δ \delta day Problem 1

Level pending

If Krish takes a random sequence such that

x i + 1 = f ( x i ) x_{i+1} = f(x_{i}) , where f(x) is parameterized by a parameter which is responsible for a pattern which amazes Krish.

The graph formed bifurcates after some time and this goes on forever. His friend Anik asks him to find the ratio of the distance the graph moves till one bifurcation. But, he gets confused because he doesn't know the intervals he has to tell between. But, after sometime, he found the answer and he was amazed to see that the ratio can be found between any intervals without knowing them.

What was the answer?(Krish doesn't like the thousandth decimal place and loves rounding everything as he did with the minds of solvers with this function)


The answer is 4.67.

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1 solution

Michael Mendrin
Aug 8, 2014

You should ask for a number rounded to the nearest hundredths. "Doesn't like the thousandth decimal place" sounds ambiguous, and could mean a floor value, in which case it would come out 4.66 4.66 .

Can you clarify the solution....I am unable to get it..

Jayakumar Krishnan - 6 years, 10 months ago

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It's Feigenbaum's constant!

Kartik Sharma - 6 years, 10 months ago

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Oh...I see..but if i am not wrong, can you please tell me what fun you get by posting problems based on unheard constants?

Jayakumar Krishnan - 6 years, 10 months ago

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@Jayakumar Krishnan That is fun, don't you think so?

Kartik Sharma - 6 years, 10 months ago

Edited! Now, I think it is fine!

Kartik Sharma - 6 years, 10 months ago

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