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…
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29Sep 2015 by Vincent Summers No Comments

Collapsing then Expanding the Equation for a Sphere

Mathematics
[caption id="attachment_8626" align="alignright" width="480"] How simple is a sphere?[/caption] Equation for the Simplest Sphere The equation for a sphere with its center at the origin is: x2 + y2 + z2 = c2 Where c is a positive constant. For simplicity, let's choose a positive constant, k, such that k = c2. Equation for a Circle by Collapsing a Sphere Collapsing it in one dimension generates the equation of one of three circles: x2 + y2 = k x2 + z2 = k y2 + z2 = k Equation for a Point by Collapsing a Circle Collapsing the three circles in one dimension generates two equations representing precisely two points for each of them: For x2 + y2 = k, x²2 = k y2 = k For x2 + z2…
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31Jul 2015 by Vincent Summers No Comments

Generate 2D Math Objects by Collapsing 3D Math Objects

Mathematics
I had some excellent high school mathematics instructors. They both loved their field and took an interest in their students. Since high school, I have had a deep interest in collapsing 3D mathematical equations to derive equations for 2D mathematical objects or modifying 2D objects into other 2D, or 2D objects into 1D. A 3D sphere becomes a 2D circle. A 2D parabola becomes a 1D line. The 2D hyperbola shown, if collapsed along the x-axis, becomes two 1D line segments stretching at one end to infinity. The same hyperbola collapsed along the y-axis becomes a complete line. A 2D circle becomes a single 1D line segment of a length equal to the diameter. An Example of Collapsing 3D into 2D What can be obtained by collapsing 3D math objects…
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07Mar 2014 by Vincent Summers No Comments

Secondary School Math Problems Plus Solutions

Mathematics
[caption id="attachment_5613" align="alignright" width="480"] Fractal[/caption] For some, it's actually fun when they come across secondary school math problems plus solutions. It's because they are no longer accountable, since they graduated years ago. Math Problems Plus Solutions Problem 1: Find the slope intercept form of the line passing through the point (– 1, 5) and parallel to the line – 6x – 7y = – 3. The line given is rewritten (in slope-intercept form, y = mx + b) as y = – 6/7 x + 3/7 Thus the slope m = – 6/7 Now two lines are parallel if they have the same slope. So, y = – 6/7 x + b is the formula for the new line, with the intercept not yet solved. We do so by inserting…
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