reply on: [Daily puzzle] Reuleaux triangle \ stacker news ~science

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I love the Reuleaux triangle so much. It's used in industry to drill squared holes! How crazy is that!!

Solution:

So, each segment

s

of the ABC inscribed triangle is 6cm because of how the Reuleaux triangle is composed. That allows us to get the center position

p

from any vertex, for it's equal to 2/3 of the triangle's height

h

, thus:

s = 6 cm

h = sen(60°) \cdot s = { \sqrt{3} \over 2 } \cdot s

p = { 2 \over 3 } h = { \sqrt{3} \over 3 } \cdot s

So, the radius

r

of the inscribed circle is:

r = s - p = s - { \sqrt{3} \over 3 } \cdot s = s \cdot \left( 1 - { \sqrt{3} \over 3 } \right)

So in numbers:

r = 2 \cdot \left( 3 - { \sqrt{3} } \right) cm = 2.536 cm

We have a winner!

Oh yes, those square holes. I had seen a little sketch of that thing, never saw it in action. Cool!

Thank you Sr! :) I love geometry. I made pen-and-paper game based on geometry, would share it with you if you are interested.

Sure thing. Feel free to share it here in ~science if that would make sense...

Ok! Will upload it there a later! :)