Need geometry help

[HarryHotspur]

Well, that was interesting. Now, how can you trisect a circle?

[Anonymous]

Using simple tools that most of us have: 

1. Take an ordinary carpenter's square and put it around the edge of the circle (pie pan). 
2. Take anything with a 45 degree angle - a drafting triangle or a carpenter's cutting triangle and put it on top of the carpenter's square.
3. Align the points of the square and the triangle.
4. Draw the 45 degree line which will bisect the center of the circle.
5. Rotate the square about 90 degrees and do it again.

-John

 

[KingConrail76]

You need to draw two chords (straight lines connecting two points on the circle) in different locations on the pan.  Then draw a line perpendicular to each of these cords.  The point where the two lines intersect is the center of the circle.

Tom

The perpendicular lines must originate at the center of each chord of course. 

Exactly . . . . . . . . . . this is why the proper procedure is to BISECT THE CHORD using a good old fashion $1.29 compass. And to insure the accuracy of your measurements you would be better served to use three chords. If everything is done correctly each and every one of those perpendicular lines will pass through the center of the circle.

And once you have found the center of that circle you would be well served to take a few measurements across the circle to insure that 1) that pan is round, and 2) that pan is 9" in diameter.

And to get a

GOOD Combination Square with a Center Finder Head

you may have to fork over a few GOOD bucks. 

True, but can you put a price on precision? And compared to that $250.00 sound equiped loco, my $230.00 Starrett Combination Square has been the far better purchase. It does much more than look and sound good...it earns it's keep. 

[Annonymous]

Any two non-parallel chords would then have their perpindicular bisectors interect at one point only and that would be the center of the circle. I like the idea of using a third measurement which would minimize the effect of any slight misallignment of the various lines drawn. Theoretically, two lines would be enough but I have find it can be difficult to draw lines exactly so the more lines should reveal any such lack of precision and help me to zero in on the center point.

Use the third chord to eliminate possible lack of precision, all lines should cross at the same point. I'm out on a limb here, but I believe a third chord rotated 90 degrees is the most accurate...

 

[selector]

I just use a compass.  Set it so that it is about 15% less than the diameter of the circle, and then draw four intersecting pairs of arcs from four different points along the permiter, with the pivot point on the perimeter line.  Draw a line through the opposing intersections of arc and you will find your centre depicted where the two lines cross.

[dehusman]

Take a drafting triangle and put the 90 degree corner on the circumference of the circle.  Mark where the two legs cross the circumference.  Draw a line between those two marks.    Move the triangle over several inches and repeat the process.  Where the lines cross is the center.

I was thinking about using a pie pan also, but I was going to drill out a large hole in the center, mount the pivot on a baseboard and then put the pan over the pivot and the bridge over that.  Then I could adjust the position of the pit to match the position of the turntable and wouldn'd need to worry about dead center.

Dave H.

[jecorbett]

Thanks to all who responded as it has jogged my memory quite a bit. It makes senses to me that a perpindicular line through the center point of any chord would at some point pass through the center of the circle. If my memory serves, we called this the perpindicular bisector of a line segment which I do remember how to find. Any two non-parallel chords would then have their perpindicular bisectors interect at one point only and that would be the center of the circle. I like the idea of using a third measurement which would minimize the effect of any slight misallignment of the various lines drawn. Theoretically, two lines would be enough but I have find it can be difficult to draw lines exactly so the more lines should reveal any such lack of precision and help me to zero in on the center point.

[R. T. POTEET]

You need to draw two chords (straight lines connecting two points on the circle) in different locations on the pan.  Then draw a line perpendicular to each of these cords.  The point where the two lines intersect is the center of the circle.

Tom

The perpendicular lines must originate at the center of each chord of course. 

Exactly . . . . . . . . . . this is why the proper procedure is to BISECT THE CHORD using a good old fashion $1.29 compass. And to insure the accuracy of your measurements you would be better served to use three chords. If everything is done correctly each and every one of those perpendicular lines will pass through the center of the circle.

And once you have found the center of that circle you would be well served to take a few measurements across the circle to insure that 1) that pan is round, and 2) that pan is 9" in diameter.

And to get a

GOOD Combination Square with a Center Finder Head

you may have to fork over a few GOOD bucks. 

[larak]

You need to draw two chords (straight lines connecting two points on the circle) in different locations on the pan.  Then draw a line perpendicular to each of these cords.  The point where the two lines intersect is the center of the circle.

 

Tom 

The perpendicular lines must originate at the center of each chord of course. 

[KingConrail76]

Have you thought about buying a good Combination Square with a Center Finder head?

Take about 10 seconds to find the center of anything smaller than your beam length, typically 12 inch.

[andrechapelon]

I recently acquired a Scale Structures turntable which consists of the bridge with suggestions for building a pit. I have an idea to use a 9 inch cake pan for my pit but to do that, I need to find the exact center for the pivot point of the TT. Past experience with TTs tells me there is no such thing as close enough with TTs. You need to be precise. I vaguely remember there is a geometric process for locating the center of a circle by drawing a triangle inside the circle but that is all I remember. Is there someone out there who is less than 40 years removed from the high school geometry class who can explain the full process?

http://www.makeitsolar.com/science-fair-ideas/90-find-circle-center.htm

Sometimes entering things in Google gets strange results. This, however, was the first result of typing find center of circle

This shows it graphically: http://www.mathopenref.com/constcirclecenter2.html

Hope this helps.

Andre

 

 

[loathar]

http://www.ares-server.com/Ares/Ares.asp?MerchantID=RET01229&Action=Catalog&Type=Product&ID=82285

Think along the lines of a larger version of this. You can probably make it yourself out of a couple peices of wood.

[fiatfan]

You need to draw two chords (straight lines connecting two points on the circle) in different locations on the pan.  Then draw a line perpendicular to each of these cords.  The point where the two lines intersect is the center of the circle.

 

Tom 

[jecorbett]

I recently acquired a Scale Structures turntable which consists of the bridge with suggestions for building a pit. I have an idea to use a 9 inch cake pan for my pit but to do that, I need to find the exact center for the pivot point of the TT. Past experience with TTs tells me there is no such thing as close enough with TTs. You need to be precise. I vaguely remember there is a geometric process for locating the center of a circle by drawing a triangle inside the circle but that is all I remember. Is there someone out there who is less than 40 years removed from the high school geometry class who can explain the full process?