Mathematical Equation for a Cone

You go to the mall and request a double scoop of Rocky Road ice cream. The fellow serving says "Yes," and then he asks you asks if you would like that on a wafer or a sugar cone? Since most have eaten ice cream since childhood (unless we are dairy or otherwise intolerant), the majority of people think of a simple v-shape hollow structure as a cone. It has a top. It has a bottom. But is this the kind of geometrical shape that mathematicians think of when they refer to deriving the mathematical equation of a cone? A Mathematics Cone The cone of the mathematician bears some resemblance to that, but there are differences. The figure included with this article demonstrates that there are two v-shaped portions, not one.…

Not Infinitesimal Point Coordinates

[caption id="attachment_7388" align="alignright" width="480"] A coordinate system.[/caption] Infinitesimal point coordinates or not? Do you occasionally enjoy speculating? Even if one has technical training, if he speculates outside his field of expertise, he is opening himself up for possible difficulty. What he speculates, if he voices it, could result in his being labeled someone who doesn’t know what he is talking about. But I never was bright enough to avoid speculation, though I always acknowledge it for what it is. So humor me here… So if you know something of all this and what I'm writing either doesn't jive, or you can 'supercharge' it, please let me know. Mathematicians’ Points – Reality? Generally, a point in space is seen as a dot in space, having infinitesimal point coordinates, that is, no…

Analytic Geometry: The Parabola

What is a parabola, and of what use is it? If a sheet of paper is likened to an infinite plane in space, the x- and y-axes, drawn at right angles to each other, provide a means of describing each point on the plane of the paper in terms of an x and a y value. Thus the point (1, 3) tells us that beginning at the origin or center where the x-axis crosses the y-axis, if we travel one unit to the right and then three units up, we will have reached the point we seek. Introducing the Parabola Now we will pass on to describing a parabola.1 The parabola is an important mathematical "curve," inasmuch as it describes, mathematically, the behavior of a number of important actions, such…

Introduction to Cylindrical Coordinates

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…