- --- danw888 <danw@...> wrote:
>

Hi Dan,

>

>

> 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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>

>

>

>

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.

___________________________________________________________

ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com - 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 . - --- In sacredlandscapelist@yahoogroups.com, john graham <ikojag@y...>

wrote:>

Hi, John:

> 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.

>

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