## Mathematics Intrinsic Value, or Simply a Tool?

It is a sunny day; you want to take a walk. We here define walking as the taking of repeated steps in any given direction. Our walk will take us into the field of mathematics. An Unusual Walk Imagine a stretch of sidewalk that is precisely 6 feet long. An initial 3 foot step is taken. Every step after that must be 1/2 the distance of the previous step. So our second step is 1/2 the length of the first step. The third step is 1/2 the length of the second step, and so on. Questions: 1. Theoretically, how long would it take you to reach the end of the 6′stretch? 2. How far would you have traveled, after each step? Answers: 1. You would, again theoretically, never make it…

## Factorials? What are They? A Simple Kind of Mathematics Shorthand

What are factorials? A variable is a symbol, often written as a letter of the alphabet that stands for a number that can vary in value. For example, take your age. That varies every year, doesn’t it? This year your age may be, say 21. If so, in 365 days your age will be 22. Another 365 days after that and your age will be 23. Thus age is a function of time. For you, we can write right now: A = 21 If the number of years that pass equals n, then for next year, n = 1 and An = 21 + n So, A₀ = 21 + 0 = 21 A₁ = 21 + 1 = 22 A₂ = 21 + 2 = 23 A₃ = 21…

## Constants and Variables: A Simple Introduction to Algebra

Please bear with me on this article. You see, I am a chemist, not a mathematician. Yet, as an individual who struggled with the concepts behind algebra (yet I grasped it soon enough to ace it), I can understand how others – intelligent individuals – can find algebra disconcerting. What are constants and variables? Two Basic Participants - Constants and Variables There are two primary participants in algebra – variables (which change) and constants (which do not change). Constants are specific numbers that never change. 27 is always 27. 43-1/4 is always 43-1/4. It never changes; it is constant. So let’s consider your age. Your age changes! This year you may be 16. Next year, you will be 17. Age is variable. Let’s write an equation. Your First Algebra Equation…

## Mathematical Powers – a Simple Insight

[caption id="attachment_14363" align="alignright" width="380"] Squaring - the Power of 2[/caption] Multiplication is one of the simpler operations we perform on numbers. As kids we had to learn the multiplication tables, one times two equals two, two times two equals three, three times two equals six, and so forth. It didn’t take long before most of us were comfortable multiplying simple numbers. But sometimes we multiply the same number times itself. In that case, we can write out the multiplication in the usual way, or we can write it in terms of mathematical powers. Mathematical Powers – a Simple Illustration Let’s consider the example of three times three. That can be written either 3 x 3 = 9, or in powers notation, 32 = 9 This tells us three to the…

## Parametric Equations: I Corrected the Text Book

A former fellow high school student, Ted L., recently contacted me. He wrote concerning our senior year, in which we shared a math course that included parametric equations. Ted Talks “I recall being in the advanced math class with Mr. Miller where I struggled quite a bit. In a discussion about solving some problem, you presented an alternative solution. Mr. Miller quickly dismissed your idea in a rather condescending fashion, shaking his head and stating, "No Summers, [you’re wrong]," with a tone that suggested your idea was rather silly, perhaps bordering on absurd. But you persisted, in a back and forth between you, that lasted for several minutes. During that discussion, I was completely lost, having no idea at all what either of you was talking about. After many gives…

## QSO Instructional Videos

[caption id="attachment_13734" align="alignright" width="340"] Blue = the parabola Black = the Lemniscate of Gerono Violet = the circle Red = QSO (1:1)[/caption] QSO Instructional Videos. Robert G. Chester, guest author at QuirkyScience.com surpassed expectation in his article on quasi-spherical orbits. A mathematics piece that should see application in many areas of physics as well, there is a distinctive flavor of art as well. To aid the reader of his article Quasi-Spherical Orbits – The Most Interesting Curves You’ve Never Heard Of, Robert has provided visual aids in the form of videos that may be seen on YouTube. In fact, they may even be downloaded if the visitor chooses to employ a download application for the purpose. Why are such videos of great value in understanding QSOs? Because most of us…

## 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.…

## Too Quirky Even for Me: The Mathematics of a Tornado

[caption id="attachment_7424" align="alignright" width="440"] The tornado spiral should be a fascinating topic for the mathematical meteorologist![/caption] I would love for someone to write an article on the mathematics of a tornado. A tornado is rather like a spiral, affected by the media and media parameters surrounding it. Doubtless, scale plays a role as well, even as scale causes the aeronautics equations of a jet to vary from those of a paper airplane. Download Mathematics of a Tornado I know of one publicly downloadable article on the subject of the mathematics of a tornado. It is written in broken English, but it was removed from its original online location. The good news is that it has been archived on Archive.org. Can you fully understand the piece and then in understandable terms,…

## Is a Circle a Polygon or Not? Implications for Calculus

[caption id="attachment_16285" align="alignright" width="380"] A 12-sided dodecagon.[/caption] What do you think? Is the circle a polygon, or not? As a result of watching a child’s video, I previously wrote a brief piece about the “corners” of a circle. The video was designed to teach children the various shapes—how many sides does a shape have, and how many corners? The video maintained a circle has no corners. I called that into question. I still do. And yet, I do not. I now think it’s all in how you look at it. Or, you might say, it’s all in the mathematical perspective. Consider. The Circle by Definition One can define the two-dimensional circle as the complete collection or “set” of points equidistant from a set point, not part of the circle. In…

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

[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,…