## Analytic Geometry Coordinate Axes and Drawing a Line

In analytical geometry (usually taught in high school), two lines are drawn on a paper that are perpendicular to each other. The vertical line represents the "y-axis," and the horizontal line represents the "x-axis." Using these two axes, every point on the paper can be given a value that defines where the point is. If the place where the two lines cross is the zero point or origin, its coordinates (x, y) are simply, (0, 0). Along the horizontal x-axis, starting to the right of the (0, 0) point, write little numbers like a ruler has, 1, 2, 3, and so forth. To the left of that point, write, -1, -2, -3, and so on. For the y-axis, the 1, 2, 3, and such go upward, whereas the -1, -2,…

## Approximate Calculus: Area Under a Curve

Is it possible to calculate the area under a curve with any degree of accuracy? If we have a strong mathematical background, we may say, "Oh, that's easy. It's a matter of calculus." But what if you didn't take calculus? In fact, what if you never even attended high school? Is it possible to achieve an answer? Is it possible to use reason to come up with the principles of calculus? The answer is, indeed it is. I met a man who did just that. He asked me how I would figure the area under a curve. But he did more. He wanted to show how me how he had succeeded in solving the matter himself on his job in construction work. I was so impressed I exclaimed, "You've just…

## More High School Math

[caption id="attachment_5627" align="alignright" width="400"] Calculations[/caption] The most practical math for people to understand is undoubtedly high school math, rather than college math. After all, how much calculus is used when you go grocery shopping, get your plumbing fixed, or you go skiing on the weekend? High School Math You've got to love it. Here's the first high school math problem. Problem 1: Simplify the mathematical expression: (x-2y3)4 (x-3y4)-2 Simplifying the first parenthetical expression, we get (x-8y12) It is the powers we multiply when powers are raised to powers. Doing similarly with the second parenthetical expression, we get for that (x6y-8) The equation now reads, (x-8y12) (x6y-8) When we multiply numbers, we add and subtract powers. This gives, (x-2y4) [Answer] ------------------------- Problem 2: 2/10 divided by n equals 3-1/2. What does…

## Math Equations for Parallel and Perpendicular Lines

It's fun and very instructive to figure out the math equations for parallel and perpendicular lines. The basic mathematical equation for a line is, ax + by = c Here are three examples of line equations: 2x + 3y = 6 4x – 2y = –5 –x/3 + 2.47y = √3 Slope-Intercept Form One of the most useful formats for the equation of a line is the slope-intercept form. That form is written, y = mx + b The variables here are x and y. The letters m and b are constants that represent the rise or tilt of the line (slope, m) and the point at which the line crosses the y-axis (intercept, b). So the first of the three equations for a line listed above is written in…

## Determining the Equation for a Line from Two Points

Lines can be drawn in three dimensions, but most analytical geometry courses stick to lines in two dimensions, generally using the Cartesian or XY coordinate system. The generic equation for a line may follow the form: y = mx + b where m is the slope (measure of tilt or steep-ness) of the line, while b is its intercept or intersection with the y-axis. Equation for a Line from Two Points A line can be determined and an equation derived from two points. In the Cartesian system, for instance, take two points, (2 , 3) and (– 1 , 5). The first number in each pair represents the x-value of a point and the second number in each pair represents the y-value. Writing these points into the general equation y…

## Geometry Stop the World – I Want to Get Off

[caption id="attachment_3951" align="alignright" width="440"] Space Time Curvature - GNU Free Documentation License Version 1.2 by Johnstone[/caption] Many of us had to take plane geometry in high school. If you remember it was, “Theorem, Proof, Theorem, Proof...” What kind of ammunition did you use for the proof of a theorem? The axioms and previously proven theorems. I know, I know. Some of you want to forget the anguish. But I want you to recall the fifth axiom... Plane Geometry - Diagram 1 Look at Diagram 1. directly below. Line a is parallel to line b. That is lines a and b don’t meet. Axiom V: Through the point where line t meets line a there is no other line that can be drawn parallel to b. Now it took about 2,000…

## Distance, Velocity, and Acceleration

[caption id="attachment_3512" align="alignright" width="440"] Porsche 911 image - CCA 2 Generic[/caption] Do you know the relationships between distance, velocity, and acceleration? In learning about a matter, the primary obstacle is likely to be understanding the concept of it. For instance, as a young teen, I was introduced to algebra. Algebra is the first form of mathematics that contains not only numbers, but letters as well. Numbers are constant (after all, 3 is three), but letters are used to indicate variance in value, i.e. they are variables. Distance The concept of distance is so very simple, it is taken for granted. But should it be? Some young ones may not fully comprehend the concept of distance. That being said, we will assume here that the reader and his or her pupil…