go into, plunge, inlay
嵌 centers on fitting one thing tightly into another: going into a space, plunging in, or setting an inlay. The idea is a snug insertion where the object becomes embedded.
嵌 combines 山 (mountain) with 甘 and 欠, but the historical development is uncertain. The modern form may be a simplified or variant shape, and the exact origin of the components is not clearly established.
Picture a mountain 山 with a deep crevice, and something sweet 甘 is wedged inside, like a candy stuck in a gap. The open mouth 欠 suggests the space where it fits tightly.
For カン, imagine a can being plunged into a tight hole in the mountain: can -> カン, and it fits perfectly like an inlay.
to fit; to get into; to go into; to be fitted with (e.g. door with a window)
to fit (e.g. a pane into a frame); to insert (e.g. a cork); to fasten (a button)
inlay; inlaying; damascening
insertion; inlaying
to put in a (plaster) cast
inlaid woodwork
setting in; inlaying; dovetailing
fitting together (e.g. nuts and bolts); fit
wait for the middle tile of a chow
wait for the middle tile of a three-in-a-row which will finish one's hand
incarceration (e.g. of a hernia); strangulation
to hoop; to put a hoop on; to bind a barrel with hoops