An architecture question

I’m sitting at the Little Café Near Home, planing my November, which is looking bright, and somewhere along the way I started thinking of triangles — not sure what set it off — and a missed opportunity by my math teachers in seventh grade.

My memory being notoriously bad, I’m amazed I remember any of this stuff, but we spent a lot of time in geometry class messing with triangles. One thing that was pounded into our heads was that once you define the lengths of the sides of a triangle, you’re done. That triangle is fixed. I think we called it the side-side-side theorem, or SSS for short. It was just another fact. Just another checkbox in the curriculum.

It might have caught my interest more, and perhaps the interest of others who didn’t take to math so well, it someone had mentioned that it could be the single most important fact in mechanical engineering and architecture. Triangles are rigid.

Now I remember how I started thinking this way — most of the chairs in this place, sturdily made of steel, are distorted. Over the months and years of use people have leaned back in them until now they are all somewhat out of shape. They are sturdy, but they are all about rectangles, not triangles. It would not take much to redesign these chairs to be much sturdier.

So you put a chair like this in front of a high school math class and say, “Behold, the power of the triangle in your everyday life.”

But then I did some more thinking. Thoughts often lead to thinking, and thinking to thoughts, in a vicious cycle interrupted only by head trauma or the presence of a member of the opposite sex. I thought of Notre Dame Cathedral. No triangles. Apparently stone is not a material for triangles. It’s good with compression, but tensile strength is laughable. It can only be flexed one direction.

But wood is certainly a good triangle material. I remember as a kid staring up at the rafters in church, seeing the triangles there, admiring the way they were made with parallel planks bolted together like a giant tinkertoy. I remember those rafters better than any sermon.

But older examples of triangles in architecture, I’m having a hard time with. There’s the old footage of the great New York skyscrapers racing each other into the sky, giant rectangular steel frames with steeplejacks racing about with hot rivets. There must have been triangles in there or the whole mess would have twisted and fallen, but they’re not apparent in those old movies.

So, architecture guys: Sacre Coeur, no triangles; then there was that skyscraper where exotriangles were added when they realized after they built the thing that the wind tunnel tests on the models were flawed. If you were given half an hour in front of a semi-comatose group of young math students who don’t give a rat’s ass about SSS, what would you tell them? How do you pass on that this seemingly esoteric fact is a cornerstone of our civilization? In your absence, how do you advise teachers to do the same?

The scope of this ramble is rapidly expanding, to where I now want to create a framework that allows professionals to pass on their passion to students who don’t have any way to recognize when they are confronted by a potentially life-changing fact. I want a footnote in the book that links to a video of an architect getting really gung-ho about triangles, or a chemist going batshit over – uh – whatever chemists go batshit over. I want to challenge leaders in every field to think back to the most basic fact their profession is based upon, the thing they take most for granted, and explain it to people who have never heard it before. They would be giving meaning to the really important bits, things that would otherwise be lost in the noise, but simple facts that could decide a career. There’s some kid in that geometry class, not so good at proofs and theorems, but when given an important tool for buildin’ stuff, might just perk up a bit, might see the connection between all these numbers and building a hotel on the moon.

For me.

10 thoughts on “An architecture question

  1. You’re prospective MOH was an AOL-er looking for “rivalry+symbols” on Yahoo (you’re episode on the Stanley Cup ranked number 3 on Yahoo, congratulations). Not an egg fryer to be sure, but no more deserving to wear the purple ermine cloak or signet ring of this most honorable office.

    I think I’ll just settle into the throne for a second term….

    The Once and Future MOH.

  2. In the construction of the Empire State Building, there were triangles in the form of diagonal bracing. Some of those were temporary until the rectangles could get riveted into place, but some were permanent parts of the building’s structure — they just sort of get lost amid all of the rectangles.

    For a really good example of diagonals at work, look at the John Hancock Building in Chicago. It had to taper so that the retail space at the bottom, the office space in the middle, and the residential space at the top would all have an appropriate ratio of windows to floor area. It also had to be strong enough for the Windy City. Those distinctive diagonal lines on the exterior of the building weren’t afterthoughts, but rather a highly effective way of strengthening the building without losing interior space to structural elements.

    Another example of the power of the diagonal, which is the power of the triangle, because it’s the hypotenuse:
    When you’re mooring a boat in a dock and you’re preparing for bad weather, you don’t simply run lines straight from the boat to the pier. You run diagonals, called springlines, from the bow of the boat to the pier at the stern and vice versa. Then when the hurricane hits, the boat is nice and secure and doesn’t smash itself to smithereens against the pier.

    In engineering, the triangle is the core, especially the hypotenuse. In grammar (not just in English, but in any language), the core is the sentence, and especially the subject and complete verb. Just as the hypotenuse is key to engineering, so the subject and verb are key to grammar. Learn to find the subject and verb, and you will be able to master all of the rest of grammar.

  3. [Pirates of Penzance]

    I am the very model of a modern Major-General
    I’ve information vegetable, animal, and mineral
    I know the kings of England, and I quote the fights historical
    From Marathon to Waterloo, in order categorical

    I’m very well acquainted, too, with matters mathematical
    I understand equations, both the simple and quadratical
    About binomial theorem I’m teeming with a lot o’ news
    With many cheerful facts about the square of the hypotenuse

    With many cheerful facts about the square of the hypotenuse
    With many cheerful facts about the square of the hypotenuse
    With many cheerful facts about the square of the hypotepotenuse

  4. You need a Bill Nye Science Guy type to do a program on triangles! He’s crazy, creative, far out and the kids love him. Never a dull moment!

  5. Actually, the parts that failed were long, open braces of steel triangles. They were coated with fireproofing material, but the initial impact of the airplaces stripped off that material, leaving the metal vulnerable to the heat of the subsequent fires. The design was able to withstand great physical trauma OR fire, but not both.

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