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Proof without words: One house is temporarily deleted. The lines connecting the remaining houses with the utilities divide the plane into three regions. Whichever region the deleted house is placed into, the similarly shaded utility is outside the region. By the Jordan curve theorem, a line connecting them must intersect one of the existing lines.
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A chain hanging from points forms a catenary. The silk on a spider's web forming multiple elastic catenaries.. In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
Spy Sinker is a 1990 spy novel by Len Deighton.It is the final novel in the second of three trilogies about Bernard Samson, a middle-aged and somewhat jaded intelligence officer working for the British Secret Intelligence Service (MI6).
A narrative hook (or just hook) is a literary technique in the opening of a story that "hooks" the reader's attention so that they will keep on reading. The "opening" may consist of several paragraphs for a short story, or several pages for a novel, and may even be the opening sentence .
On an ordinary two-wire telephone line, off-hook status is communicated to the telephone exchange by a resistance short across the pair. When an off-hook condition persists without dialing, for example because the handset has fallen off or the cable has been flooded, it is treated as a permanent loop or permanent signal .