## What are Radians? Where Do They Come From?

Consider a simple equilateral triangle (a triangle that has 3 equal sides and 3 equal angles). Most high-school students know the three angles of such a triangle are 60 degrees (60°) each, for a total of 180°. But degrees is not the only unit used to quantify an angle. Alternately radians can be used. What are radians? Are they just another number? Where do they come from? Degrees Before we get into radians, however, let’s consider where degrees came from, and why it may not be the best choice for the measurement of an angle. If you are facing north and turn to the east, you have turned 90 degrees. Now turn south and you’ve turned another 90 degrees. Turn west, another 90 degrees. Continue the turn so you once…

## 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.…

## Analytic Geometry: The Ellipse and the Circle

The circle is really a special type of ellipse. In analytic geometry, an ellipse is a mathematical equation that, when graphed, resembles an egg. An ellipse has two focal points. The distance apart between the two points is one way of describing a particular ellipse. If the two points come together the ellipses become a circle with the point at its center. The equation for an ellipse is, x2/a2 + y2/b2 = 1 In this equation, "a" and "b" are constants that determine the shape of the ellipse, whereas x and y are variables, i.e., they can take on a host of values. When the value for x is known, the value for y is determined. Or, if it is y that is known, then x is determined. If a…

## Why Balloons Blow Up Round

[caption id="attachment_13619" align="alignright" width="440"] Balloons.[/caption] When you blow up latex balloons and build up some pressure in them, unless they are especially made to become some other shape, they tends toward roundness—they assume a spherical shape. Balloons blow up round! Why does it do that? Let’s look at the simple math and physics of the thing. Stretching Requires Force Take an ordinary piece of burst balloon and pull on it with your fingers. It takes a definite force to accomplish that, doesn’t it? And the task becomes more difficult the more you stretch it. We call the exertion “force.” It takes force to stretch the rubber. Since the required force becomes greater the more you stretch the skin of balloons, it is clear the more air you blow into them,…