Drilling a Square Hole (with a rotating bit)

http://www.maa.org/mathtourist/mathtourist_08_31_09.html

by three14 • 17 years ago

91 20 17 years ago

jacquesm• 17 years ago

There used to be one of these in my toolbox:

http://www.machinemart.co.uk/images/library/range/large/0104...

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.

PonyGumbo• 17 years ago

I've been pleasantly surprised at how often I get to use my bench-top mortising machine for projects outside of mortise and tenon work.

giardini• 17 years ago

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.

chime• 17 years ago

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.

lucifer• 17 years ago

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• 17 years ago

Funny I'd forgotten that that was possible. http://upload.wikimedia.org/wikipedia/en/d/dc/Trisectsegment...

ubernostrum• 17 years ago

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

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

riffic• 17 years ago

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

http://technology.timesonline.co.uk/tol/news/tech_and_web/ar...

http://www.china.org.cn/china/photos/2009-05/07/content_1773...

jrockway• 17 years ago

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."

uuilly2• 17 years ago

Here is an animation showing how it works:

http://upload.wikimedia.org/wikipedia/en/2/20/Rouleaux_trian...

misterbwong• 17 years ago

The link above is an animation of the Rouleaux Triangle and will draw a square with rounded corners. In this article, the author talks about a variant of that triangle that will draw exact squares.

silentOpen• 17 years ago

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

uuilly2• 17 years ago

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.

bcl• 17 years ago

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• 17 years ago

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...). although if it's hard wood, you may need to use a solid chisel and a hammer to pound the heck out if it.

ianferrel• 17 years ago

That's what I thought, too, but then I realized that what we were both missing is that the edges of the cutting surface are not the same as the edges of the shape.

The vertices really do trace out a right angled square, so if you just put cutting surfaces at the vertices and inside them, it really will cut a square.

roundsquare• 17 years ago

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

brunoc• 17 years ago

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

fishercs• 17 years ago

rotary engines.

newsdog• 17 years ago

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

Nice to see it again.

Drilling a Square Hole (with a rotating bit)

Related Stories