Ovals for Dummy Geometry Students

Ellipse (L), regular Oval (R)

The idea that "Some are born great, some achieve greatness, and some have greatness thrust upon them" is attributed to Shakespeare. Here at the Antisocial Network, we have our own version of that adage: "Some are born dumbasses and some achieve dumbassery, but no one is forced to be a dumbass." No kidding: no one ever makes our awardees be stupid in print, they (almost) all do it to themselves! We can forgive a foolish mistake or two (heck, our founder made one just a couple of years ago), but going back to that well of stupidity time and again really tends to piss us off. Speaking of serial stupidity, however, brings us to today's awardee, multiple repeater (and we do mean multiple) Joan Whetzel found this time spreading her brand of misinformation at HubPages.com about "Determining an Oval's Perimeter Measurement."¹

As is typical of Joan's posts, she reveals her ignorance of the topic right up front: in other words, she starts out with a redundant title: "perimeter measurement"? Give us a break... Joan opens by introducing the topic in her typical semi-coherent fashion:

"In geometry, we study points, lines, angles, surfaces, shapes (i.e. circles and ovals) and solids (e.g. a sphere, or elliptical sphere). We want to know their properties, their relationship to each other and how to measure them. Take a drawing of an oval, for instance. It has no angles to examine or measure. It doesn't have points around its surface like an egg would. It does, however, have a line defining its outline called the perimeter."

We're a little curious about those "points around [the] surface" of an egg, but hey -- if Joan says they're there, who are we to argue. OK, rhetorical question there: we can argue because we know she's full of crap. Joanie then goes on to explain to us that "The length of the oval's perimeter can be determined through the use of calculus. But that's too complicated. A rough estimate can be obtained by taking two measurements inside the oval - the semi-major axis and the semi-minor axis - and performing this geometry equation..." At which point she transcribes one of the equations for the circumference of an ellipse. According to Joan, "An oval... has a major axis (diameter that runs the long way across the oval) and a minor axis (diameter that runs the short way across the oval)..."

And there, dear reader, is where Whetzel's post goes utterly to junk. It's junk because Joan's definition of "oval" has a fatal flaw. You see, she has decided that an ellipse and an oval are the same thing, but that is not true. An ellipse is a (very) special form of an oval, so you could say, "All ellipses are ovals," and you would be right. However, to say, "All ovals are ellipses" would be incorrect. An ellipse does, indeed, have semi-major and semi-minor radii, along with two foci. If you draw an ellipse, you can create a rectangle that is tangential to the ellipse at the midpoints of all four sides - exactly like you can draw a square that circumscribes a circle (after all, a square is a special rectangle and a circle is a special ellipse).

You cannot, however, always draw a rectangle that circumscribes an oval in the same manner: consider the egg Whetzel keeps mentioning. The polygon that circumscribes an egg is not a rectangle, it is a trapezoid.

In other words, Joan lied – out of ignorance, we presume, rather than out of malice – when she claimed she would explain how to "determine an oval's perimeter." She didn't. What she did do was explain (rather clumsily, we think) how to approximate the circumference of an ellipse. And we think not knowing the difference is plenty of reason for why Joan has been, once again (fifteen times!), named our Dumbass of the Day.

¹ Joan deleted her post (out of shame?), and archive.org's Wayback machine never made a copy of the post. Oh, well, no loss...

copyright © 2016-2021 scmrak

DD, MM - GEOMETRY