Geometry question

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jtate

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If you have an equilateral triangle inside a circle and you know the radius of the circle how do you figure out the length of the sides of the triangle?
I'm doing some off-center turning and I want to have a little more precision in things. I can make a fairly exact circle - it's woodturning after all, that's what we do. I can measure the radius. But the three points on the circle that would be exactly the same distance from one another - I can't figure out how to do that.

I can just eyeball it but that seems so - I don't know - imprecise.

ANy help?

Julia
 
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Dario

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use cosine law

length of side = 2a

where
a = (cos 30*)(radius)

Please correct me if I am wrong...its been too long since I took these.
 
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Dario

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Not too sure again but try this shortcut...

Side length = S
where S = 2L
where L = (4 x radius) / 5

or S = 1.6 x radius
 
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Mudder

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Try this link:

http://experts.about.com/q/Geometry-2060/triangle-inside-circle.htm

I think it will give you a simple solution.
 
C

ctEaglesc

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Use a compass and draw a circle.
DOn't change the setting of the compass.
Start anywhere on the circle and swing an arc thru the circumfrence.Put the point of the compass on that intersection.swing another arc.
Repeat arorund the circumfrence.
You will have six arcs.
Connect three that look like an equilateral triangle.
Measure any one of the lines.
That's Mudders answer with my interpretation.
[:D]
 
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JimGo

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Or, since you know the radius, you can multiply that by 2, then by pi, to give you the circumference. Divide the circumference by three, and you know how far apart along the points need to be along the circumference. If it's a cylinder, you can cut a piece of paper or the like to the circumference, then mark the three points on the paper and transfer the marks to the cylinder by wrapping the paper around the cylinder. You could also simply cut a piece of paper to the length of the circumference, then fold it into thirds, but that's likely to be less precise.

Still another way is to set dividers at 120 degrees (this requires that the dividers, or your custom-made version thereof, have arms long enough to intersect the outer diameter of your circle). Locate the joint between the dividers at the center of your circle. The dividers intersect the circle at two points on the circle; mark those. Now, keeping the joint in the middle of the circle, align the dividers so that the arm intersects the circle at one of the marks you just made; the other arm will intersect the circle at the third point on the triangle.
 
its_virgil

its_virgil

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You have the center. draw three radii from the center making angles of 120* and where these radii hit the circumference of the cirle is the three points you desire.
Do a good turn daily!
Don
Originally posted by jtate
<br />If you have an equilateral triangle inside a circle and you know the radius of the circle how do you figure out the length of the sides of the triangle?
I'm doing some off-center turning and I want to have a little more precision in things. I can make a fairly exact circle - it's woodturning after all, that's what we do. I can measure the radius. But the three points on the circle that would be exactly the same distance from one another - I can't figure out how to do that.

I can just eyeball it but that seems so - I don't know - imprecise.

ANy help?

Julia
Click to expand...
 
panini

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It turns out to be square root of 3 time the radius. This comes form the fact that the equilateral triangle is 60 degrees at each vertex and if you draw a right trianlge linside the equilateral triangle you can get a 30-60-90 triangle in the ratio 1,2 square root of 3.

A good construction technique is if you draw the circle, keep your protractor at the same radius and then draw marks around the outside of the circle with the compass it will divide the circle into 6 equal parts, connect every other mark and you have a perfect equilateral triangle.
 
kent4Him

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Sorry to be anal, but I graduated with a major in math. Panini's rational is slighly incomplete, but it is the correct answer. But as others have said, using a good compass will give you your triangle without measuring.
 
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ctEaglesc

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Originally posted by kent4Him
<br />Sorry to be anal, but I graduated with a major in math. Panini's rational is slighly incomplete, but it is the correct answer. But as others have said, using a good compass will give you your triangle without measuring.
Click to expand...
USing a bad compass will give you a triangle without any math at all.
It's called the KISS method.
 
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bonefish

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I'm not sure what you are tring to do, whether you are drawing the circle first, or the triangle, then trying to get it into the circle, or drowing the circle around the triangle.

Depending on what you want to do, draw the triangle first, using any length you want for the sides, as long as they are the same length.

Then, divide the equalateral triangle into three right triangles with angles of 30, 60, and 90 degrees, inside the equalaterial triangle. Where the long sides intersect will be the center of the triangle.

Then, using the compass, draw the circle, touching the three tips of the triangle.

By doing this, you have the radious, and diameter of the circle, and the angles and length of the sides of the triangle.

Multiply the diameter of the circle by 3.14, and you have the circumference.

What you don't have is the length of the arc from tip to tip of the triangle, but you do have the circumference of the circle, divided into three parts by the tips of the triangle.

Divide the circumference by three, and you have the length of the arcs.


Using A sq. times B sq. = C sq. You don't even have to measure the sides of the triangle or the diameter of the circle to get what you need length of the sides or circumference.

Bonefish

P.S. This is a geometry test. Not a spelling test.
 
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bonefish

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I went back and re-read the original question for the third time, and discovered that he wants to know the length of the sides of the triangle.

The way I described it is simple for me.

After writing the above, I went to a simple drawing program I have, and tried it.

If he has a drawing program, he can draw a circle and/or triangle any size he whats and the format function, using size, will tell the length and diameter.

Bonefish
 
D

DCBluesman

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Originally posted by bonefish
<br />Using A sq. times B sq. = C sq.
Bonefish
Click to expand...
No, A^2 <b>+</b> B^2 = C^2 But geez folks, get a grip. Swing the arcs, connect any two of the three points and measure to get the length of one side. Since it's equilateral, the other two sides are the same...by definition.
 
wdcav1952

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Jim, Ron Mc "made" a pen from a pickle, at least in cyber space.[:)] It often is shown when a discussion turns heated or goes from the sublime to the ridiculous. Not that I am calling any posts here or anywere else on the Net heated, sublime, or ridiculous. [:D]

Ron, save me and show the pen!
 
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Ron Mc

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Jim,
I'll post a link to the "pickle pen" for your enjoyment. The pen actually did exist but I made it before lunch so I added it to my sandwich.[;)]

This thread is amazing. I had no idea that so many people knew anything about math at all![:eek:)] I guess I need to go find my sons math books and start reading.

Here you go Jim: http://www.mckinneypens.com/images/penpics2/MVC-123S.JPG
 
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bonefish

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Lou is correct about the plus, instead of times, and I also think the question is about trigonometry instead of geomotry.[:I]

Yes, you can do it with a compass and/or dividers, depending on how accurate you want to get.

Dividers and a compass are positioned by eyeballing, which, for me, is an improcise method of measuring. Doing it with math, or with calculous, as Lou used (I think), you can take it to as many decimal points and you desire.

There is a big difference in building watches compared to measuring bull dozer tracks.

I must be the exception, because I don't consider the thread to be out in left field, or as what someone referred to when comparing triangles to pickles.[:D]

I like problems like this. Maybe I should go to a math or calculous forum to feel more at home.

Saturday, I went to the Bubbysvile get-togather, and I didn't see Bruce using a yardstick to do his calculations. [;)]

Bonefish
 
wdcav1952

wdcav1952

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Originally posted by bonefish
<br />

I must be the exception, because I don't consider the thread to be out in left field, or as what someone referred to when comparing triangles to pickles.[:D]



Bonefish
Click to expand...

Hey, Ron's pickle pen isn't triangular! [:D] At least I didn't compare the discussion to the old "How many angels will fit on the head of a pen" debate. [;)]
 
btboone

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Although this math problem was pretty straightforward, I like to draw out geometrical stuff in cad and pick off whatever dimensions I need. If it had something like 7 sides, the math gets a lot trickier, but the cad drawing still takes 15 seconds. There's lots of free cad packages out there on the internet.
 
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Mudder

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Originally posted by btboone
<br />Although this math problem was pretty straightforward, I like to draw out geometrical stuff in cad and pick off whatever dimensions I need. If it had something like 7 sides, the math gets a lot trickier, but the cad drawing still takes 15 seconds. There's lots of free cad packages out there on the internet.
Click to expand...

Same here.... If I'm looking for a dimension I draw it out in solidworks and take the measurement.

But not everyone wants to go through the trouble of the learning curve for a couple answers.
 
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jtate

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I had to work at this one!

"Gee! Oh, me tree!"

I started this thread and I must say I'm amazed and enthralled by all of this. As the kids would say, you guys rule! (pun intended)

Jim, did you really decide not to make triangular pens? I think it would be neat and I want to try it. That's why I asked the original question.

Julia
 
wdcav1952

wdcav1952

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Originally posted by alamocdc
<br />
Originally posted by angboy
<br />Damn, you people are smart! [:D][:D]
Click to expand...

And they ain't even the ones with a PhD! At least as far as I know... my apologies in advance if I'm wrong.[;)]
Click to expand...

Naturally you know what the progession of degrees actually stand for:

B.S.
M.S.
PhD

[:D][}:)][:D][}:)]
 
A

angboy

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Originally posted by wdcav1952
<br />
Originally posted by alamocdc
<br />
Originally posted by angboy
<br />Damn, you people are smart! [:D][:D]
Click to expand...

And they ain't even the ones with a PhD! At least as far as I know... my apologies in advance if I'm wrong.[;)]
Click to expand...

Naturally you know what the progession of degrees actually stand for:

B.S.
M.S.
PhD

[:D][}:)][:D][}:)]
Click to expand...

Billy, see there's a good reason I got my Ph.D. in something other than math and numbers[8)]! So I have an excuse for probably only functioning at about the high school level on this topic.

Cav- (just so I can open myself up for some sort of bashing[:D][:D]) what does the progression stand for?
 
pssherman

pssherman

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Angela,
Are you serious? You've never heard of it before?
B.S. bull s**t
M.S. more of the same
Ph.D. piled higher and deeper

Since I was crazy enough to get 2 B.S.'s at the same time, I really did have 'more of the same' and after attempting to teach college students for 18 years the 'piled higher and deeper' definitely applies.

Paul in AR
 
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