Who likes math? Everyone, of course! That's why it sometimes happens to me when I'm bored at work. A couple days ago I was thinking about how my wedding cake had been cut. An inner circle was cut, and the inner circle and outer wheel shapes were sliced into pieces (Fig. 1).

I began to wonder how wide the inner circle would have to be in relation to the outer circle (Fig. 2) for the pieces to all have the same volume. First I made the simplification that the cake was a uniform height, meaning as long as the surface areas were all the same, the volumes would be too. Next I decided that the outer wheel could be cut into twice as many pieces as the inner circle, meaning it has to have twice the surface area (Fig. 3). Phrased as a problem:
Given that: Ab=2Aa
Solve for: Ra as a function of R
( Here's my solution )
Okay, that wasn't fun. How about something easier?
One of these things does not belong here,
One of these things is not the same.
One of these things does not belong here,
Now it's time to play our game!
Beef
Chicken
Pencil Sharpener
Cthulhu
Godzilla
A box of tissues
Gort
Torg
The Tin Woodsman
Scantily clad, skinny girls doing (supposedly) sexy gyrations under flashing lights
Drum machine dance beats
Polka
Okay, that last one was a trick question, they all go together, at least according to Slovenian Group Atomik Harmonik. Their videos are in the right column under "Videospot". If you only watch one, watch Turbo Polka, a song that put them on the charts in Germany and Austria. The accordian pimp in the ice cream suit is not to be missed. The sad thing is that Scandahoovian choreography doesn't seem to have improved much since the days of Armi and Danny from Finland, but at least the dancers are moving at the same time and the camera work makes it harder to see what they're actually doing.

I began to wonder how wide the inner circle would have to be in relation to the outer circle (Fig. 2) for the pieces to all have the same volume. First I made the simplification that the cake was a uniform height, meaning as long as the surface areas were all the same, the volumes would be too. Next I decided that the outer wheel could be cut into twice as many pieces as the inner circle, meaning it has to have twice the surface area (Fig. 3). Phrased as a problem:
Given that: Ab=2Aa
Solve for: Ra as a function of R
( Here's my solution )
Okay, that wasn't fun. How about something easier?
One of these things does not belong here,
One of these things is not the same.
One of these things does not belong here,
Now it's time to play our game!
Beef
Chicken
Pencil Sharpener
Cthulhu
Godzilla
A box of tissues
Gort
Torg
The Tin Woodsman
Scantily clad, skinny girls doing (supposedly) sexy gyrations under flashing lights
Drum machine dance beats
Polka
Okay, that last one was a trick question, they all go together, at least according to Slovenian Group Atomik Harmonik. Their videos are in the right column under "Videospot". If you only watch one, watch Turbo Polka, a song that put them on the charts in Germany and Austria. The accordian pimp in the ice cream suit is not to be missed. The sad thing is that Scandahoovian choreography doesn't seem to have improved much since the days of Armi and Danny from Finland, but at least the dancers are moving at the same time and the camera work makes it harder to see what they're actually doing.
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