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
"Old Guy" <[email protected]> wrote in message
news:80e8aebd-d4e4-4f40-b924-98843ada5bbe@e20g2000vbc.googlegroups.com...
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
On May 18, 5:42 pm, "Kerry Montgomery" <[email protected]> wrote:
> 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
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
"CW" <[email protected]> wrote in message
news:[email protected]...
> Sometimes this group amazes me. How does a simple question with a simple
> answer turn in to a two day discussion?
Cuz answers like yours aren't the answer? ;~)
"-MIKE-" <[email protected]> wrote in message
news:[email protected]...
> Leon wrote:
>> "Doug Miller" <[email protected]> wrote in message
>> news:[email protected]...
>>> In article <[email protected]>, "Leon"
>>> <[email protected]> wrote:
>>>> 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.
>>> How do you propose to measure the circumference?
>>
>> Wrap a string around it, measure the string.
>
> Fabric tape measure.
> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>
>
Or... how about measuring the diameter and multiplying by 3.14.
--
-Mike-
[email protected]
"Mike Marlow" <[email protected]> wrote in message
news:[email protected]...
>
> "Leon" <[email protected]> wrote in message
> news:[email protected]...
>>
>> "Mike Marlow" <[email protected]> wrote in message
>
>>>
>>> Or... how about measuring the diameter and multiplying by 3.14.
>>
>> That will work but introduces one more step than simply measuring the
>> circumference.
>>
>
> Yes it will. If the object is thin, or otherwise a bit awkward though, a
> tape around the circumference can be troublesome.
That is why I keep a FastCap flat tape measure around. ;~)
"David G. Nagel" <[email protected]> wrote in message
news:[email protected]...
> Mike Marlow wrote:
>> "-MIKE-" <[email protected]> wrote in message
>> news:[email protected]...
>>> Leon wrote:
>>>> "Doug Miller" <[email protected]> wrote in message
>>>> news:[email protected]...
>>>>> In article <[email protected]>, "Leon"
>>>>> <[email protected]> wrote:
>>>>>> 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.
>>>>> How do you propose to measure the circumference?
>>>> Wrap a string around it, measure the string.
>>> Fabric tape measure.
>>> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>>>
>>>
>>
>> Or... how about measuring the diameter and multiplying by 3.14.
>>
>
> Yah But 3.14 isn't exact. You need to use the value to a million or two
> decimal places for a more exact but not completely exact value.
Correct - it is not exact, but it is exact enough for a pencil mark. No
need to take it to extreme decimal places. The increase in accuracy once
you get out past the hundredths place is irrelevant to woodworking.
--
-Mike-
[email protected]
On 5/18/2009 4:02 PM David G. Nagel spake thus:
> Kerry Montgomery wrote:
>
>> 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?
>>
> 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
> 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.
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.)
--
Found--the gene that causes belief in genetic determinism
On 5/18/2009 6:15 PM Bill spake thus:
> "Kerry Montgomery" <[email protected]> wrote in message
> news:[email protected]...
>
>> I'm don't know how that would work.
>
> It would work since there is a hexagon, comprised of 6 equilateral
> triangles sharing a vertex in the center of the circle with the other
> vertices on the boundary of the circle. The length of the sides of
> every one of these triangles is the same as the radius of the
> circle.
Not quite. As you yourself point out, pi != 3. Close, but no cigar.
--
Found--the gene that causes belief in genetic determinism
"Doug Miller" <[email protected]> wrote in message
news:[email protected]...
> In article <[email protected]>, David
> Nebenzahl <[email protected]> wrote:
>>On 5/18/2009 6:15 PM Bill spake thus:
>>
>>> "Kerry Montgomery" <[email protected]> wrote in message
>>> news:[email protected]...
>>>
>>>> I'm don't know how that would work.
>>>
>>> It would work since there is a hexagon, comprised of 6 equilateral
>>> triangles sharing a vertex in the center of the circle with the other
>>> vertices on the boundary of the circle. The length of the sides of
>>> every one of these triangles is the same as the radius of the
>>> circle.
>>
>>Not quite. As you yourself point out, pi != 3. Close, but no cigar.
>>
>
> 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.
On 5/19/2009 1:40 PM Tom Veatch spake thus:
> But, the last time I looked, the best approximate value of Pi was such
> that a difference in the last digit yields a difference in
> circumference less than the diameter of an electron on a circle the
> size of the Earth's orbit.
But--but--what "last digit"? You said yourself it's non-repeating.
[just pokin' you]
--
Found--the gene that causes belief in genetic determinism
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
On May 18, 5:42=A0pm, "Kerry Montgomery" <[email protected]> wrote:
> Hi all,
> Was working on marking a disk into three equal pie sections, and was offe=
red
> 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 t=
hat
> square, it would make finding the thirds of the disk easier or more
> foolproof. This suggestion was made by a boatbuilder/woodworker, and I ha=
ve
> 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
On Tue, 19 May 2009 17:28:01 -0700, David Nebenzahl
<[email protected]> wrote:
>
>But--but--what "last digit"? You said yourself it's non-repeating.
>
>[just pokin' you]
Pokin' accepted in the spirit in which it was "poked". Change my
original post to read "last KNOWN digit".
Mike Marlow wrote:
> "-MIKE-" <[email protected]> wrote in message
> news:[email protected]...
>> Leon wrote:
>>> "Doug Miller" <[email protected]> wrote in message
>>> news:[email protected]...
>>>> In article <[email protected]>, "Leon"
>>>> <[email protected]> wrote:
>>>>> 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.
>>>> How do you propose to measure the circumference?
>>> Wrap a string around it, measure the string.
>> Fabric tape measure.
>> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>>
>>
>
> Or... how about measuring the diameter and multiplying by 3.14.
>
Yah But 3.14 isn't exact. You need to use the value to a million or two
decimal places for a more exact but not completely exact value.
"Leon" <[email protected]> wrote in message
news:[email protected]...
>
> "CW" <[email protected]> wrote in message
> news:[email protected]...
>> Sometimes this group amazes me. How does a simple question with a simple
>> answer turn in to a two day discussion?
>
>
> Cuz answers like yours aren't the answer? ;~)
>
The answer was given early on by Old Guy. I do believe that others gave
usable answers too.
"Leon" <[email protected]> wrote in message
news:[email protected]...
>
> "notbob" <[email protected]> wrote in message
> news:[email protected]...
>> On 2009-05-18, Kerry Montgomery <[email protected]> wrote:
>>> 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.........
>>
>> Use bisection to bisect the circle with a line, then bisect the 1st line
>> at a
>> right angle. Draw lines from the points where the two lines intersect
>> the
>> circle (4 pts). Voila! Square in circle.
>>
>> http://en.wikipedia.org/wiki/Bisection
>>
>> nb
> Now that you have the square, do you have a solution for the problem,
> dividing the circle into 3 equal pie sections?
>
Leon,
Thanks, I was about to ask notbob that same thing.
Kerry
In article <[email protected]>, Dan Coby <[email protected]> wrote:
>Doug Miller wrote:
>> In article <[email protected]>, David
> Nebenzahl <[email protected]> wrote:
>
>....snip...
>
>>> 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.
>>
>> Ummmmm..... no.
>
>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.
You're right -- my mistake. Had a brain fart doing the math...
"notbob" <[email protected]> wrote in message
news:[email protected]...
> On 2009-05-18, Kerry Montgomery <[email protected]> wrote:
>> 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.........
>
> Use bisection to bisect the circle with a line, then bisect the 1st line
> at a
> right angle. Draw lines from the points where the two lines intersect the
> circle (4 pts). Voila! Square in circle.
>
> http://en.wikipedia.org/wiki/Bisection
>
> nb
Now that you have the square, do you have a solution for the problem,
dividing the circle into 3 equal pie sections?
snipped -- response below.
>>>>
>>>
>>> Or... how about measuring the diameter and multiplying by 3.14.
>>>
>>
>> Yah But 3.14 isn't exact. You need to use the value to a million or two
>> decimal places for a more exact but not completely exact value.
>
> Correct - it is not exact, but it is exact enough for a pencil mark. No
> need to take it to extreme decimal places. The increase in accuracy once
> you get out past the hundredths place is irrelevant to woodworking.
>
> --
>
> -Mike-
> [email protected]
>
This reminds me of an article on Pi Isaac Asimov wrote for his magazine.
Basically he stated that if you took every single atom in the entire known
universe, lined them up in a row and then used that as the diameter of a
circle, you would only need Pi to 22 digits to compute the circumference of
that circle to within a few millimeters of accuracy. So, forget about
woodworking, once you get past a few digits the accuracy is irrelevant to
everything in the scope of human knowledge. The only reason we have people
working on Pi to several billion digits is bragging rights.
In article <[email protected]>, "John G." <[email protected]> wrote:
>
>"Doug Miller" <[email protected]> wrote in message
>news:[email protected]...
>> In article <[email protected]>, David
>> Nebenzahl <[email protected]> wrote:
>>>On 5/18/2009 6:15 PM Bill spake thus:
>>>
>>>> "Kerry Montgomery" <[email protected]> wrote in message
>>>> news:[email protected]...
>>>>
>>>>> I'm don't know how that would work.
>>>>
>>>> It would work since there is a hexagon, comprised of 6 equilateral
>>>> triangles sharing a vertex in the center of the circle with the other
>>>> vertices on the boundary of the circle. The length of the sides of
>>>> every one of these triangles is the same as the radius of the
>>>> circle.
>>>
>>>Not quite. As you yourself point out, pi != 3. Close, but no cigar.
>>>
>>
>> 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.
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?
"Mike Marlow" <[email protected]> wrote in message
news:[email protected]...
>
> "-MIKE-" <[email protected]> wrote in message
> news:[email protected]...
>> Leon wrote:
>>> "Doug Miller" <[email protected]> wrote in message
>>> news:[email protected]...
>>>> In article <[email protected]>, "Leon"
>>>> <[email protected]> wrote:
>>>>> 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.
>>>> How do you propose to measure the circumference?
>>>
>>> Wrap a string around it, measure the string.
>>
>> Fabric tape measure.
>> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>>
>>
>
> Or... how about measuring the diameter and multiplying by 3.14.
That will work but introduces one more step than simply measuring the
circumference.
Sometimes this group amazes me. How does a simple question with a simple
answer turn in to a two day discussion?
"Mike Marlow" <[email protected]> wrote in message
news:[email protected]...
>
> "-MIKE-" <[email protected]> wrote in message
> news:[email protected]...
>> Leon wrote:
>>>>>>> How do you propose to measure the circumference?
>>>>>> Wrap a string around it, measure the string.
>>>>> Fabric tape measure.
>>>>> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>>>>>
>>>>>
>>>> Or... how about measuring the diameter and multiplying by 3.14.
>>>
>>> That will work but introduces one more step than simply measuring the
>>> circumference.
>>
>> Plus, it's easy to multiply an error in the measurement of the diameter.
>> Guess it depends on how accessible & critical the measurement is.
>>
>
> Yeah - but you have to assume some level of proficiency. Though the error
> would indeed be multiplied, any error in measurement - even if measuring
> around the circumerence, or a chord, is going to result in an incorrect
> trisection of the circle. You're still going to have to do it again.
>
>> If both factors are high, measure directly. If both are low, do the
>> math.
>>
>> I run into this with drum shells all the time.
>> It's easy for me to throw a cloth tape around them.
>>
>>
>
> Yup - but some objects are not so easy to wrap a tape around.
>
> --
>
> -Mike-
> [email protected]
>
"Old Guy" <[email protected]> wrote in message
news:80e8aebd-d4e4-4f40-b924-98843ada5bbe@e20g2000vbc.googlegroups.com...
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.
On Tue, 19 May 2009 21:09:07 -0400, "Bill" <[email protected]>
wrote:
>Folks seemed to have so much fun with this problem
>I thought I would suggest another one.
>
>Bob Barker tells you that there is a fine table saw
>behind door #1, door #2, or door #3 and tells
>you that you can have it if you choose the right door.
>
>So you pick a door.
>
>Bob knows where the saw is, and he opens one of the
>other doors to show you that the saw is not behind it,
>and then he gives you the opportunity to switch to the remaining door.
>
>(This is multiple choice)
>Should you:
>A) Should stay with first choice
>B) Switch to the remaining door
>C) Both choices are just as good
>
>If you've seen this before, you may as well not spoil it for others.
>
>Bill
>
>
Tom Veatch
Wichita, KS
USA
An armed society is a polite society.
Manners are good when one may have to back up his acts with his life.
Robert A. Heinlein
On Tue, 19 May 2009 21:09:07 -0400, "Bill" <[email protected]>
wrote:
>Folks seemed to have so much fun with this problem
>I thought I would suggest another one.
>
>Bob Barker tells you that there is a fine table saw
>behind door #1, door #2, or door #3 and tells
>you that you can have it if you choose the right door.
>
>So you pick a door.
>
>Bob knows where the saw is, and he opens one of the
>other doors to show you that the saw is not behind it,
>and then he gives you the opportunity to switch to the remaining door.
>
>(This is multiple choice)
>Should you:
>A) Should stay with first choice
>B) Switch to the remaining door
>C) Both choices are just as good
>
>If you've seen this before, you may as well not spoil it for others.
>
>Bill
>
>
The correct answer (defined as the one that gives you the best chance
at winning the TS) is surprising and is sure to generate some
controversy.
Tom Veatch
Wichita, KS
USA
An armed society is a polite society.
Manners are good when one may have to back up his acts with his life.
Robert A. Heinlein
In article <[email protected]>, "Leon" <[email protected]> wrote:
>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.
How do you propose to measure the circumference?
Kerry Montgomery wrote:
> 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
>
>
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
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
"David Nebenzahl" <[email protected]> wrote in message
news:[email protected]...
> On 5/18/2009 4:02 PM David G. Nagel spake thus:
>
>> Kerry Montgomery wrote:
>>
>>> 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?
>>>
>> 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 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.
>
> 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.)
>
>
> --
> Found--the gene that causes belief in genetic determinism
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
"Kerry Montgomery" <[email protected]> wrote in message
news:[email protected]...
> 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
>
Get yourself a shashigane (Japanese Carpenter's Square) marked in the
shaku/sun system and learn to use it. Unlike American style framing
squares, they are marked on the back side for folks that work with
logs (circles). They are very handy for marking squares, and other
geometric shapes, on the end of a log, or inside a circle, without a
lot of fuss.
Len
In article <[email protected]>, David Nebenzahl <[email protected]> wrote:
>On 5/18/2009 4:02 PM David G. Nagel spake thus:
>
>> Kerry Montgomery wrote:
>>
>>> 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?
>>>
>> 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
>> 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.
>
>Not *quite* exact; your method uses the fact that the relationship
>between a circle's circumference and diameter is pi, about 3.14159.
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.
>
>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.
Ummmmm..... no.
In article <[email protected]>, David Nebenzahl <[email protected]> wrote:
>On 5/18/2009 6:15 PM Bill spake thus:
>
>> "Kerry Montgomery" <[email protected]> wrote in message
>> news:[email protected]...
>>
>>> I'm don't know how that would work.
>>
>> It would work since there is a hexagon, comprised of 6 equilateral
>> triangles sharing a vertex in the center of the circle with the other
>> vertices on the boundary of the circle. The length of the sides of
>> every one of these triangles is the same as the radius of the
>> circle.
>
>Not quite. As you yourself point out, pi != 3. Close, but no cigar.
>
He's absolutely right. Read it again -- draw it if you need to.
"-MIKE-" <[email protected]> wrote in message
news:[email protected]...
> Leon wrote:
>>>>>> How do you propose to measure the circumference?
>>>>> Wrap a string around it, measure the string.
>>>> Fabric tape measure.
>>>> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>>>>
>>>>
>>> Or... how about measuring the diameter and multiplying by 3.14.
>>
>> That will work but introduces one more step than simply measuring the
>> circumference.
>
> Plus, it's easy to multiply an error in the measurement of the diameter.
> Guess it depends on how accessible & critical the measurement is.
>
Yeah - but you have to assume some level of proficiency. Though the error
would indeed be multiplied, any error in measurement - even if measuring
around the circumerence, or a chord, is going to result in an incorrect
trisection of the circle. You're still going to have to do it again.
> If both factors are high, measure directly. If both are low, do the math.
>
> I run into this with drum shells all the time.
> It's easy for me to throw a cloth tape around them.
>
>
Yup - but some objects are not so easy to wrap a tape around.
--
-Mike-
[email protected]
"Doug Miller" <[email protected]> wrote in message
news:[email protected]...
> In article <[email protected]>, "Leon"
> <[email protected]> wrote:
>>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.
>
> How do you propose to measure the circumference?
Wrap a string around it, measure the string.
"Leon" <[email protected]> wrote in message
news:[email protected]...
>
> "Mike Marlow" <[email protected]> wrote in message
>>
>> Or... how about measuring the diameter and multiplying by 3.14.
>
> That will work but introduces one more step than simply measuring the
> circumference.
>
Yes it will. If the object is thin, or otherwise a bit awkward though, a
tape around the circumference can be troublesome.
--
-Mike-
[email protected]
It could be a gannin square? It has 9 points so picking 3 would be a snap?
Rich
"Kerry Montgomery" <[email protected]> wrote in message
news:[email protected]...
>
> "Old Guy" <[email protected]> wrote in message
> news:80e8aebd-d4e4-4f40-b924-98843ada5bbe@e20g2000vbc.googlegroups.com...
> 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
>
>
>
> On May 18, 5:42 pm, "Kerry Montgomery" <[email protected]> wrote:
>> 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
>
> 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
>
>
"Kerry Montgomery" <[email protected]> wrote in message
news:[email protected]...
>
> "Old Guy" <[email protected]> wrote in message
> news:80e8aebd-d4e4-4f40-b924-98843ada5bbe@e20g2000vbc.googlegroups.com...
> I'm don't know how that would work.
It would work since there is a hexagon, comprised of 6 equilateral triangles
sharing a vertex in the center of the circle with the other vertices on the
boundary of the circle. The length of the sides of every one of these
triangles
is the same as the radius of the circle. Draw a picture. Then note that if
you chose every
other vertex on the boundary of the circle, they will form an equilateral
triangle.
Measured along the boudary, the distance between the 3 vertices of an
inscribed equilateral triangle should be Pi times D , where Pi ~ 3.1415...
and
D is the diameter.
Both of these techniques assume you have a "perfect" disk/circle to work
with.
I would verify that the (shortest) distance between each of them is
the same before I cut anything.
I hope that something I wrote is helpful!
Bill
>
> 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
>
>
>
> On May 18, 5:42 pm, "Kerry Montgomery" <[email protected]> wrote:
>> 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
>
> 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
>
>
"Kerry Montgomery" <[email protected]> wrote in message
news:[email protected]...
> 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
Once you draw a square in the circle, then you could draw both diagonals the
find the center (of course, you probably already know where the center is by
the time you've drawn a square!). Use your compass to pick up the measure
of the radius, and starting anywhere, scribe 6 consecutive arcs along the
boundary of the circle (they are the vertices of a hexagon as I described in
my previous post). Choose every other one to obtain the vertices of a
triangle.
Bill
>
"Lew Hodgett" <[email protected]> wrote in message
news:[email protected]...
> "Kerry Montgomery" wrote:
>
>> 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.
> <snip>
>
> Neither do I.
>
> Lew
>
I've uploaded a simple excel spreadsheet that will calculate
the chords for any divisions of a circle "bolt circle.xls, it is
here:
http://www.woodwrangler.net
should open directly in excel if you have it installed.
I haven't tried it in open office.
basilisk
Leon wrote:
> "Doug Miller" <[email protected]> wrote in message
> news:[email protected]...
>> In article <[email protected]>, "Leon"
>> <[email protected]> wrote:
>>> 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.
>> How do you propose to measure the circumference?
>
> Wrap a string around it, measure the string.
>
Fabric tape measure.
<http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
--
-MIKE-
"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com
[email protected]
---remove "DOT" ^^^^ to reply
Kerry Montgomery wrote:
> 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
Dunno how a four sided figure would help, but here's a way to inscribe an
equilateral triangle using a steel square:
http://chestofbooks.com/home-improvement/woodworking/Constructive-Carpentry/34-To-Lay-Out-Regular-Polygons-With-A-Steel-Square.html
Leon wrote:
>>>>> How do you propose to measure the circumference?
>>>> Wrap a string around it, measure the string.
>>> Fabric tape measure.
>>> <http://www.joann.com/joann/catalog.jsp?CATID=cat3439&PRODID=prd2809>
>>>
>>>
>> Or... how about measuring the diameter and multiplying by 3.14.
>
> That will work but introduces one more step than simply measuring the
> circumference.
>
Plus, it's easy to multiply an error in the measurement of the diameter.
Guess it depends on how accessible & critical the measurement is.
If both factors are high, measure directly. If both are low, do the math.
I run into this with drum shells all the time.
It's easy for me to throw a cloth tape around them.
--
-MIKE-
"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com
[email protected]
---remove "DOT" ^^^^ to reply
Mike Marlow wrote:
>>>> Or... how about measuring the diameter and multiplying by 3.14.
>>> That will work but introduces one more step than simply measuring the
>>> circumference.
>> Plus, it's easy to multiply an error in the measurement of the diameter.
>> Guess it depends on how accessible & critical the measurement is.
>>
>
> Yeah - but you have to assume some level of proficiency. Though the error
> would indeed be multiplied, any error in measurement - even if measuring
> around the circumerence, or a chord, is going to result in an incorrect
> trisection of the circle. You're still going to have to do it again.
>
>> If both factors are high, measure directly. If both are low, do the math.
>>
>> I run into this with drum shells all the time.
>> It's easy for me to throw a cloth tape around them.
>>
>>
>
> Yup - but some objects are not so easy to wrap a tape around.
>
That would fall into my "accessible" category. :-)
--
-MIKE-
"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com
[email protected]
---remove "DOT" ^^^^ to reply
Folks seemed to have so much fun with this problem
I thought I would suggest another one.
Bob Barker tells you that there is a fine table saw
behind door #1, door #2, or door #3 and tells
you that you can have it if you choose the right door.
So you pick a door.
Bob knows where the saw is, and he opens one of the
other doors to show you that the saw is not behind it,
and then he gives you the opportunity to switch to the remaining door.
(This is multiple choice)
Should you:
A) Should stay with first choice
B) Switch to the remaining door
C) Both choices are just as good
If you've seen this before, you may as well not spoil it for others.
Bill
David Nebenzahl wrote:
> On 5/18/2009 4:02 PM David G. Nagel spake thus:
>
>> Kerry Montgomery wrote:
>>
>>> 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?
>>>
>> 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
>> 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.
>
> 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.)
>
>
Your Geometry teachers are rolling over in the grave if they ever become
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.
"Kerry Montgomery" wrote:
> 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.
<snip>
Neither do I.
Lew
On 2009-05-18, Kerry Montgomery <[email protected]> wrote:
> 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.........
Use bisection to bisect the circle with a line, then bisect the 1st line at a
right angle. Draw lines from the points where the two lines intersect the
circle (4 pts). Voila! Square in circle.
http://en.wikipedia.org/wiki/Bisection
nb
On 2009-05-20, Leon <[email protected]> wrote:
> Now that you have the square, do you have a solution for the problem,
> dividing the circle into 3 equal pie sections?
Ask the boatbuilder.
I was jes showing an easy way to make a square inside a circle. For the
three angles in a circle, I'd use a hexagon.
http://en.wikipedia.org/wiki/Hexagon
nb
On Tue, 19 May 2009 11:07:59 -0500, "David G. Nagel"
<[email protected]> wrote:
>Yah But 3.14 isn't exact. You need to use the value to a million or two
>decimal places for a more exact but not completely exact value.
We'll never know an exact value of Pi since it's a non-repeating
decimal value.
But, the last time I looked, the best approximate value of Pi was such
that a difference in the last digit yields a difference in
circumference less than the diameter of an electron on a circle the
size of the Earth's orbit.
That's probably close enough for most woodworking tasks.
Doug Miller wrote:
> In article <[email protected]>, David Nebenzahl <[email protected]> wrote:
...snip...
>> 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.
>
> Ummmmm..... no.
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.
"David Nebenzahl" wrote:
Dave's Hypothesis states:
> Not *quite* exact; your method uses the fact that the relationship
> between a circle's circumference and diameter is pi, about 3.14159.
Dave's Hypothesis is incorrect.
Basic plane geometry proofs do not allow calculated values to be used
in the proof.
For the subject under discusion, the actual value of circumference is
an innocent bystander, not a player
Lew
.