Daylight Atheism > Photo Sunday: Parabola

Daylight Atheism has moved! Please visit the new address at:
http://bigthink.com/blogs/daylight-atheism

Photo Sunday: Parabola

This photo is from my trip to St. Louis last weekend, taken from the base of the famous Gateway Arch. Besides the sheer scale of the structure, I was attracted to its stark, geometrical shape - almost like a mathematical equation in the form of a building. In the enlarged version, you can see the windows of the observation deck at the apex.

Gateway Arch, St. Louis, January 2010. Photo by the author. Camera details: Canon PowerShot SD1200 IS. Click for larger version.

10 Comments

The gateway arch is a catenary, not a parabola ;)</pedant>

Comment #1 by: mike | January 24, 2010, 2:09 pm

That picture gives me the same wonderfully terrifying feeling of falling up that looking up at the sky sometimes does.

Comment #2 by: Erika | January 24, 2010, 2:14 pm

almost like a mathematical equation in the form of a building

Strike the "almost". As Mike points out, the arch is a catenary. I don\'t know the specific mathematical equation for a catenary, but AIUI it has the interesting property that the stresses at every point are as small as they can be, which is a desirable property in a tall structure. It probably involves differential equations.

But the other way of constructing a catenary is hidden in its name, which is Latin for "like a chain": hang a rope or a chain from two pegs and see how it hangs. The individual links will work out for themselves how they want to hang so that the stresses on them are as small as they can be under the pull of gravity. Then you flip it upside-down to get a structure that can stand up against gravity with the least effort.

A longish explanation, I know, but for me, this symmetry is part of the beauty of the Gateway Arch.

Comment #3 by: arensb | January 24, 2010, 2:37 pm

Its a hyperbolic cosine function,

y = 693.8597 - 68.7672cosh(0.0100333 x)

y = height in feet
x = distance from center of base in feet

-299.2239 ft <= x <= 299.2239 ft

Comment #4 by: Marshall Schreiber | January 24, 2010, 3:08 pm

This photo makes me a bit wistful. My only trip to St. Louis was in the spring of 1998. I took a picture just like this, but the whole roll of film ended up getting ruined.

Comment #5 by: Andrew T. | January 24, 2010, 4:52 pm

Wow, that is awesome! Thanks for sharing! How was St. Louis, by the way? I wish I could have made it, but I had a prior commitment.

Comment #6 by: D | January 24, 2010, 8:34 pm

Going to the lookout point at the top was an exercise in confronting my claustrophobia.

Comment #7 by: Polly | January 24, 2010, 9:51 pm

D.J. Grothe wasn't able to make it, but other than that, we had a great time at the St. Louis meetup. Some people traveled from impressively far out of town, which made me feel more than a little flattered, and Erich Vieth and his wife very graciously opened up their house to the whole atheist crew and provided a catered dinner for us. They also recommended we visit City Museum, which I'm glad I did.

Oh yes - and we had an unexpected mini-raffle after dinner, courtesy of one of our guests (thanks Shelby!). I won a copy of R. Crumb's Genesis Illustrated, which was an amazingly cool prize. I'm still reading through it and finding good pages to scan.

Comment #8 by: Ebonmuse | January 24, 2010, 10:41 pm

almost like a mathematical equation in the form of a building

No, no, no! It is like the solution to a mathematical formula.

Comment #9 by: Reginald Selkirk | January 25, 2010, 9:37 am

It's a beautiful picture and I appreciate the civil engineering accomplishment but damn, it gives me a headache looking at it.

Comment #10 by: Caiphen | January 26, 2010, 9:01 pm