Prediction and Controls
Click the shapes in the order you think they will melt, from fastest to slowest.
1st
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2nd
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3rd
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4th
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5th
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Time
0.0 min
3D Melting Visual
Shared volume, different surface areas. You can drag the visual to rotate it.
Volume vs Time
This graph uses your updated Desmos state and takes the minute slider directly as
T.Where It Started
This project began with one basic related-rates problem from Math 124, one of the first problems in the Section 3.9 homework. We asked follow-up questions about melting, changed the assumptions, compared new shapes, and this is where it led.
There is interesting math around every corner and inside every question.
Going Further
Melting is still an active area of mathematical research. Our model assumes self-similar shrinking, but real melting can change shape in much more complicated ways.
We found reference to a breakthrough in something called the "Stefan problem" which shows that even when a melting surface becomes irregular, a certain amount of smoothness must still appear.