

Drilling a Square Hole (with a rotating bit) - three14
http://www.maa.org/mathtourist/mathtourist_08_31_09.html

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jacquesm
There used to be one of these in my toolbox:

[http://www.machinemart.co.uk/images/library/range/large/0104...](http://www.machinemart.co.uk/images/library/range/large/0104.jpg)

The small remaining bits at the corners were pushed out by the pointed
segments by feeding the bits of leftover wood into the rotating bit.

Worked wonderfully, I wonder during which move i managed to lose it, I always
thought it to be a pretty ingenious device.

Mathematically not as clever as the one in the article but definitely simpler
and it did the job.

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giardini
Thanks, found it! It's a "mortise chisel and drill": a much more practical
solution that I can buy!

While the Reuleaux concept is mathematically cute, it isn't very practical and
is only approximate. And the Reuleaux bit requires a special chuck to ensure
that the square is "upright" (not tipped at some arbitrary angle):
<http://upper.us.edu/faculty/smith/reuleaux.htm> for details.

There's a joke in this somewhere about mathematicians and carpenters.

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uuilly
Here is an animation showing how it works:

[http://upload.wikimedia.org/wikipedia/en/2/20/Rouleaux_trian...](http://upload.wikimedia.org/wikipedia/en/2/20/Rouleaux_triangle_Animation.gif)

~~~
silentOpen
That's only the Rouleaux bit. The article details a bit that produces sharp
(vs. rounded) squares.

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uuilly
It was confusing b/c the pictures didn't show that the bit's axel had to orbit
independently of the bit. This animation cleared that up for me even if it
wasn't the exact case.

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roundsquare
Ok, given my login name, I feel like I have to comment on this article.

Also, here is a video of this in action.
<http://www.youtube.com/watch?v=9qEhyQfbImY>

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brunoc
Rounded corners.. giving problems to engineers for 100+ years. :)

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ubernostrum
This and other amusing/interesting mathematical diversions are covered in one
of Martin Gardner's books:

<http://www.amazon.com/dp/0226282562/>

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bcl
Am I missing something? The holes can't be square, because of the rotating
motion required to create them they will always have rounded corners.

I'd like to see pictures of the holes created with this bit.

~~~
iguanatom
You are right, it's not really square, but the rounded edges can be chiseled
away fairly easy, especially if the drill bit has the chisel built right into
it as jacquesm's earlier image showed
([http://www.machinemart.co.uk/images/library/range/large/0104...](http://www.machinemart.co.uk/images/library/range/large/0104.jpg)).
although if it's hard wood, you may need to use a solid chisel and a hammer to
pound the heck out if it.

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riffic
a man in china invented a bike with non-circular wheels

[http://technology.timesonline.co.uk/tol/news/tech_and_web/ar...](http://technology.timesonline.co.uk/tol/news/tech_and_web/article6366308.ece)

[http://www.china.org.cn/china/photos/2009-05/07/content_1773...](http://www.china.org.cn/china/photos/2009-05/07/content_17738257.htm)

~~~
jrockway
Amusing: "He believes that people will be drawn to the bike because it
requires more work to cycle and therefore will provide more exercise for the
cyclist than a conventional bike."

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chime
I wonder if the unsolved problem of drilling a triangle hole is related to the
geometric problem of dividing a line into three equal parts with just a
compass.

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lucifer
You can't trisect an arc using only a compass and a straightedge. (You can
simulate a straightedge using a compass.) Dividing a line into 3 parts is
trivial.

~~~
sp332
Funny I'd forgotten that that was possible.
[http://upload.wikimedia.org/wikipedia/en/d/dc/Trisectsegment...](http://upload.wikimedia.org/wikipedia/en/d/dc/Trisectsegment.gif)

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newsdog
The curve of constant width, square drill thing was in Martin Gardner's
Scientific American column 30 years ago....

Nice to see it again.

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fishercs
rotary engines.

