square in circle?

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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
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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

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

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wrote:

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

Not quite. As you yourself point out, pi != 3. Close, but no cigar.
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He's absolutely right. Read it again -- draw it if you need to.
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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.
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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?
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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.
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How do you propose to measure the circumference?
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wrote:

Wrap a string around it, measure the string.
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Leon wrote:

Fabric tape measure. <http://www.joann.com/joann/catalog.jsp?CATIDt3439&PRODID=prd2809>
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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
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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.)
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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.
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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.
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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.
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You're right -- my mistake. Had a brain fart doing the math...
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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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