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Anyone good at maths?


XmisterIS
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I have a simple problem (but on closer inspection it isn't so simple!).


Consider two non-intersecting circles with locii C1 and C2 and with radii r1 and r2, respectively. Now, consider a third circle with locus C3 and radius r3. Find r3 as a function of the angle between the vectors C1C3 and C1C2 for all cases where the third circle touches the other two.


Seems simple enough in concept ...

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Lol!


It's a continuum of triangles. The trouble is, I think it's probably partially differential because I think the solution is probably a symmetric hyperbolic equation, with one imaginary half. My differential calculus is a little rusty!

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If im understanding the question correctly, it shouldn't be that bad... you know the length of all three sides of the triangle, so given the angle at C1 or C2 you can calculate the other two angles.

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If im understanding the question correctly, it shouldn't be that bad... you know the length of all three sides of the triangle, so given the angle at C1 or C2 you can calculate the other two angles.

 

Not quite - there is a continuum of angles and if you think about it, you don't know the length of all three sides - because you don't know the radius of the third circle (which is what you are trying to find). Trying the cosine rule to form a set of simultaneous equations over which to integrate very quickly leads to nastiness!

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If im understanding the question correctly, it shouldn't be that bad... you know the length of all three sides of the triangle, so given the angle at C1 or C2 you can calculate the other two angles.

 

Not quite - there is a continuum of angles and if you think about it, you don't know the length of all three sides - because you don't know the radius of the third circle (which is what you are trying to find). Trying the cosine rule to form a set of simultaneous equations over which to integrate very quickly leads to nastiness!

 

like this?


http://www.mylnk.net/joeman/Circles.png


So you know the angle at C1 and the length C1-C2.

you also know r1 and r2.

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When I used to work in a factory we were in the canteen one day queueing for lunch and one of the old girls was chatting to one of the old fellas in front of us. She was a lovely old girl, but definitely a sandwich or 2 short of a picnic and she was telling the old fella that her husband was an accountant. The old fella just shook his head slowly and said "it just don't add up".......and we all fell about laughing.......poor old girl just didn't see what we were laughing about..... :lol: :lol:

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For those that are still like: :scratch:


A hyperbolic function is an analogue for circular and triangular functions.


Go back to high school stuff where "cos t" and "sin t" with a radius in unit form creates a circle, a hyperbolic function finds the equilateral hyperbola (the right half)


In the real world, a hyperbola can be seen with the triangular lighting effect from some down lighting. It's that shape.


Using it with differentiation, which is just a way of taking real values and deciphering their rates of change. You can work out using the angle between the vectors where C3 will fall.


I think... :lol:


http://www.stasheverything.com/wp-content/uploads/2012/11/math-meme.jpeg

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:stupid:


That is the principle of it, yes.

 

http://www.stasheverything.com/wp-content/uploads/2012/11/math-meme.jpeg

 

When I was at Uni, we had a similar in-joke: "Hence find the mass of the Sun, using the approximation of a spherical horse in a vacuum".

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