Curved Surfaces for Dummies

neither sphere nor cylinder, but still a curved surface

A lot of things trip our staffers' bogosity detectors while they're looking for DotD nominees. One of them is overly-specific writing for a rather general question. We see that a lot in the family of niche sites where Leaf Group stashed old eHow.com posts. That's precisely what we found for today's awardee, a freelancer who calls herself Stephanie Ellen (and sometimes S. Deviant). Her text for today is from Sciencing.com; a little something the leafies call "How to Calculate the Area of a Curved Surface."

Self-described as a "mathematics and statistics [teacher] at the university and college level," Ellen's answer led our staff to believe that her course load must be restricted to remedial arithmetic and some form of "numbers for kindergarten teachers." That's because her answer, such as it was, proved incomplete at best and more likely worthless. Stephanie started off on the wrong foot, blithely informing her readers that,

"Calculating a square area is as easy as multiplying the length by the width."

At that, several of our staffers blanched and mumbled something about "Not 'squares,' planes!" Ellen then launched into her "help," but first she had to define a "curved surface" as a "sphere or a cylinder." Apparently she was afraid of opening the whole can of worms that is curvature... Oh, Steph managed to walk people through the formula for the surface area of a sphere (A = 4πr²), though the process took her 47 words. Then she tackled the surface area of a cylinder (A = 2πr² + 2πrh); another 91 words, including the rather puzzling instruction to, "Square the radius... Multiply Step 1 by 6.28..."

...which turns out to be her version of "multiply by 2π"! Wow! For whatever it's worth, one of Ms. Deviant's habits irritated the bejeepers out of our staff numbers guy, who fumed over statements like "2 inches * 10 inches = 20 inches squared": he was heard muttering, "It's 'square inches,' dummy!"

We won't argue that Stephanie got the wrong answers for her two examples. They were both correct, although we found her instructions exceedingly clumsy. No, we're here to argue that no one asked her to provide formulas for the surface area of a sphere and a cylinder – we aren't even sure one could rightfully consider a cylinder to be a "curved surface," although clearly the side forms a curve.
We're also here to point out that Ellen's/Deviant's answer was woefully inadequate, even by eHow standards. There are myriad curved surfaces beyond a sphere and the side of a cylinder. Think about it: hemispheres... ovoids... half pipes... cones... And that doesn't even touch on complex curved surfaces ranging from a teardrop to the hood of a Lotus Elise. Stephanie didn't even mention that complex curves will require more complex mathematical operations. For that deliberate omission, we hereby name her the Dumbass of the Day.

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