As seen on Reels · 90-second aha
The ant, the mug and the honey
An ant at the bottom of a mug wants the honey on the rim, on the opposite side. The mug is 10 cm tall and 8 cm wide. Which crawl is shortest?
1 · Bet first
Which route to the honey is shortest?
2 · Try it
Slide (or drag the mug) to unroll its side into flat paper. Watch what each route becomes.
3 · Why
Cut the mug open and flatten it into a rectangle. The honey is half the width away (4π ≈ 12.6 cm) and 10 cm up. A straight line, √(10² + 12.6²) ≈ 16.1 cm, beats up-then-around at 22.6 cm.
4 · Twist
Now the honey is inside the mug, 2 cm below the rim, and the ant starts 1 cm up the outside, opposite. Shortest crawl?
Mirror the inside wall above the rim, so the honey sits 2 cm above it on the paper. The straight line is √(11² + 12.6²) ≈ 16.7 cm and crosses the rim at a slant. Up, around and down is 23.6 cm. Try the toggle.
Done · you got the aha
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