Etymology
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Words related to catty-cornered

*kwetwer- 
Proto-Indo-European root meaning "four."

It forms all or part of: cadre; cahier; carillon; carrefour; catty-cornered; diatessaron; escadrille; farthing; firkin; fortnight; forty; four; fourteen; fourth; quadrant; quadraphonic; quadratic; quadri-; quadrilateral; quadriliteral; quadrille; quadriplegia; quadrivium; quadroon; quadru-; quadruped; quadruple; quadruplicate; quarantine; quarrel (n.2) "square-headed bolt for a crossbow;" quarry (n.2) "open place where rocks are excavated;" quart; quarter; quarterback; quartermaster; quarters; quartet; quarto; quaternary; quatrain; quattrocento; quire (n.1) "set of four folded pages for a book;" squad; square; tessellated; tetra-; tetracycline; tetrad; tetragrammaton; tetrameter; tetrarch; trapezium.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit catvarah, Avestan čathwaro, Persian čatvar, Greek tessares, Latin quattuor, Oscan petora, Old Church Slavonic četyre, Lithuanian keturi, Old Irish cethir, Welsh pedwar.
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carrefour (n.)
late 15c., "place where four ways meet," from Old French carrefor (13c., quarrefour), from Medieval Latin quadrifurcus "four-forked," from Latin quatuor "four" (from PIE root *kwetwer- "four") + furca "two-pronged fork" (a word of unknown etymology). "Formerly quite naturalized, but now treated only as French" [OED]. Englished variant carfax is from Middle English carfourkes.
catawampus (adj.)

also catawampous, cattywampus, catiwampus, etc. (see "Dictionary of American Slang" for more), American colloquial. The first element perhaps is from obsolete cater "to set or move diagonally" (see catty-cornered); the second element perhaps is related to Scottish wampish "to wriggle, twist, or swerve about." Or perhaps the whole is simply the sort of jocular pseudo-classical formation popular in the slang of the times, with the first element suggesting cata-.

Earliest use seems to be in adverbial form, catawampusly (1834), expressing no certain meaning but adding intensity to the action: "utterly, completely; with avidity, fiercely, eagerly." It appears as a noun from 1843, as a name for an imaginary hobgoblin or fright, perhaps from influence of catamount. The adjective is attested from the 1840s as an intensive, but this is only in British lampoons of American speech and might not be authentic. It was used in the U.S. by 1864 in a sense of "askew, awry, wrong" and by 1873 (noted as a peculiarity of North Carolina speech) as "in a diagonal position, on a bias, crooked."

kitty-corner 

also kittycorner, kitty-cornered, kittycornered, etc., see catty-cornered.