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Re: [sl] Re: water pentegons

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  • john graham
    ... Hi Dan, this is a really interesting point. I am fascinated by 3-D geometry and as you may know the angle 109.5 degrees is of particular significance.
    Message 1 of 5 , Dec 30, 2004
      --- danw888 <danw@...> wrote:
      >
      >
      >
      > Hi, Ambrose -
      >
      > Glad you liked the water info. Fine by me to speed
      > it along in the
      > form you have given us.
      >
      > A bunch is from Kurzweil's copyrighted book, but
      > since the ref is
      > given and under the fair use doctrine its ok to
      > quote small pieces, I
      > think we are ok in saying that we are not infringing
      > his copyright.
      >
      > So hit the send button with my blessing.
      >
      > Dan
      >
      >
      >
      >
      > --- In sacredlandscapelist@yahoogroups.com, Ambrose
      > Hawk <ahawk@c...>
      > wrote:
      > > Dan, that was a very interesting post ...
      > > mind if I spread it around my lists too?
      > > I've modified it slightly as follows:
      > >
      > > Ray Kurzweil, one of the worlds great inventors,
      > has written a book
      > on
      > > how to become immortal, called Fantastic Voyage.
      > There's some
      > info in
      > > it on water.
      > >
      > > p44. The two hydrogen atoms make a 104.5 degree
      > angle with the
      > oxygen
      > > atom, which increases to 109.5 degrees when water
      > freezes.
      > >
      > > The side of the molecule with the hydrogen atoms
      > is slightly
      > positive in
      > > electric charge. The oxygen side is slightly
      > negative.
      > >
      > > Water molecules, because of positive/negative
      > bonding, combine into
      > > small groups, assuming typically pentagonal or
      > hexagonal shapes.
      > > These multimolecule structures can change back and
      > forth between
      > > hexagonal and pentagonal configurations 100
      > billion times a second.
      > > At room temperature, only about 3 percent of the
      > clusters are
      > hexagonal,
      > > but this increases to 100 percent as the water
      > gets colder. That
      > is why
      > > most snowflakes are hexagonal.
      > >
      > > Since 96 percent of our blood is water; it sounds
      > like most of us,
      > at
      > > body temperature, are made up of pentagons.
      > >
      > >
      > >
      > > --
      > > IN HOC MODO MILLIS FRANGITVR .
      >
      >
      >
      >
      >
      > Topics suitable for discussion in this e-list can be
      > found at:
      > http://www.luckymojo.com/sacredland.html
      >
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      >
      >
      Hi Dan,
      this is a really interesting point. I am fascinated
      by 3-D geometry and as you may know the angle 109.5
      degrees is of particular significance. Basically it
      is the angle at which the four lines from the vertices
      of a regular tetrahedron meet at the centroid. The
      angle between any two pairs of these lines is the
      same i.e. 109.5 degrees. It is unique in 3-D. the
      equivalent in 2-D would be three lines meeting at 120
      degrees.

      This angle has some interesting implications in the
      field of structural mechanics. If, for instance, a
      geometric framework of uniform members were
      constructed in 3-D space such that all the members
      were conjoined in these four way junction nodes, then,
      taking into account that the framework was
      structurally contained at its edges, if a force were
      applied at any one of the nodes it would be
      distributed with complete uniformity over all the
      members in the system so that the forces acting along
      each of the members would be the same.

      This has implications also for for molecular
      structures. The diamond molecule, carbon 5, follows
      this structural pattern, which explains why diamond is
      such a strong material.

      It is interesting to learn that when water is frozen
      two hydrogen atoms maintain this angle with the oxygen
      atom. If there were four hydrogen atoms, instead of
      two then the nature of ice would be quite different,
      it would probably be much stronger and a much more
      stable material.
      The billions of molecular oscillations per second may
      be explained by the fact that the molecule is tending
      to achieve this four way state but cannot as the ratio
      of nodes to members (or lines) is uneven due to any
      physical system having to be bounded in space. If
      however the four way system were extended into
      infinite space then the ratio of nodes to members
      would be 2 to 1` and would fit the water molecule
      perfectly.
      I hope this is making sense incidentally, and please
      feel free to correct me if I am wrong.

      I do know however that 109.5 degrees, called the
      Maraldi angle by the way, occurs in nature noteably in
      its use by bees in the building of honeycombs.
      The hexagonal appearance of the honeycomb arises from
      the fact that seen from four particular angles in
      space the four way system does indeed look like a
      network of perfect hexagons.

      Incidentally the pentagonal angle of 108 degrees, 1.5
      degrees short of the Maraldi angle, is geometrically
      unrelated to the four way system. It seems as though
      it should be but it isn't. In fact I only stumbled on
      the Maraldi angle myself having initially supposed,
      wrongly of course, that four pentagonal dodecahedra
      could fit snugly together in space.
      I look on that assumpton now as my geometric fabled
      route to the Spice Islands. What I discovered instead
      was the North America of the Maraldi angle - a much
      greater find!

      John.





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    • Ambrose Hawk
      Another feature of interest in this dynamic is something I heard about back in the 60 s. I forget when the experiment was done, and how they did it, but
      Message 2 of 5 , Jan 4, 2005
        Another feature of interest in this dynamic is something I heard about
        back in the '60's.
        I forget when the experiment was done, and how they did it, but somebody
        found that spring water formed what they called "cells" of clusters of
        molecules, and that this structure clearly changed when the water was
        blessed ... when this is joined to the recent Japanese experiments, I
        think the whole set up might indicate some interesting dynamics ...
        Ambrose

        --
        IN HOC MODO MILLIS FRANGITVR .
      • danw888
        ... Hi, John: Thanks for a very interesting intro to the Miraldi angle! I found a web site that explains more clearly how the water molecule is related to the
        Message 3 of 5 , Jan 13, 2005
          --- In sacredlandscapelist@yahoogroups.com, john graham <ikojag@y...>
          wrote:
          >
          > Hi Dan,
          > this is a really interesting point. I am fascinated
          > by 3-D geometry and as you may know the angle 109.5
          > degrees is of particular significance. Basically it
          > is the angle at which the four lines from the vertices
          > of a regular tetrahedron meet at the centroid. The
          > angle between any two pairs of these lines is the
          > same i.e. 109.5 degrees. It is unique in 3-D. the
          > equivalent in 2-D would be three lines meeting at 120
          > degrees.
          >
          > This angle has some interesting implications in the
          > field of structural mechanics. If, for instance, a
          > geometric framework of uniform members were
          > constructed in 3-D space such that all the members
          > were conjoined in these four way junction nodes, then,
          > taking into account that the framework was
          > structurally contained at its edges, if a force were
          > applied at any one of the nodes it would be
          > distributed with complete uniformity over all the
          > members in the system so that the forces acting along
          > each of the members would be the same.
          >
          > This has implications also for for molecular
          > structures. The diamond molecule, carbon 5, follows
          > this structural pattern, which explains why diamond is
          > such a strong material.
          >
          > It is interesting to learn that when water is frozen
          > two hydrogen atoms maintain this angle with the oxygen
          > atom. If there were four hydrogen atoms, instead of
          > two then the nature of ice would be quite different,
          > it would probably be much stronger and a much more
          > stable material.
          > The billions of molecular oscillations per second may
          > be explained by the fact that the molecule is tending
          > to achieve this four way state but cannot as the ratio
          > of nodes to members (or lines) is uneven due to any
          > physical system having to be bounded in space. If
          > however the four way system were extended into
          > infinite space then the ratio of nodes to members
          > would be 2 to 1` and would fit the water molecule
          > perfectly.
          > I hope this is making sense incidentally, and please
          > feel free to correct me if I am wrong.
          >
          > I do know however that 109.5 degrees, called the
          > Maraldi angle by the way, occurs in nature noteably in
          > its use by bees in the building of honeycombs.
          > The hexagonal appearance of the honeycomb arises from
          > the fact that seen from four particular angles in
          > space the four way system does indeed look like a
          > network of perfect hexagons.
          >
          > Incidentally the pentagonal angle of 108 degrees, 1.5
          > degrees short of the Maraldi angle, is geometrically
          > unrelated to the four way system. It seems as though
          > it should be but it isn't. In fact I only stumbled on
          > the Maraldi angle myself having initially supposed,
          > wrongly of course, that four pentagonal dodecahedra
          > could fit snugly together in space.
          > I look on that assumpton now as my geometric fabled
          > route to the Spice Islands. What I discovered instead
          > was the North America of the Maraldi angle - a much
          > greater find!
          >
          > John.
          >

          Hi, John:

          Thanks for a very interesting intro to the Miraldi angle!

          I found a web site that explains more clearly how the water molecule
          is related to the tetrahedron. Take a look.

          http://witcombe.sbc.edu/water/chemistrystructure.html

          Dan
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