I have long wondered about the similarity between some math words and some English grammar words. In particular ellipse vs. ellipsis and hyperbola vs. hyperbole.
I finally decided to look up their etymologies, and amazingly there is good rhyme to the reason!
Ellipse and Ellipsis
Both of these words come from a Latin root meaning, “a falling short or deficit.”
The grammar term, ellipsis, means the three dots used to designate missing words, or a deficit of words. Like … well…, you get the picture!
For the mathematical shape, or graph, an ellipse is created when a cone is cut by a line whose angle is less than (or falls short of) the angle of the side of the cone to the bottom of it. (#ARG, I know. Check out the pix.)
The brown line that creates the ellipse has a 25° angle which is much smaller than the 60° angle between the bottom and side of the cone:
You can see it “in action” here with the line falling:
Hyperbola and Hyperbole
A hyperbole is the fancy English grammar term for exaggeration. Everyone has used a hyperbole at least once!
And a hyperbola in math is the graph/shape that looks like the light beams from a two-sided flashlight.
Both of these words come from a Latin word that means extravagance or “throwing beyond.” You can see how an exaggeration (a hyperbole) is throwing beyond. But what’s up with the math word, hyperbola?
We look to the angle of the cutting line again. A hyperbola is cut from a cone (actually stacked cones – see the picture) with a line who’s angle is “beyond” or more than the angle of the side of the cone to the bottom. It’s just the opposite of the ellipse!
Check it out: (This one is somewhat drawn to scale so you can really see what’s going on.)
Are there more?
These are the only two that have bugged me through the years. But now I’m wondering if there are other math words that have cousins over in the English department.
Any ideas? Let me know in the comments or via twitter, would you?
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