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GEOMETRY GURUS!!! Area of an Oval - SOLVE!
OK...here's the deal. Take a look at the image below. An oval (an oddball ellipse) is made up of four intersecting circles. The ONLY dimensions known are shown on the image. What forumla would be needed to find the area, or even the lenghth (on the Y axis) of the oval? Myself and my boss have beat ourselves up for the last 2 hours trying to figure this out.
Keep in mind that this is NOT a true ellipse. A true ellipse is easy to figure out Pi(R1*R2). This DOES NOT work in this scenario.
Let's see how smart the TAs truly are 
why do ppl come to the chillout room to do their homework...and they make it sound like theyre trying to test u to see how intelligent u are but really theyre just stuck on question 6 on page 5
hm, 4 intersecting circles...?
i'd say try to use calculus & integrals; maybe arclength, but it's not gonna be pretty.
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| Originally posted by Vivid Boy why do ppl come to the chillout room to do their homework...and they make it sound like theyre trying to test u to see how intelligent u are but really theyre just stuck on question 6 on page 5 |
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| Originally posted by Vivid Boy why do ppl come to the chillout room to do their homework...and they make it sound like theyre trying to test u to see how intelligent u are but really theyre just stuck on question 6 on page 5 |
would you get the right answer if you just found the perimeter and changed it into a circle?
is this like something from that math test that's the hardest in the world and only has like 12 questions? cus it sure looks like it... i say there is no way you can really find it.. that's what i wanna say
looks like you did this in autocad or osmehting similar, can you find the area and just work backwards.
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| Originally posted by MERTON would you get the right answer if you just found the perimeter and changed it into a circle? is this like something from that math test that's the hardest in the world and only has like 12 questions? cus it sure looks like it... i say there is no way you can really find it.. that's what i wanna say |
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| Originally posted by DJ_NRG No, this is not from that test. This is an actual scenario that I have encountered at work (I work IS/Programming for a glass manufacturing facility). We need to determine the actual yield of a particular shape when the piece of glass is cut. We have pretty much decided, as well, that it may be impossible... |
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| Originally posted by Boomer187 looks like you did this in autocad or osmehting similar, can you find the area and just work backwards. |
if you're the ones making the dimensions.. then where is the rest of the info? i mean.. damn.. this is like beyond a resonable level of difficulty for something you're actually able to physically deal with.
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| Originally posted by DJ_NRG It was done in AutoCad 2004, and even that program does not find the area of an oval. It will give us the length, but in our workplace, the length is an unknown value, because it is not necessary to actually know the length to draw the shape. |
here's my 0.02:
find the equations for the circles (you know the radii)
guess and check where they should intersect
then place each circle on a set of axes to find the intercepts and find the area under each parth. then find the area of the rectangle.
if all fails, make a detailed cardboard model, cut it into 5 pieces like i've shown, and put teh circles over a set of coord. axes and measure where they intersect, if you can't figure out by equations.
and P.S. an oval = ellipse, and what you have is an area of 4 intersecting circles, but it's NOT an oval.
oh my god, math hurts my brain, check online maybe. i think math.com has a bunch of resources you might be able to find your answer there, or a math forum (yes there are actually forums devoted to math) good luck man
i really think this is possible, just it would take way too much work for me
k so here's my thoughts
since you only have the radius' of the two circles, you find the derivatives of the two, and at the places where the circles intercect each other, their derivatives would = each other
so with the derivate of that point plus the radius with some weird more derivative shit you can find the angle of the arc that we see for each circle
using the arc length and the radius, we can find the arc length
with that we can find the area of the sector created with (the line that intersects the two points of intersetction for the larger circles) and (the arc)
so you do that for both circles, then you have the area of all but the inner rectangle, which since you know the length of the straight line from the sectors you can find it easily
anyone follow that?
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| Originally posted by mezzir i really think this is possible, just it would take way too much work for me k so here's my thoughts since you only have the radius' of the two circles, you find the derivatives of the two, and at the places where the circles intercect each other, their derivatives would = each other so with the derivate of that point plus the radius with some weird more derivative shit you can find the angle of the arc that we see for each circle using the arc length and the radius, we can find the arc length with that we can find the area of the sector created with (the line that intersects the two points of intersetction for the larger circles) and (the arc) so you do that for both circles, then you have the area of all but the inner rectangle, which since you know the length of the straight line from the sectors you can find it easily anyone follow that? |
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| Originally posted by whiskers the derivatives aka the slopes won't be equal at points of intersection, but the xy coordinates would be. plus a derivative of a point won't do you much good |
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| Originally posted by mezzir yeah dammit this is hard and i got all involved and now i wanna figure it out |
damn, I threw out my autocad 2004 disk. I will find it on a computer on campus and try to find that option I was thinking of...or just sit in front of the screen looking like a jackass.
hm, well on second thought fuck the derivatives part, i wasn't thinking real hard about it
and i think i have it, lmme just do a bit more algebra then i'll post it if it makes sense
lotsa geometry
hm...arrived at an answer but i'm unsure of it
~725.5 sq units of w/e seem reasonable?
oh come on....anyone?
i'm just asking if its reasonable, that was the first actual math i did and like 1/2 way enjoyed and i don't even know if i did it right
I think they need it to be exact, not reasonable.
If you know that it's 4 intersecting circles, why can't you show us where those circles are? It says they meet at a tangent point. Great, the 3 radii shown (I'm assuming the 13.6120 is supposed to be a diameter of one of the circles) don't even have a common intersection point. What the hell?
Please clarify. If you designed this, you can surely give more info.
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| Originally posted by mezzir ... anyone follow that? |
I've got an answer
I've got an answer, it took a lot of calculation. For now I'll just give you my answer so far: 421.4756 units^2.
I'm working on creating some step by step with the equations.
The basic method I used was to find the equation of the two circles and calculate their derivative. I set the two derivatives equal to each other and found the point where they were equal.
From that I used trig/geometry to calculate all the areas involved.
Give me a bit to write something up, but there is an answer for now...
Jonathan
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