In geometry, the side of a right triangle opposite the right angle.

“About binomial theorem I’m teeming with a lot o’ news,

With many cheerful facts about the square of the hypotenuse.”

– Gilbert and Sullivan,The Pirates of Penzance(1879)

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Act 2, Scene 3 – Frasier’s ApartmentFade in. Niles is playing the piano, with Leland and Frasier looking on. They are singing “Modern Major-General” from “The Pirates of Penzance.”Frasier:I know the kings of England and I quote the fights historical, From Marathon to Waterloo in order categorical.Niles:I’m very well acquainted, too, with matters mathematical, I understand equations both the simple and quadratical.Martin watches them, looking a bit left out.Leland:About binomial theorem I’m teeming with a lot of news, With many cheerful facts about the square of the hypotenuse.Together:With many cheerful facts about the square of the hypotenuse, With many cheerful facts about the square of the hypotenuse, With many cheerful facts about the square of the hypotenuse!Martin tries to join in.Martin:With awful facts about the scary hippopotamus!The others turn and look at him.Leland:What a wonderfully musical family you are.– Frasier (2003) Season 10, Episode 22; “Fathers and Sons” [No. 240]

Actually, that’s a misspelling. It’s not hypotenuse, it high pot in use: the king is on his throne about to engage in a great movement.

I wondered where you’d gone.

I took a wrong turn at Albuquerque

and that’s went it all became quirky

so I travelled the multiverse,

but I think I was in reverse,

I ended up back here

landed on my ear;

I still couldn’t hear a thing

so I began to sing:

the crowd gave a resounding frown,

that’s when the curtain went down…

Let me know if you can make sense of the above, I certainly can’t. And how are you? I’ve seen your comments along the way but I didn’t want to spoil the flow, it was simply too beautiful to behold…

Landed on your

what–?yeah, exactly! (Have you never read that expression: landing on your ear? = that was before it was OK to write swear and say, landed on your arse or ass for those who don’t like donkeys. Falling sideways, on the side of the head, that sort of thing.) Or were you just pulling my leg a little bit there, Mr. Arch?

Both.

And then there’s that old college football cheer:

I’m not really sure, however, what any of this has to do with Hypotenuse —

Sorry, back to the beginning. The “high pot in use” and attendant imagery is how I remembered the hypotenuse theorem in geometry. I am in love with the concept of the right angle triangle; that you can measure the length of the long side by using squares on the right angled sides: that’s magic to me. That knowledge has so many uses in construction. I remember my math 11 textbook had a picture of the RAT on the front cover with the squares attached. Beautiful!