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1817, literally "observer of beautiful forms," coined by its inventor, Scottish scientist David Brewster (1781-1868), from Greek kalos "beautiful" + eidos "shape" (see -oid) + -scope, on model of telescope, etc. They sold by the thousands in the few years after their invention, but Brewster failed to secure a patent.
Figurative meaning "constantly changing pattern" is first attested 1819 in Lord Byron, whose publisher had sent him one. As a verb, from 1891. A kaleidophone (1827) was invented by English physicist Sir Charles Wheatstone (1802-1875) to make sound waves visible.