Monday, July 13, 2009

Math In The Bellagio Conservatory

If the fountains in front of Bellagio aren't enough, you can see more in the Conservatory:
click on the pictures to enlarge
I marvel at the flawless parabolas made by the squirting fountains, showing that gravity is a t-squared function.

And how much math and engineering had to go into the design and building of this fountain, whose four jets meet right at the center. Again, click on the pictures to enlarge them, as they look so much better full size:

And all this water in the middle of a desert!


Fritz J. said...

Darren, are they actually parabolas? I've never really studied parabolas, but my understanding is that curves have to be equal on both sides of the mid point and in the case of a stream of water, friction from passing through the air would make the decent side curve different from the ascent, or pressure side curve, because the decent side is traveling slower in the horizontal plane. If there was no air resistance to overcome, the water would make a perfect parabola. And to be honest, I could very well be wrong on my understanding of this because what little I remember from school was many years ago and parabolas are something I never had reason to work with. It may be that a ballistic trajectory is a parabola, but that was not my understanding and a ballistic trajectory is what the streams of water most resemble.

Darren said...

It *is* a ballistic trajectory, but of course given the short duration of the water stream I'm ignoring any wind resistance. I'm sure Newton would cut us a little slack on that!

Eric W. said...

I recently visited La Sagrada Familia, among many other Gaudí buildings, in Barcelona. They had some fascinating exhibits up showing all of the math tricks employed by Gaudí in the design of the buildings, and the way he incorporated lots of interesting shapes (Hyperbolic paraboloids and the like) into his designs.