Etymology
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Words related to cycle

*kwel- (1)
also *kwelə-, Proto-Indo-European root meaning "revolve, move round; sojourn, dwell."

It forms all or part of: accolade; ancillary; atelo-; bazaar; bicycle; bucolic; chakra; chukker; collar; collet; colonial; colony; cult; cultivate; culture; cyclamen; cycle; cyclo-; cyclone; cyclops; decollete; encyclical; encyclopedia; entelechy; epicycle; hauberk; hawse; inquiline; Kultur; lapidocolous; nidicolous; palimpsest; palindrome; palinode; pole (n.2) "ends of Earth's axis;" pulley; rickshaw; talisman; teleology; telic; telophase; telos; torticollis; wheel.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit cakram "circle, wheel," carati "he moves, wanders;" Avestan caraiti "applies himself," c'axra "chariot, wagon;" Greek kyklos "circle, wheel, any circular body, circular motion, cycle of events,"polos "a round axis" (PIE *kw- becomes Greek p- before some vowels), polein "move around;" Latin colere "to frequent, dwell in, to cultivate, move around," cultus "tended, cultivated," hence also "polished," colonus "husbandman, tenant farmer, settler, colonist;" Lithuanian kelias "a road, a way;" Old Norse hvel, Old English hweol "wheel;" Old Church Slavonic kolo, Old Russian kolo, Polish koło, Russian koleso "a wheel."
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bicycle (n.)

1868, from bi- "two" + a Latinized form of Greek kyklos "circle, wheel" (see cycle (n.)), on the pattern of tricycle; both the word and the vehicle superseding earlier velocipede.

The English word is said in some dictionaries to be probably not from French, but the 1868 citations are in a French context: The velocipedes, about which the Parisians have run mad at the present moment, are of various kinds. ... The two wheel velocipedes, the bicycles as they are styled, are intended for the male sex only, and are by far the swiftest machines. ["Supplement to the Courant," Hartford, Conn., Dec. 16, 1868]. Pierre Lallement, employee of a French carriage works, improved Macmillan's 1839 pedal velocipede in 1865 and took the invention to America. See also pennyfarthing. As a verb, from 1869.

The velocipede of 1869 was worked by treadles operating cranks on the axle oi the front wheel. This was modified in the earliest form of the bicycle by greatly increasing the relative size of the driving-wheel and bringing the rider directly over it. Later the "safety" bicycle was introduced, in which the wheels were made of equal or nearly equal size, and for the direct action upon the front wheel was substituted indirect action upon the rear wheel, by means of a chain and sprocket-wheels .... [Century Dictionary]
cyclic (adj.)

1794, "pertaining to or moving in a cycle or circle," from French cyclique (16c.), from Latin cyclicus, from Greek kyklikos "moving in a circle," from kyklos "circle, wheel, any circular body, circular motion, cycle of events" (see cycle (n.)). Sense of "connected to a literary cycle" is by 1822.

kilocycle (n.)
also kilo-cycle, 1921, from kilo- + cycle (n.).
Ku Klux Klan 
1867, American English, originally Kuklux Klan, a made-up name, supposedly from Greek kuklos, kyklos "circle" (see cycle (n.)) + English clan. Originally an organization of former Confederate officers and soldiers, it was put down by the U.S. military in the 1870s. Revived 1915 as a national racist Protestant fraternal organization, it grew to prominence but fractured in the 1930s. It had a smaller national revival 1950s as an anti-civil rights group, later with anti-government leanings. In late 19c. often simply Kuklux.
megacycle (n.)

"one million cycles" (of oscillation), 1928, from mega- + cycle (n.). Often meaning "one million cycles per second."

tricycle (n.)
1828, "three-wheeled horse-drawn carriage," from French tricycle (1827); see tri- + cycle (n.). The pedal-powered version is first attested 1868.
recycle (v.)

"to reuse material," 1922, originally of industrial processes; see re- + cycle (v.). Specifically of waste material reclaimed or converted into usable form, by 1960. General or figurative use is by 1969. Related: Recycled; recycling.