Loading ...
Sorry, an error occurred while loading the content.

Re: The light comes on !

Expand Messages
  • Roger Kaufman
    Hi John, ... Yes. Not practical. Dropping. Roger
    Message 1 of 8 , Feb 1, 2011
    View Source
    • 0 Attachment
      Hi John,

      > I must say, only if all elements shared one base area kept the same height,
      > during the flexing....

      Yes. Not practical. Dropping.

      Roger
    • richardfischbeck
      I think: Vertexes - 2 = 2*triangles Vertexes - 2 = 3*edges or just, n-2=2*area and volume= [rt ((2/5)(n-2)^3]/10 for icosahedral shells, or at least, that s
      Message 2 of 8 , Feb 2, 2011
      View Source
      • 0 Attachment
        I think:

        Vertexes - 2 = 2*triangles

        Vertexes - 2 = 3*edges

        or just,

        n-2=2*area

        and

        volume= [rt ((2/5)(n-2)^3]/10

        for icosahedral shells, or at least, that's how many tetrahedrons it has.

        This is true for all Euler #2 shell structures.

        So, if triangle is counted as area and tetrahedrons are counted as volume, we have a new and maybe powerful generalized counting principle at our finger tips.

        No school. Big snowstorm. Hanging by the wood stove. Beautiful day.
      • richardfischbeck
        Sorry, I got that backwards. 2(n-2)=area, 3(n-2)=edges ... This parts is okay.
        Message 3 of 8 , Feb 2, 2011
        View Source
        • 0 Attachment
          Sorry, I got that backwards. 2(n-2)=area, 3(n-2)=edges

          --- In antiprism@yahoogroups.com, "richardfischbeck" <dick.fischbeck@...> wrote:
          >
          > I think:
          >
          > Vertexes - 2 = 2*triangles
          >
          > Vertexes - 2 = 3*edges
          >
          > or just,
          >
          > n-2=2*area


          This parts is okay.

          >
          > and
          >
          > volume= [rt ((2/5)(n-2)^3]/10
          >
          > for icosahedral shells, or at least, that's how many tetrahedrons it has.
          >
          > This is true for all Euler #2 shell structures.
          >
          > So, if triangle is counted as area and tetrahedrons are counted as volume, we have a new and maybe powerful generalized counting principle at our finger tips.
          >
        • Adrian Rossiter
          Hi Dick and John ... Cavalieri s Principle applies to this http://en.wikipedia.org/wiki/Cavalieri%27s_principle A horizontal slice through the two tetrahedra
          Message 4 of 8 , Feb 3, 2011
          View Source
          • 0 Attachment
            Hi Dick and John

            On Tue, 1 Feb 2011, richardfischbeck wrote:
            > Fwd from another group:
            >
            > "I find it interesting that all tetrahedra with the same base area and height
            > have the same volume no matter what their shape is." - JB

            Cavalieri's Principle applies to this

            http://en.wikipedia.org/wiki/Cavalieri%27s_principle

            A horizontal slice through the two tetrahedra being compared
            always interesects them in two triangles of the same area,
            as can be seen by considering that these sections are the base
            triangles scaled down by the same factor.

            Adrian.
            --
            Adrian Rossiter
            adrian@...
            http://antiprism.com/adrian
          • Alan M
            ... height ... * Pyramid (geometry) Volume * Cone (geometry) Volume
            Message 5 of 8 , Aug 16, 2012
            View Source
            • 0 Attachment

              --- In antiprism@yahoogroups.com, "richardfischbeck" <dick.fischbeck@...> wrote:

              > Ta-Da.

              > Fwd from another group:

              > "I find it interesting that all tetrahedra with the same base area and height
              > have the same volume no matter what their shape is." - JB

            Your message has been successfully submitted and would be delivered to recipients shortly.