Hexagon Diagonals for Dummies (Again) - The Freelance Files MMLXXXIX

nine hexagon diagonals

We recheck the content we've given DotD awards on a semi-regular basis, mostly to see if someone has been so ashamed they deleted it or the content farm hosting it has decided it is so bad it needs to be rewritten. A while back, we noticed that a geometry post (by Jess Kroll, proud possessor a MFA in creative writing) had been deleted by Leaf Group. We didn't pay much attention until we realized that it had actually been sent to the "cleanup team" for a rewrite. The problem? rewrite specialist Rosann Kozlowski did little more than reword and lengthen Kroll's version of "How to Find the Diagonal of a Hexagon."

While Kozlowski more than doubled the length of Kroll's version (600-plus words vs. 280) by adding such useful information as,

"A carbon ring is a hexagon shape with a carbon at each corner..."

...(as befits a chemistry major turned word hack); Rosann still neglected to address Kroll's most glaring shortcoming. According to both authors, a hexagon has nine diagonals. Kozslowski even chirped that,

"For regular hexagons, the nine diagonals form into six equilateral triangles."

Uh, no, Rosann, they don't, they form eight: six of the diagonals (blue above) form two equilateral triangles, in the shape of the familiar Star of David. The other three (green above) form six equilateral triangles, each with a side of the hexagon as one side and a point at the center.

Oh, sure, like Kroll before her Kozlowski managed to spit out the information that, for a regular hexagon, the diagonal lines connecting a pair of vertices separated by two others (the green lines above) are twice the length of a side of the polygon. As for the lines separated by a single vertex? Well, you need to do some math. The half length of one of those blue lines can be calculated using trigonometry. We'll let you figure out how to get there, but the simple answer is that length of a blue line is 

2 * (sin60° * length of a side).

In other words, like Kroll before her Kozlowski only gave half an answer and, like Kroll before her, Kozlowski's failure of logic is more than enough to win her the coveted Dumbass of the Day award, rewrite division. Oh, yeah, and a tip of the hat to biology major Lana Bandoim, B.S., who also failed to remember the definition of diagonal while "reviewing" the content.

MM - GEOMETRY