Coming and Going

Sorry to have disappointed my regular readers with a dearth of posts lately.  One last good post before I head off for spring break.

Katie came to visit the first week of March, and we had a great time exploring Budapest together.

 Budapest -- two thumbs up! (at the Ludwig Museum)

Budapest has an unusual number of bronze statues of famous Hungarians.  I think Budapest must have gone through a period of extreme fondness for producing these.

One of many.

Cool church a few blocks from my house

At the Great Market, Katie went straight for the mulled wine.  (Just kidding; it is delicious and I recommended it.)

Visiting the Castle Hill district

Enjoying a sunny afternoon on Castle Hill.

Katie was a fan of Budapest's many graffitos...

...and I was a fan of scaling the local architecture.

The Iron Curtain sculpture outside Terror Háza.

Seeing Degas to Picasso at the Fine Arts Museum

Just hangin out.

Hungary's deep-fried specialty, lángos.

Since Katie's visit, it's been back to life as usual in Budapest.  I have several observations.  First, it has come to my attention that may Budapesters are under the impression that they are dog owners, when in fact, they are owners of large wolves and other non-domesticated members of genus canis.  For an idea of the size of Budapest's average dog, see below:

The one in back.

All kidding aside, Budapest seems to have an unusually high number of dogs for a big city, and many of these dogs are quite large.

Budapest also seems to not care so much about inefficiency.  The most glaring example of this lack is the metro checking system.  You either buy a ticket or pass to ride the metro, bus, tram, or trolley (four different systems?  really?) and you have to validate your ticket in one of the self-serve ticket punchers at the beginning of your journey.  This system is enforced by checkers, who occasionally greet you as you exit the metro, and you are fined 6000 HUF if you are riding without a pass or a validated ticket.  Sounds fine?  In addition to this already semi-clumsy system, each and every metro station employs 2 to 4 individuals to look at your pass/ticket as you walk toward the escalator down to the platform.  All these guys do is stand there and glance at passes/tickets and (in theory, although I never see this) inform people without a proper ticket.  Anyhow.  I am also amused by the city's solution to a sidewalk under construction along Museum Boulevard (a fairly big-traffic street downtown).  No, don't redirect pedestrian traffic to the other side of the street, where there is a perfectly good sidewalk.  Yes, let's shut down an entire lane of traffic on this side and designate it as a sidewalk.  Brilliant.

I'll close with, first, a couple of youtube videos and then some interesting math problems.

I love this video (click the image again to watch it on youtube's website and read the story behind the fan-created video to the right).

Loving some March Madness.

And now for the math.  To respect Prof. Csirmaz's desire for his problems to remain relatively un-Google-able, I ask that if you want to discuss them with me, do so by email.  These are the coolest of the often-cool Conjecture and Proof problems from last week's set.

A) Find a function f: R->R such that f(f(x)) = -x for all real x.
Can you find such a function that is continuous at 0 and 1?
Can you find such a function continuous on R?

B) We have n+1 positive integers whose prime factors are among the first n prime numbers.  Show that you can pick some (at least one, but maybe all) of the numbers such that their product is a perfect square.

Sziasztok!