Google on Harry Nilsson

http://www.google.com/search?q=the+loneliest+number

I guess this qualifies as a cute math thing--after all, one is a number divided by two. Also you have to be pretty good at math, and pretty cute, to work for Google.

Inscribed dog

Credit for this goes to ihasahotdog: the loldog blog (I can't believe I just wrote that). There are a bunch of other suggested captions there, which are all less good.

Ampersandwich

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Cutting a bagel into interlinked halves

George Hart shows how to slice a bagel into two linked halves.

The surface of the cut is a Möbius strip with two twists. As Hart remarks, you can also cut a bagel where the cutting surface is a regular (one-twist) Möbius strip:

You can still get cream cheese into the cut, but it doesn't separate into two parts.