A new house number ...(thelastdanishpastry.deviantart.com)

25 pointsby RiderOfGiraffesvor 17 Jahren26 comments

thelastdanishpastry.deviantart.com

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

27 comments

antirezvor 17 Jahren

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

RiderOfGiraffesvor 17 Jahren

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

jrockwayvor 17 Jahren

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

apgwozvor 17 Jahren

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

antirezvor 17 Jahren

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.

RiderOfGiraffesvor 17 Jahren

Each to his/her own. This isn't intended to be a language war. If you prefer map and reduce then you can have them:

  >>> from math import pi
  >>> add = float.__add__
  >>> def f(x): return (pi*x)**(-2)
  >>> 1/reduce(add, map(f,range(1,1000)) )
  6.0036796863530508

Or, as a one-liner:

  >>> 1/reduce(float.__add__, map(lambda x:1.0/(3.1416*x)**2,range(1,1000)) )

People who aren't mathmos often find the list comprehensions more comprehensible, hence the version I wrote not as a competitor, but as an alternative, to yours.

Horses for courses. Personally, I've found the Python version to look more like math when I choose to express it like math, but I'm programming, so why not make it look like what I'm doing? Golf is a stupid game in programming. Understandability is the goal, but different readers find different things natural.

That's never going to go away.

antirezvor 17 Jahren

I guess it's really a matter of tastes indeed. My point is that, no matter the fact that I can try to mimic the Python idiomatic way or the reverse, there is a real difference between this languages, and is a difference that I see in many other languages, splitting them into two families: the "tools" languages that try to provide already build abstractions able to solve common problems, and the "concepts" languages where there are just a few rules you can combine to solve problems. I love the latter approach.

andrewparkervor 17 Jahren

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

RiderOfGiraffesvor 17 Jahren

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...

stilistvor 17 Jahren

Last link needs to swap %20 for the space.

RiderOfGiraffesvor 17 Jahren

Done - thanks.

Edinburgervor 17 Jahren

I'm glad I am not your mailman.

RiderOfGiraffesvor 17 Jahren

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

robertkvor 17 Jahren

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

RiderOfGiraffesvor 17 Jahren

That depends on which school you went to, but point taken. I've inserted the parentheses.

jacquesmvor 17 Jahren

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

bhouselvor 17 Jahren

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.

anamaxvor 17 Jahren

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.)

jgrahamcvor 17 Jahren

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

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

RiderOfGiraffesvor 17 Jahren

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.

bonsaitreevor 17 Jahren

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

RiderOfGiraffesvor 17 Jahren

I'm not sure what you mean by the double inversion. You inverting a sum of invertions - that can't be undone in any sensible way. Can you explain a little more what you mean?

ynnivvor 17 Jahren

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

aeroevanvor 17 Jahren

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

abalashovvor 17 Jahren

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.

modocvor 17 Jahren

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

[deleted]vor 17 Jahren