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Advanced Math/Trilateration question


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Hi Scott,

Thanks for your reply, however it does not seem to work right for even 3 points, without even extending it to 4 or more.

I have attached a spreadsheet, showing your method based on the example you gave, and the more demonstrable one I originally forwarded.

where the cirles are (4,8) r=5, (11,7) r=5, (16,17) r=10
you can see is the diagram originally posted;
that the point of focus would be about (8,11)

however, your formula produces (13,13) which is way off really.

To extend it to 4 or more points, it would really need to prodce a far more accurate  result for when just 3, to have confidence it the output of 4 or more...

I really appreciate your effort so far, as I really don't know how to tackle this. About all I can do is validate any formula! haha

I hope you are able to look a little deeper :)

Perhaps I didn't say it right, so I'll use the example you gave ...

What I get from (4,8) r=5, (11,7) r=5, and (16,17) r=10 is ...

For the x, I get (4*25 + 11*25 + 16*100)/(25+25+100) = (100 + 275 + 1600)/150
= 1,975/150 = 13 1/6 or 13.1666...

For the y I get (8*25 + 7*25 + 17*100)/150 = 2,025/150 = 13.5.

So the middle point to those by my method is (13 11/6, 13 1/2).  Looking back at the points,
this looks like it might be what we're looking for.

The straight average would be (10 1/3, 10 2/3), which is just a little bit off from my weighted point.  

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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