Coordinates

Mathematics
What are cylindrical coordinates? A coordinate system is a system that provides a way to describe points and other features of geometric figures in Euclidean space. Generally the best coordinate system is that system which adequately does the job in simplest fashion. In this article, we will use (r, Φ, z) for our new coordinate system. Many use this, but others use a different assortment of letters, unfortunately. Forewarned is forearmed. Cylindrical Coordinates - Introspection When we're working in two dimension, we are able to draw our coordinate axes using the sheet of the paper, representing a plane. Two orthogonal axes are drawn, one horizontal the other vertical. When using r and Φ the way we view the axes is really different from how we view them when they represent x…
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