Math Problem Find the Arc

metron9

Some of you folks are pretty smart when it comes to electronics and that makes you pretty good at math as well I would think.

I need to know the diameter of a circle given the following:


If you have a circle and slice off 1/16 of an inch and the length of that slice is 22 inches.

Could someone give me the equasion to calculate the diameter of the circle?

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Think outside the BOX!

Paul Baker

Im pretty good at deriving geometric equations, but I don't understand what you mean by a slice. Are you refering to a chord of the circle whose maximum distance from the circle is 1/16th an inch and whose length is 22 inches? Perhaps if you can sketch out what you are asking I can help you.

Attached is a pdf of my understand of your question

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·1+1=10

Post Edited (Paul Baker) : 12/2/2005 4:57:56 PM GMT

Ryan Clarke

Hehe, don't tell him I have a degree in math Paul, then you can just answer his question and I can work on other things [noparse];)[/noparse]

Paul's take on the original question is how I interpreted it as well....

Ryan

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Ryan Clarke
Parallax Tech Support

RClarke@Parallax.com

Robert Kubichek

metron9 said...
Some of you folks are pretty smart when it comes to electronics and that makes you pretty good at math as well I would think.

I need to know the diameter of a circle given the following:


If you have a circle and slice off 1/16 of an inch and the length of that slice is 22 inches.

Could someone give me the equasion to calculate the diameter of the circle?

If the length of a slice is 22 inches that is the same as 1/2 diameter...

2x22=44 inches diameter

It would be easier to understand what you are asking if you had a drawing attached..

Bob N9LVU

Post Edited (Robert Kubichek) : 12/2/2005 8:16:28 PM GMT

Paul Baker

Ok if Ryan and I are correct, and you draw another line from the center of the circle to the end of the chord, you get a nice right triangle. By the pythagorean theorem, a²+b²=c². Substituting in the values we have, we get (d-c)²+l²=d², where c is the max distance of the chord from the circle, and l is the length of the chord/2. Expanding the terms out we get d²-2cd+c²+l²=d². Solving for d we get d = (c²+l²)/2c, or for c = 1/16 and l = 11, d= 968.03125 inches for the diameter of the circle.

Sorry, the calculation I gave you is actually the radius of the circle, to calculate the diameter, multiply the result by 2 or 1936.0625 inches or 53.78 yards or ~ 1/2 a football field. Good luck designing a compass large enough to draw the arc, since youll need 26.89 yards of string and a large enough space to sweep it for a 22" chord.

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·1+1=10

Post Edited (Paul Baker) : 12/2/2005 5:34:18 PM GMT

Ryan Clarke

Again, the problem here is in the presentation of the problem- it lends itself to several interpretations...


So here is my challenge- interpret the original question in as many ways as possible-

Ryan

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Ryan Clarke
Parallax Tech Support

RClarke@Parallax.com

Robert Kubichek

metron9 said...
Some of you folks are pretty smart when it comes to electronics and that makes you pretty good at math as well I would think.

I need to know the diameter of a circle given the following:


If you have a circle and slice off 1/16 of an inch and the length of that slice is 22 inches.

Could someone give me the equasion to calculate the diameter of the circle?

So, the chord length is 22", the depth of the chord to arc is 1/16", and you want the diameter of the circle???

c is cord length, or 22"
h is the distance of middle of chord to middle of arc segment that the cord ends bisect, or .0625"
solve for (r)adius

(c2+4h2)/(8h) = r

((22*2) + (4x.0625*2)) / (8x.0625)= 968.0313" radius
( 484 + 0.015625) / .5 = 968.0313" radius

968.0313 x 2 = 1936.0626" diameter...

Then the diameter is 1,936.0626" and radius is 968.0313"

It has been awhile, I had to go back and my check my book...


Bob N9LVU

metron9

Thank you Robert.

I had this problem last year and I was able to get my math genius daughter to calculate it for me , I made a little program but due to my lack of bookeeping skills I lost it. It is for a cosmetic display label we are working on to fit a molded plastic display. Now I can order the die and distort the image to the corrrect arc.

As I remember the formula I was given before, I thought it had an ARCTAN function in it wich is maby what your formula above is. (I only have an 8th grade education in math as I was a hippy back then and did not think I would ever need to learn all that stuff.)

It's fun to pull up those old math skills I bet.

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Think outside the BOX!

Robert Kubichek

metron9 said...
Thank you Robert.

I had this problem last year and I was able to get my math genius daughter to calculate it for me , I made a little program but due to my lack of bookeeping skills I lost it. It is for a cosmetic display label we are working on to fit a molded plastic display. Now I can order the die and distort the image to the corrrect arc.

As I remember the formula I was given before, I thought it had an ARCTAN function in it wich is maby what your formula above is. (I only have an 8th grade education in math as I was a hippy back then and did not think I would ever need to learn all that stuff.)

It's fun to pull up those old math skills I bet.

Yup

Check this link, it has all you would need and more!

mathforum.org/dr.math/faq/faq.circle.segment.html

Bob N9LVU

Paul Baker

hey, I get no credit? I even derived it by hand. *sulk* (just kidding).

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·1+1=10