Formula that has made my head explode.

[cavman]

The formula is quite simple but the results do not make sense to me. The formula is;

pi x (square root of L² + F²)²

result 1 When F = 4372 and L = 6157 I get a result of 562 794 777
result 2 When F = 4377 and L = 6181 I get a result of 566 149 032

So far so good but when i compared these results strange things happened.

Difference between both results = 335 4255
Difference between sums of L and F = 29

335 4255/29 = 115 664

result 1/sum of L+F = 53452
result 2/sum of L+F = 53305

How is any of this possible? how can a marginal difference of only 29 cause the result to be more than double? I need to understand this in order to bring balance back to the universe.

Thanks for any help here

Tim

 

[stapel]

The formula is quite simple but the results do not make sense to me. The formula is;

pi x (square root of L² + F²)²

This is just an expression, not an equation or formula, because there is no "equals" sign in it. What is the rest of the formula? And for what do F, L, and x stand?

By the way, as currently formatted, the expression does not make much sense, since the square root of the square takes you back to the original sum:

. . . . .\(\displaystyle \pi \, x\, \left(\, \sqrt{\strut \, L^2\, +\, F^2\, }\, \right)^2\, =\, \pi\, x\, (L^2\, +\, F^2)\)

result 1 When F = 4372 and L = 6157 I get a result of 562 794 777
result 2 When F = 4377 and L = 6181 I get a result of 566 149 032

What is the value of x?

So far so good but when i compared these results strange things happened.

Difference between both results = 335 4255
Difference between sums of L and F = 29

335 4255/29 = 115 664

result 1/sum of L+F = 53452
result 2/sum of L+F = 53305

How is any of this possible? how can a marginal difference of only 29 cause the result to be more than double?

You're squaring and summing. That will tend to make for large values.

You're in intermediate or advanced algebra (based on the category to which you've posted your question), so you've already encountered cubics, quartics, and exponentials when you were back in beginning algebra. This is large, just like those.

 

[cavman]

Thank you for your reply.

First of all I probably am in the wrong category. I am 39 years old and it didn't seem right to go in with the school kids.

in answer to your questions x has no value. It was a multiplication sign. All I was trying to do was Pythagoras with a pi r² on the end of it. It worked well on the calculator but I seem to have failed in expressing what I was doing in proper mathematical terms.

I find mathmatics very fascinating. I regularly calculate things for example I recently had a blood test and I can tell you that I am the proud owner of just over 1 500 000 000 000 red blood cells. I've also been known to work out how many seconds I've been alive.

But this one stumped me when I compared the results. I wanted to work out if there was another way of doing the calculation. I wanted to know if the values of the result divided by sum of L and F behaved in a uniform way. All I ended up with was confusion.

Just so you know F = my ebay feedback L = how many items I have listed. Calculation 1 was yesterday calculation 2 was today.

Tim

 

[Ishuda]

The formula is quite simple but the results do not make sense to me. The formula is;

pi x (square root of L² + F²)²

result 1 When F = 4372 and L = 6157 I get a result of 562 794 777
result 2 When F = 4377 and L = 6181 I get a result of 566 149 032

...

From your answers, it looks like you are computing
S(F, L) = \(\displaystyle \pi^2\, (F^2\, +\, L^2)\)

Note that differences in the case of squares grow as twice the original number
(F+a)² + (L + b)² = F² + L² + 2 (a F + b L) + a² + b²
so
(F+a)² + (L + b)² - (F² + L²) = 2 (a F + b L) + a² + b²

Looking at the numbers the average of F & L is about 5K, the average difference is about 15 or a product of 75K for each is 150K for both times 2 is about 300K times 10 [for the \(\displaystyle \pi^2\)] is about 3,000K which is what you got. So, what's the problem.

 

[cavman]

Thank you everybody for your help. I now fully understand what is going on. I think I also now know how to correctly express what I was doing here goes;

T = Tims number

F^2 + L^2 = T1^2 (T1 * pi)^2 = T

The problem never was the calculation. The problem was that the results did not behave how I expected them to. I just needed to understand what was going on.

Thanks again

Tim