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200 sats \ 3 replies \ @Scroogey 30 Oct 2024 \ on: [Daily puzzle] Reuleaux triangle science
The inscribed equilateral triangle has sides of length 6.
The perpendicular has length 5, because Pythagoras 3^2 + 5^2 = 6^2.
The extension of the perpendicular must be 1, because 5 + 1 = 6.
Platon says the sides of an equilateral triangle's half have ratio 1:2:\sqrt{3}.
Therefore, the radius of the inscribed circle is \frac{3}{\sqrt{3}}+1 \approx 2.732.
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1 sat \ 2 replies \ @south_korea_ln OP 30 Oct 2024
I think there is an error in your Pythagoras calculation...
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0 sats \ 1 reply \ @Scroogey 30 Oct 2024
Doh, that makes it much less elegant :) Thanks for checking and the hint.
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1 sat \ 0 replies \ @south_korea_ln OP 30 Oct 2024
I didn't check further, but this small difference on the perpendicular probably explains the small mismatch at the end with the value given by @didiplaywell.
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