Mathematics Archives - Page 2 of 5

23Oct 2016 by Vincent Summers 2 Comments

Memorizing Long Numbers – Two Quick Memory Aids

[caption id="attachment_15687" align="alignright" width="440"] Dice - Image Pixabay[/caption] Memorizing long numbers? How can I do that? I recall being told the average American can repeat quickly only numbers with five or fewer digits. For example, hearing several numbers, say 17, 38294, 584, and 127532, most can only say back the 17, 38294, and 584 – not the 127532. How can such a person improve in memorizing long numbers so he can recall 6, 7, and even more digits? There are two ways. The first involves a kind of 'device'. One definition of mnemonic device is “a memory technique to help your brain better encode and recall important information”. Memory Aid – Grouping Numbers Almost anyone can repeat a string of three. Jill speaks a three-digit number. Bob repeats it back…

05Oct 2016 by Vincent Summers 1 Comment

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

Education, Mathematics

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…

09Aug 2016 by Vincent Summers 2 Comments

The Algebra Distributive Property – A Simple Introduction

Logic, Mathematics

The algebra distributive property lets you multiply a sum by multiplying each part separately and then adding those amounts together. These words are bound to confuse the reader, so let’s consider an example that will demonstrate what we mean. The Example We want to multiply 4x7. Let’s write it as (4)(7). Then, (4)(7) = 28 Now let’s replace 4 with its equivalent, 3+1. And let’s replace 7 with its equivalent, 5+2. Then, (3+1)(5+2) = 28 This seems to be a pretty strange way to write 4x7, doesn’t it? Yet in mathematics – in algebra-style notation – it is just as correct as 4x7. In this form, we can hopefully explain in an understandable way, how the algebra distributive property works. Refer to the diagram to see how we can do…

08Aug 2016 by Vincent Summers 1 Comment

Constants and Variables: A Simple Introduction to Algebra

Logic, Mathematics

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…

05Aug 2016 by Vincent Summers 2 Comments

A Negative Times a Negative Makes a Positive Number

Logic, Mathematics

In high school we were introduced to negative numbers. Why high school? Why not earlier? Because we cannot picture in our minds what a negative number is. We know what positive numbers are. For instance, if we have three apples and someone gives us four more apples, we know we now have seven apples. And as to multiplication, if we have three groups of four three apples each, we know we have 12 apples. But can you visualize what a negative apple might be? How can you demonstrate negative times negative makes positive? Pure Numbers Forget units for the moment. We will concentrate on pure numbers. In the above example, the four groups of three apples becomes simply 4(3) = 12. Suppose, instead of 4(3) we make on of the…

02Aug 2016 by Vincent Summers 2 Comments

XY-Coordinate System Symmetry with Examples

Logic, Mathematics

[caption id="attachment_28582" align="alignright" width="480"] Image Department of Energy[/caption]In high school mathematics, the topic of symmetry is bound to arise. Especially is this so in analytic geometry. For curve C, what is its XY coordinate system symmetry? How is it symmetric about the y-axis? The x-axis? The origin? The line y = x? The line y = -x? Symmetric about some point other than the origin? Symmetry About the Y-Axis Symmetry about the y-axis means that if there is a curve that lies to the right of the y-axis, there is an identical copy of it to the left of the y-axis. That is, it is symmetrical if each x value can be replaced with –x. Thus, the parabola y = 1/2x2 is symmetric with regard to the y-axis. For every…

31Jul 2016 by Vincent Summers 2 Comments

Point on a Line, a Line on a Plane, and a Plane in Space

Logic, Mathematics

Each point has a specific location. Two points determine a line. Three points determine a plane. Let us consider some simple math derivations to arrive at a format for each. For simplicity’s sake, we will use the familiar x, y, z Cartesian coordinate system. We begin with a point on a line. First, Point on a Line In space, a single point has an x value, a y value, and a z value. If the coordinate system chosen for the point is a simple 1-D line, then only one variable – say x – is needed to describe it. Then, since there is no y or z to consider, the mathematical description of the point is x = c But let us, for reasons that will be understood later, write…

13May 2016 by Vincent Summers 1 Comment

Mathematical Powers – a Simple Insight

Education, Mathematics

[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…

18Apr 2016 by Vincent Summers 3 Comments

Parametric Equations: I Corrected the Text Book

Education, Mathematics

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…

11Mar 2016 by Vincent Summers No Comments

QSO Instructional Videos

Mathematics, Physics

[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…