Multi-Pole Problem

So we all know the infamous Two-Pole Problem, which doesn't rely on the distances between the two poles. I have a situation where there are a n poles. Each pair of consecutive poles is used to create a Two-Pole situation, thus creating n-1 shorter poles. Using these, n-2 shorter poles are created in a similar fashion. This continues until there is one pole, which for reference I will call the "supporting pole". if $x_{1}, x_{2}, x_{3}, ..., x_{n}$ are the lengths of the starting poles, find a formula for the length of the supporting pole in a n-Pole Problem.

Easy Math Editor

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Comments

$\frac{1}{\sum_{i=1}^n\frac{1}{x_{i}}}$

Mohammad Sarfaraz - 7 years, 1 month ago

That's close. Try a few other cases that can disprove this(try 5 poles, for instance).

Tristan Shin - 7 years, 1 month ago

I don't get it...so please can you reveal the answer...:)

Mohammad Sarfaraz - 7 years, 1 month ago

I don't know that problem (you said it's infamous then why not show it)

Amr Saber - 7 years, 1 month ago

For clarification, the Two-Pole Problem is where there are two poles of length a and b. Lines are drawn from the top of each to the bottom of the other. From the intersection of these two new lines, a vertical line segment parallel to the original poles is drawn. It turns out that the distance between the two poles is irrelevant. To solve this problem, try playing around with a few two-pole scenarios.

Tristan Shin - 7 years, 1 month ago

I'll reveal this solution within the next week(April 21-April 25).

Tristan Shin - 7 years, 1 month ago

I think now you should reveal the solution.....

Mohammad Sarfaraz - 7 years, 1 month ago

We use the formula $\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{z}$ where $x,y$ are the two poles and $z$ is the height of the middle pole. Solving for the supporting pole is pretty trivial, just plug 'n' chug.

Daniel Liu - 7 years, 1 month ago

But is there a generic formula for the supporting pole, not just plugging it in?

Tristan Shin - 7 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$