Although that might be common-ish knowledge, here's some information which isn't so commonly-ish known:
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Captain Jed R. wrote:
Ok, so the purpose of the various symbols used on different uniforms during TOS was to denote the ship an officer was assigned to. Common-ish knowledge, decent enough concept. What that doesn't explain though is the absolutely batshit crazy design of some of them. I can sort of see the simplicity of the Exeter design, and everyone loves the iconic arrowhead (I should imagine), but what the hell was the Constellation design about? Or that off-centre arrow for Defiant? Or the vaguely-rear-end shape of the Antares? And what is it about a squiggly line that says "Constellation", assuming it wasn't just the Admiralty deciding "the hell with it, go crazy, design me a patch that looks like a rear end".