pdp1@EARTHLINK.NET on tue 7 oct 03
and their being imaginable as planes I suppose, as well...
Thank you Ivor...
A much welcome and kind foray...
Anyway...
I am curious...I cannot see a Teapot as you say, as a plane
with two holes. But I can see it as a distortion, or
variation, of a 'tube'...or Cylinder...or, as a curved plane
(may a
Cylinder be called a plane?) which has assumed a
Cylindrical manner, and is open on the ends...
If it were a 'plane with two holes', how may the plane
accomidate stretching, to have the two holes occur IN a
plane? (Or I take the term 'plane' to mean ideally, a 'flat'
plane, hence my difficulty) - or strectching from 'where'
to so have them?
If it ( a Tea Pot) were to be stretched into a flat plane, I
imagine it
to do so 'from' one of the holes, which would then become a
periphery's edge or end...and, to then, of necessity, have
only one hole in it...
Does that make sense?
...as to the Mug...I cannot see it as a plane as would have
any holes at all. (Oh! I was thinking of maybe more a
'Tumbler', or there being no Handle - a 'Cup' or Bowl in
effect...) So I see it as a plane as has assumed a
'cupped' aspect for itself, and, has no 'holes'
anywhere...which if stretched out, flattenned out, would be
simply a
plane...Or I see it as a Sphere as has a 'dimple' in it...
If a Cup with a Handle...then...I am lost! Is a Cup in this
sense ( or Mug) as a Sphere with a deep dimple ( and a
Handle) ? Or as a
plane as assumes a 'cupped' form?
The Handle presents a problem for me in either
event...since, I cannot resolve imagining the form then to
be made 'flat' to say from there just how the Handle would
work out...hmmmm! I am stuck now...!
But the Inner-tube with the valve...similarly, being
ostensibly
enclosed, would, if stretched around, in my imagination
anyway - be merely something of a flat plane as had been
'cupped' previously into it's 'Innertube' version of
itself...
If the Inner-tube had a puncture, I can then see it as able
to be stretched into either a 'tube' ( or Cylinder) open at
both ends, or, as a flat plane with one hole in the middle,
for having been stretched from one of the ( previous)
holes...
Does that make sense to you?
As for the Vest...I understand the same may be noticed of
Brassiers, and I have seen it done. But one may argue, that
in successive stages, or retractions of limb at any rate,
the outer garment or Jacket or what, cumulatively, were
taken off afterall...
However, one is less likely to see either of them put on in
that manner...even in haste!
Now...a 'disk', with a hole in it...I can see massaged into
being a Tea Pot.
Once the 'edges' or old periphery is brought 'in', to
converge, we have
the second 'hole'...
I do not understand the 'rings' being drawn, or I do not
understand the outcome as stated...if annular 'rings' were
drawn inside the inner-tube? - and, the Inner-tube were then
turned inside-out through the Valve stem, I would expect the
rings to be still 'rings' as are on (now) the outside, as
whether
inside-out or not, the Inner-tube would still have it's
'Do-nut' shape...
Conversely, if one painted 'rings' on the outside of the
inner-tube...and turned it inside-out...I would expect the
rings to be merely on the inside then, in their interior of
annular arrangement...
How may this be resolved? Or described otherwise?
Fun to wonder about...!
Phil
Las Vegas
----- Original Message -----
From: "iandol"
Dear Phil,
An esoteric topic but it is amazing what can be done with
clay. The Topological equivalent of a tea pot is a plane
with two holes perforated in it, while a Mug is a plane with
one hole. The Inner Tube with a valve hole is curious. If
you were to draw rings around the minor diameter, then turn
it inside out through its valve hole, the rings would become
stripes around the larger diameter on the inside.
Now a Fellow who is wearing a Vest,( Weskit for Janet and
other "Poms"), can be divested of same garment even if he is
wearing a Jacket, without removing said jacket. Which seems
to show, topologically, that he was not wearing the vest at
all.
What useless information we accumulate!!!but as you say,
FUN.
Best regards,
Ivor.
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Earl Krueger on tue 7 oct 03
and their being imaginable as planes I suppose, as well...
On Tuesday, October 7, 2003, at 01:59 AM, pdp1@EARTHLINK.NET wrote:
> I am curious...I cannot see a Teapot as you say, as a plane
> with two holes. But I can see it as a distortion, or
> variation, of a 'tube'...or Cylinder...
Am excellent book for the layman who has an interest in
the beauty of mathematics but doesn't want to get into
the heavy stuff.
The Mathematical Tourist
Ivars Peterson
Barnes and Noble, Inc
W.H. Freeman and Company
ISBN 0-7607-2361-3
According to Peterson a mug, with handle, is the topological
equivalent of a doughnut (torus). The book shows a sequence
of how to convert one into the other.
The book also has a pretty good description of data encryption
, as used by the Internet, for those who are curious how it works.
I was somewhat disappointed because the book doesn't
have a single equation in it !!
Earl...
Bothell, WA
pdp1@EARTHLINK.NET on tue 7 oct 03
and their being imaginable as planes I suppose, as well...
Ahhhh...thanks Earl !
Ivor had also recommended a Book, but I could not find it on
the 'Amazon' in either new or used.
Too...I am confused I think bout the handle of the Tea Pot
being either hollow or being a curved 'line' or something in
the model as allows outcomes different from what I was
thinking..in fact, I omeiited the handle in my thought,
being really over worked here lately and tired...
I can imagine the human-form to assume an adjustment unto a
'torus' or Do-nut...or, being an elaboration of one.
Be for now!
Phil
Las Vegas
Where I am nearly done with a difficult commission of
several (five) tedious items to make, and for which I was
just not in the mood at all and had already procrastinated
all I could...so, 14 hour days for two weeks and now allmost
'there'...
Sheeesh! I am ready for a pic-nic or something...SOME
seguay, anyway...
'Moods'...
----- Original Message -----
From: "Earl Krueger"
To:
Sent: Tuesday, October 07, 2003 8:48 AM
Subject: Re: : Re: Klein bottle - or, considerations of form
and shape, and their being imaginable as planes I suppose,
as well...
> On Tuesday, October 7, 2003, at 01:59 AM,
pdp1@EARTHLINK.NET wrote:
>
> > I am curious...I cannot see a Teapot as you say, as a
plane
> > with two holes. But I can see it as a distortion, or
> > variation, of a 'tube'...or Cylinder...
>
> Am excellent book for the layman who has an interest in
> the beauty of mathematics but doesn't want to get into
> the heavy stuff.
>
> The Mathematical Tourist
> Ivars Peterson
> Barnes and Noble, Inc
> W.H. Freeman and Company
> ISBN 0-7607-2361-3
>
> According to Peterson a mug, with handle, is the
topological
> equivalent of a doughnut (torus). The book shows a
sequence
> of how to convert one into the other.
>
> The book also has a pretty good description of data
encryption
> , as used by the Internet, for those who are curious how
it works.
>
> I was somewhat disappointed because the book doesn't
> have a single equation in it !!
>
> Earl...
> Bothell, WA
>
>
____________________________________________________________
__________________
> Send postings to clayart@lsv.ceramics.org
>
> You may look at the archives for the list or change your
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> settings from http://www.ceramics.org/clayart/
>
> Moderator of the list is Mel Jacobson who may be reached
at melpots@pclink.com.
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