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Hi all,
Was working on marking a disk into three equal pie sections, and was offered
a suggestion that I could put a square (4 sided figure, not a carpenter's
square) on the circle (maybe an inscribed square) and that, by rotating that
square, it would make finding the thirds of the disk easier or more
foolproof. This suggestion was made by a boatbuilder/woodworker, and I have
to admit that I couldn't see how this would help me. Is there a method of
using a square on a circle that does make dividing the circle easier?
Thanks,
Kerry

I'm don't know how that would work.

If you measure the radius, then start from a point on the circumference, and set off a chord (a straight line that touches the circumference at both ends, equal to the radius, and from the end of that chord set off another one, the end of the second chord will be on a point 1/3 of the circumference.

Old guy

He's absolutely right. Read it again -- draw it if you need to.

The the sides of the six triangles are straight lines and hence a bit shorter than the 6th part of the circumference so are closer to a good fit than Pi would imply. John G.

Yes, of course the sides of the triangles are shorter than the arcs -- but surely it's clear that the vertices of the hexagon divide the circle into six exactly equal parts, no?

How do you propose to measure the circumference?

No, it***is*** exact, and in no way relies on the fact that pi is close to 3.

Rather, it relies on the facts that a circle can be circumscribed about any regular polygon, and that a regular hexagon can be decomposed into six equilateral triangles. Draw it yourself if you don't believe me.

Ummmmm..... no.

You're right -- my mistake. Had a brain fart doing the math...

Hi David, The radius method is exact, as the radius is being used as chords across the circle, not following along the circumference. Thanks, Kerry

#### Site Timeline

- posted on May 18, 2009, 10:42 pm

- posted on May 18, 2009, 10:53 pm

If you measure the radius, then start from a point on the circumference, and set off a chord (a straight line that touches the circumference at both ends, equal to the radius, and from the end of that chord set off another one, the end of the second chord will be on a point 1/3 of the circumference.

Old guy

- posted on May 18, 2009, 10:57 pm

wrote:

Old Guy, Yep, that's what I did all right. This fellow sounded like he used this square in a circle technique fairly often, so was wondering if it might be some secret bit of knowledge that I hadn't come across. Thanks, Kerry

Old Guy, Yep, that's what I did all right. This fellow sounded like he used this square in a circle technique fairly often, so was wondering if it might be some secret bit of knowledge that I hadn't come across. Thanks, Kerry

- posted on May 18, 2009, 11:00 pm

It could be a gannin square? It has 9 points so picking 3 would be a snap?

Rich

wrote:

Rich

wrote:

- posted on May 19, 2009, 1:15 am

wrote:

- posted on May 19, 2009, 1:31 am

On 5/18/2009 6:15 PM Bill spake thus:

Not quite. As you yourself point out, pi != 3. Close, but no cigar.

Not quite. As you yourself point out, pi != 3. Close, but no cigar.

--

Found--the gene that causes belief in genetic determinism

Found--the gene that causes belief in genetic determinism

- posted on May 19, 2009, 2:38 am

He's absolutely right. Read it again -- draw it if you need to.

- posted on May 19, 2009, 6:12 am

The the sides of the six triangles are straight lines and hence a bit shorter than the 6th part of the circumference so are closer to a good fit than Pi would imply. John G.

- posted on May 19, 2009, 11:26 am

Yes, of course the sides of the triangles are shorter than the arcs -- but surely it's clear that the vertices of the hexagon divide the circle into six exactly equal parts, no?

- posted on May 19, 2009, 12:15 pm

I'm don't know how that would work.

If you measure the radius, then start from a point on the circumference, and set off a chord (a straight line that touches the circumference at both ends, equal to the radius, and from the end of that chord set off another one, the end of the second chord will be on a point 1/3 of the circumference.

Old guy

How about measuring the circumference, dividing by 3 and marking the circumference by the result. Draw a line to the center from those 3 points.

If you measure the radius, then start from a point on the circumference, and set off a chord (a straight line that touches the circumference at both ends, equal to the radius, and from the end of that chord set off another one, the end of the second chord will be on a point 1/3 of the circumference.

Old guy

How about measuring the circumference, dividing by 3 and marking the circumference by the result. Draw a line to the center from those 3 points.

- posted on May 19, 2009, 1:03 pm

How do you propose to measure the circumference?

- posted on May 19, 2009, 1:28 pm

wrote:

Wrap a string around it, measure the string.

Wrap a string around it, measure the string.

- posted on May 19, 2009, 2:25 pm

Leon wrote:

Fabric tape measure. <http://www.joann.com/joann/catalog.jsp?CATIDÊt3439&PRODID=prd2809>

Fabric tape measure. <http://www.joann.com/joann/catalog.jsp?CATIDÊt3439&PRODID=prd2809>

--

-MIKE-

"Playing is not something I do at night, it's my function in life"

-MIKE-

"Playing is not something I do at night, it's my function in life"

Click to see the full signature.

- posted on May 18, 2009, 11:02 pm

Kerry Montgomery wrote:

line with the compass from one edge of the circle to the center and to toe other edge. Move the compass to one of the intersections just scribed and repeat the action. Continue until you return to the first point. Pick every other intersection and scribe a line from the intersection to the center. You will have your three EXACT wedges. Draw your square.

Dave N

line with the compass from one edge of the circle to the center and to toe other edge. Move the compass to one of the intersections just scribed and repeat the action. Continue until you return to the first point. Pick every other intersection and scribe a line from the intersection to the center. You will have your three EXACT wedges. Draw your square.

Dave N

- posted on May 19, 2009, 1:17 am

On 5/18/2009 4:02 PM David G. Nagel spake thus:

Not***quite*** exact; your method uses the fact that the relationship
between a circle's circumference and diameter is pi, about 3.14159.

I know about this 'cuz I was just rereading the* /Fine Woodworking/ *book
of "Proven Shop Tips". One of them is a table for dividing a circle into
equal parts. For three equal parts, take the diameter of the circle and
multiply it by 0.866. Set your dividers to the resulting size and "walk"
it around the circle to evenly divide it. (There's a table in this tip
that goes up to 100 parts.)

Not

I know about this 'cuz I was just rereading the

--

Found--the gene that causes belief in genetic determinism

Found--the gene that causes belief in genetic determinism

- posted on May 19, 2009, 2:05 am

David Nebenzahl wrote:

aware of this discussion. The most accurate way to divide a circle three parts is to use the radius on the circumference technique.

or as stated above >>Set your compass to the radius of the circle. Pick a point. Scribe a >> line with the compass from one edge of the circle to the center and to >> to other edge. Move the compass to one of the intersections just >> scribed and repeat the action. Continue until you return to the first >> point. Pick every other intersection and scribe a line from the >> intersection to the center. You will have your three EXACT wedges.

aware of this discussion. The most accurate way to divide a circle three parts is to use the radius on the circumference technique.

or as stated above >>Set your compass to the radius of the circle. Pick a point. Scribe a >> line with the compass from one edge of the circle to the center and to >> to other edge. Move the compass to one of the intersections just >> scribed and repeat the action. Continue until you return to the first >> point. Pick every other intersection and scribe a line from the >> intersection to the center. You will have your three EXACT wedges.

- posted on May 19, 2009, 2:45 am

No, it

Rather, it relies on the facts that a circle can be circumscribed about any regular polygon, and that a regular hexagon can be decomposed into six equilateral triangles. Draw it yourself if you don't believe me.

Ummmmm..... no.

- posted on May 19, 2009, 3:24 am

Doug Miller wrote:

...snip...

Ummmm....yes.

If you mark off chords whose length is 0.866 (actually sqrt(3)/2) times the diameter, then you will get an equilateral triangle.

...snip...

Ummmm....yes.

If you mark off chords whose length is 0.866 (actually sqrt(3)/2) times the diameter, then you will get an equilateral triangle.

- posted on May 19, 2009, 11:32 am

You're right -- my mistake. Had a brain fart doing the math...

- posted on May 19, 2009, 2:58 am

Hi David, The radius method is exact, as the radius is being used as chords across the circle, not following along the circumference. Thanks, Kerry

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