Curves and Angles for Dummies

Road curvature angle

We may have mentioned this before, but what the heck: you probably didn't read it. We're aware from both first-hand experience and observation that many a Demand Media Studios (DMS) writer would grab several "titles" that appeared related and then pound out variations on the same answer for them all. Since the people  supposedly fact-checking the articles (aka content editors) only checked for format, the result is something we call "compound ignorance" – and today's DotD is a prime example. Ryan Menezes dipped his pen into the algebra well (at least) three too many times, one of which is "How to Find the Angle of a Curve" at Sciencing.com.

That's a hard one... mainly because the question is either ambiguous or simply stupid. However, the closest we can figure is that the OQ wanted to know something along the line of how to determine the change in direction at a curve, perhaps on a highway. Pretty simple, really: merely project the straight sections past the curved section and measure (or calculate) the angle. But that's not what Menezes said. Having already "defined" slope twice ("the extent of its slant" and some crap about a best-fit line), Ryan figured he'd use it again:

"A curved line on a graph changes continuously in gradient. This means the rate of change of the y-axis's values changes constantly as the values of x change. The most common way for describing this gradient is a decimal value ranging from 0 to infinity. An alternate way of describing the slope is a line's angle of inclination. To find this vale [sic] for a curved line, you must draw a tangent, which is straight line, to the curve."

Menezes' problems here are multiple:

1. That word "continuously" isn't necessarily true – think "circle"...
2. Where did this "most common way" crap come from?
3. How does slope differ from angle of inclination? and how can a curve even have an angle of inclination?
4. That's not the definition of a tangent, Ryan

Most important, this isn't what the OQ was looking for in the first place. As near as we can tell, the question is really about degree of curvature. It could also be about the angle described by an arc of a circle, the angle between a curved line and the tangent, or even the angle between two intersecting curves. It sure as hell, however, is not about the slope of the tangent at a random point – but that's exactly what Ryan described doing, including this moronic statement about tangents:

"Draw a straight line that touches the curve at a single point. This line must be equally close to the curve on either end of this contact point."

Nope, here's some cretin who claims to have a "BS in Journalism" and even to be a member of Mensa. Whether or not either is true, he certainly doesn't know anything about the topics of curves, tangents, slopes, derivatives, algebra, calculus... and yet he tried to write about them: the perfect candidate for Dumbass of the Day, right? Right!

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