1. CARLTON BANKS-- Carlton was the cousin of Will Smith's character in the TV show Fresh Prince of Bel-Air. As evidenced by the picture above, he was a fan of the draped-sweater look.
2. LUPUS-- Here's another TV reference. On the show House, Hugh Laurie plays the magnificently crotchety Dr. House, who likes to inform people that the mysterious illness of the week is not lupus.
3. THE TWILIGHTS HE WAS LOOKING FOR-- These aren't them. Obi-Wan Kenobi said so.
4. FORMING A HYPOTENUSE-- The hypotenuse is the side opposite the 90-degree angle of a right triangle. This applies to all right triangles, not only the isosceles right triangle pictured (another common example is the 30 degree-60-degree-90-degree right triangle).
I believe that, in the context used, Mr. Gumption actually meant 'hypothesis', but that's a different matter.
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