Buckingham Palace wins.

Hollywood sign (4)
vs
Guggenheim Bilboa (13)

http://cellar.org/fieldof64/64.php?field=landmarks

Hollywood sign

Guggenheim Bilboa

Guggenheim Bilboa

Guggenheim Bilboa wins.

St. Louis Arch (6)
vs
The Everglades (11)

http://cellar.org/fieldof64/64.php?field=landmarks

Everglades

The Arch...

What? I'm sorry, but could you explain?:confused:

We have to skip a matchup between votes. :)

OH! OK, thanks! ;)

St. Louis Arch

The design of the arch is an inverted catenary (known to your graphing calculators as -cosh[x]).

A catenary is the curve of a flexible chain held at each end and pulled down by gravity.

St. Louis Arch wins.

Empire State Building (3)
vs
Trafalgar Square (14)

http://cellar.org/fieldof64/64.php?field=landmarks

Empire State Building

Used to be a time when you could go to Trafalgar Square and climb aboard the lions at its base - I remember being photographed astride one - now it's cordoned off, and the Square is just one of many open spaces to gather. Even after 'Sleepless in Seattle'. I still go for:

Empire State Building

Still a great symbol of American achievement