[Daily puzzle] Reuleaux triangle \ stacker news ~science

695 sats \ 12 comments \ @south_korea_ln 30 Oct science

Can you find the radius of the circle inscribed in this Reuleaux triangle? A Reuleaux triangle comprises three arcs of circles with centers A, B, and C. The radius of each of these circles is equal to 6cm.

Previous iteration: #744872 (brute force answers in #745445 are correct, I'll give the reasoned answer later tonight, hopefully).

Also, check out @0xbitcoiner's problem: #746482

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501 sats \ 4 replies \ @didiplaywell 30 Oct

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

Solution:

So, each segment

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

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

, thus:

So, the radius

of the inscribed circle is:

So in numbers:

20 sats \ 3 replies \ @south_korea_ln OP 30 Oct

We have a winner!

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

0 sats \ 2 replies \ @didiplaywell 30 Oct

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

20 sats \ 1 reply \ @south_korea_ln OP 30 Oct

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

126 sats \ 0 replies \ @didiplaywell 30 Oct

Ok! Will upload it there a later! :)

200 sats \ 3 replies \ @Scroogey 30 Oct

The inscribed equilateral triangle has sides of length 6.

The perpendicular has length 5, because Pythagoras

The extension of the perpendicular must be 1, because

Platon says the sides of an equilateral triangle's half have ratio

Therefore, the radius of the inscribed circle is

1 sat \ 2 replies \ @south_korea_ln OP 30 Oct

I think there is an error in your Pythagoras calculation...

0 sats \ 1 reply \ @Scroogey 30 Oct

Doh, that makes it much less elegant :) Thanks for checking and the hint.

1 sat \ 0 replies \ @south_korea_ln OP 30 Oct

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.

0 sats \ 1 reply \ @0xbitcoiner 30 Oct

I thought of a way to answer the puzzles without showing the answer. We can use 'SN's private messages' to send the answer to you. The stacker who answers you privately leaves a comment on the post saying that they've answered.

wallet > withdraw > lightning address

33 sats \ 0 replies \ @south_korea_ln OP 30 Oct

I think a GitHub PR is forthcoming, solving this in a clean way.

Not sure i wanna act as intermediary between stackers and other stackers, curating answers. It would take me too much time. It's nice to have it in the open so people can learn from eachother.

Thanks for thinking about this though ;)

0 sats \ 0 replies \ @south_korea_ln OP 30 Oct

Update:

Reasoned answer for previous iteration: see #746568

Fun fact about Reuleaux triangles: they have a constant width, meaning that for every pair of parallel supporting lines (two lines of the same slope that both touch the shape without crossing through it) the two lines have the same Euclidean distance from each other, regardless of the orientation of these lines, leading to this kind of surprising behavior (short YT clip)