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Math Help - What is the strongest shape?

  1. #1
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    What is the strongest shape?

    A friend and I are having a debate; which shape is the strongest?

    Our defintion of strongest is rather vague, but is essentially the mount of external force the shape can resist - be it a single force acting in a single direction or multiple forces in multiple directions.

    We are arguing seperately for both the 2D scenario, and the 3D scenario.

    I am unable to find much about this online - so I am hoping someone here can help settle the argument.

    Many thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TigerTom View Post
    A friend and I are having a debate; which shape is the strongest?

    Our defintion of strongest is rather vague, but is essentially the mount of external force the shape can resist - be it a single force acting in a single direction or multiple forces in multiple directions.

    We are arguing seperately for both the 2D scenario, and the 3D scenario.

    I am unable to find much about this online - so I am hoping someone here can help settle the argument.

    Many thanks!
    It will depend on where the forces are acting on the shape, of course.

    -Dan
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    Dan - look at it like this; you have to choose the shape, not knowing how many forces will be applied to it and from what direction. What's your best bet?
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    A pyramid is best balanced, I think.

    An "I" shaped steel beam is used in building.

    A sphere can never fall over.
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    Quote Originally Posted by TigerTom View Post
    A friend and I are having a debate; which shape is the strongest?

    Our defintion of strongest is rather vague, but is essentially the mount of external force the shape can resist - be it a single force acting in a single direction or multiple forces in multiple directions.

    We are arguing seperately for both the 2D scenario, and the 3D scenario.

    I am unable to find much about this online - so I am hoping someone here can help settle the argument.

    Many thanks!
    Buckminster Fuller's geodesic domes were made of triangles. So 2D, I'd say triangles. For 3D, TPH's pyramid sounds good, but then what about those domes? Hmmm, isn't a pyramid the geodesic dome with the minimal number of faces?
    Attached Thumbnails Attached Thumbnails What is the strongest shape?-geodomesm.jpg  
    Last edited by JakeD; July 31st 2007 at 08:14 PM.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JakeD View Post
    Hmmm, isn't a pyramid the geodesic dome with the minimal number of faces?
    (Chuckles) Yeah, just like a triangle is a circle with the minimal number of sides...

    -Dan
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    Quote Originally Posted by TigerTom View Post
    A friend and I are having a debate; which shape is the strongest?

    Our defintion of strongest is rather vague, but is essentially the mount of external force the shape can resist - be it a single force acting in a single direction or multiple forces in multiple directions.

    We are arguing seperately for both the 2D scenario, and the 3D scenario.

    I am unable to find much about this online - so I am hoping someone here can help settle the argument.

    Many thanks!
    I think you and your friend are making a category error, shapes as such do
    not have strength, a structure fabricated out of some particular material
    may well have strength, but even then you may need to define exactly what
    you mean and under what loads you want to measure/compare this.

    RonL
    Last edited by CaptainBlack; August 1st 2007 at 11:47 AM.
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    Quote Originally Posted by topsquark View Post
    (Chuckles) Yeah, just like a triangle is a circle with the minimal number of sides...

    -Dan
    It is clearly the best shape for a wheel as there are a minimum number of
    bumps per revolution.

    RonL
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    Quote Originally Posted by topsquark View Post
    (Chuckles) Yeah, just like a triangle is a circle with the minimal number of sides...

    -Dan
    (Smiles) OK, that is analogous to what I said. But, not knowing any better, I just read the definition from here and conclude the minimal geodesic dome would be 1 tetrahedron and 0 octahedrons.

    A geodesic dome is a spherical building in which the supporting structure is a lattice of interconnecting tetrahedrons (a pyramid with three sides and a base) and octahedrons (an eight sided figure—two pyramids with four sides and a base, placed base to base).
    Last edited by JakeD; August 1st 2007 at 06:48 AM.
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  10. #10
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    I have always learned that a domes, spheres, and ellipsoids are the srongest.

    It certainly depends on the application. A triangle is a strong design in some areas. Bridges, for example.

    As for domes, look at the Hajia Sofia. Fantastic piece of architecture.

    One may look in nature for some strongest designs. Sometimes those are the best designs for strength.
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  11. #11
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    Quote Originally Posted by galactus View Post
    As for domes, look at the Hajia Sofia. Fantastic piece of architecture.
    The dome of Hagia Sophia is strong because stone and concrete (though there
    is no significant concrete in the structure of Hagia Sophia apparently but there
    is in the Pantheon) are strong in compression (though brittle and weak in tension)
    and the structure is designed to keep the stone work and concrete in compression.
    If built of rubber the dome would probably not be able to bear its own weight. The
    strength is due to using a structure that exploits the strength of the materials
    while avoiding their weaknesses.

    RonL
    Last edited by CaptainBlack; August 1st 2007 at 01:31 PM.
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  12. #12
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    Quote Originally Posted by CaptainBlack View Post
    I think you and your friend are making a category error, shapes as such do
    not have strength, a structure fabricated out of some particular material
    may well have strength, but even then you may need to define exactly what
    you mean and under what loads you want to measure/compare this.
    Yes, we had discussed that to the extent that joints on a triangle could be weak, but the argument dismisses the idea that the shape could be weakened by poor construction. Whilst it is impossible to do, we are trying to dismiss the impact that various contruction methods or different materials bring to the table.

    I argued a triangle would be strongest, and he argued for a circle.

    My logic was a triangle would dissipate a single force acting on it over the largest possible area for a shape constructed with a set perimeter. I though a circle, resting on a surface, would have an infinitely small area though which the force would act.

    Yes, I realise it is a silly argument and there are a million factors to consider...
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