Tag Archives: cones

Sideband #81: Tangent Cones

It’s been a while since my last Sidebands post. That’s partly because I’ve been working on a project that I’m sure will become a multi-post series and thought it would be nice to start with #81. But I’m not done (or actually started on the writing) yet, and this one has also been lurking for a while.

Essentially, I needed to figure out how to join a cone to a sphere in a seamless way (as in the picture here). This requires the sides of the cone meet the sphere at a tangent point.

It’s yet another case of actually needing the trigonometry I learned in school.

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Cones Can Fool You!

It’s happy hour and you and a friend go out for drinks. The bar is serving a new drink that catches your eye, and you both order one. They’re served in martini glasses (which are upside down hollow cones) and look quite tasty (see picture).

More to the point here, the glasses look acceptably full. Not a lot of “headroom” between the top of the drink and the top of the glass. Your friend, a mathematician, bets you they can pour all of your drink into their glass without spilling a drop.

Should you take that bet?

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