Every so often, my muggle side and mathematical side conflict, and this clip from @marksettle shows one of them.
My toddler’s train track is freaking me out right now. What is going on here?! http://pic.twitter.com/9o8bVWF5KO
— marc blank-settle (@MarcSettle) April 6, 2016
My muggle side says “wait, what, how can that be?” My mathematician says “aha! neat! Arc lengths!”
The two curved sides of the track are – presumably – arcs of concentric circles with radius $r$. The smaller arc has length $r\theta$, and the longer length $(r+w)\theta)$, where $w$ is the width of the track and $\theta$…
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