A new house number ...

http://thelastdanishpastry.deviantart.com/art/We-moved-into-a-new-house-138857094

by RiderOfGiraffes • 17 years ago

25 26 17 years ago

thelastdanishpastry.deviantart.com

jgrahamc• 17 years ago

Feels annoying to me that the pi^2 is left inside the infinite sum at the bottom:

http://equationater.com/3887e31ec88fbf35d331554e06353358.png

RiderOfGiraffes8• 17 years ago

I think the reasoning there is that sum(1/(n^2)) is rather well-known to be pi^2/6. They then need to invert and remove the pi^2.

I think it's a reasonable part of the game to put the pi on the inside.

bonsaitree• 17 years ago

It's just intentional obfuscation. Just like the double inversion.

antirez3• 17 years ago

I had to write the following to understand this is going to converge to 6:

    >> 1/((1..1000000).map{|n| (1/((n*3.14)**2))}.inject{|a,b| a+b})
    => 5.99392169730553

RiderOfGiraffes8• 17 years ago

    >>> from math import pi
    >>> 1/sum( [1/(pi*n)**2 for n in xrange(1,1000)] )
    6.00365160802217

apgwoz• 17 years ago

let's not get all fizzbuzz-y in here...

antirez3• 17 years ago

Shorter but, "ad hoc" like everything in Python (the reason I never liked it). The Ruby version looks like math, if you know the concepts of map and reduce it's trivial to understand what's going on.

Compare this with sum() + "for n" and "xrange". Also if I remember some Python correctly "xrange" is almost like "range" but it's something like a lazy version, another ad-hoc stuff.

Sorry, didn't resisted.

jrockway• 17 years ago

    Prelude> 1/sum ([1..1000] >>= \x -> [(pi*x)**(-2)])
    6.003647956020607

andrewparker• 17 years ago

Sorry if this is obvious, dusting off the math mind here... How is this solved without brute force computation?

RiderOfGiraffes8• 17 years ago

It's neither obvious nor easy. It was an outstanding problem in the mid 1700's, and it was Euler that solved it but some superbly reckless arguments.

Euler's original paper:

http://www.17centurymaths.com/contents/euler/e041tr.pdf

The bottom of this page has a more modern treatment, although it takes a lot for granted:

http://www.math.wpi.edu/IQP/BVCalcHist/calc3.html

Another treatment of Euler's proof is here:

http://library.thinkquest.org/28049/Summing%20reciprocals.ht...

abalashov• 17 years ago

Congratulations, now I'll never find your address if you invite me over. Last math I took was "advanced" algebra & trigonometry my junior year of high school.

modoc• 17 years ago

It works as a visitor filtering mechanism. "You must be at least this good at maths..."

Edinburger• 17 years ago

I'm glad I am not your mailman.

RiderOfGiraffes8• 17 years ago

It's not me - I live at http://www.penzba.co.uk/my_house_number.png

jacquesm• 17 years ago

Humor for mathematicians. I really should come to attend one of your talks. Need 48 hour days. And a calculus course.

robertk• 17 years ago

You need parentheses around the -1. Otherwise the series is divergent. I presume you do not live at a divergent address? :)

bhousel• 17 years ago

Or the local EMS, Fire, Police, etc..

Seriously, I'd get that changed. There are plenty of reasons someone might want to find your house quickly.

anamax• 17 years ago

People often need to solve the problem of finding a house where the number is readily apparent.

In some/many places, one could find that house by interpolation. (In the US, even numbers tend to be on one side of the street and odd numbers on the other. And they're almost always in-order.) With an apartment, things can be more complicated.

That said, there are instances of "vanity addresses", where "<some number> 5th Ave" appears to not be on 5th Ave.

I don't know what one does in Japan, where the numbers are supposedly assigned chronologically. (Hmm - I wonder what triggers number generation and if they ever reuse or allow transfers.)

ynniv• 17 years ago

Hey, a use for Wolfram Alpha! [ http://www.wolframalpha.com/input/?i=sum%281%2F%28n+*+pi%29%... ]

aeroevan• 17 years ago

This works for me: http://www.wolframalpha.com/input/?i=%28sum+1%2F+%28n+*+pi%2...

A new house number ...

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