STRUTTURE GEODETICHE

[Biagio Di Carlo]

Dear Taff, 

I am creating the new revised edition of  my books about synergetic structures. I added several new pages to the first edition.

In this book  'STRUTTURE GEODETICHE' (only in italian) I have added your name too because  sometime 

I make  use of your useful drawings on Sketch Up.    

http://ilmiolibro.kataweb.it/schedalibro.asp?id=484089      (new paper edition)     

http://stores.lulu.com/biagiodicarlo  (first digital/paper edition)

STRUTTURE GEODETICHE e' la nuova edizione aggiornata (186 pagine) del precedente libro 'CUPOLE GEODETICHE' del 2004 (222pagine) con ISBN 978-88-904581-2-5. La parte sulle GEODETICHE ELLISSOIDICHE sara' pubblicata in seguito. Il libro raccoglie oltre 35 anni di esperienze sulle strutture geodetiche. 

La versione digitale del libro 'CUPOLE  GEODETICHE' e' in vendita presso lulu.com

Si ringraziano per la loro disponibilita': David Anderson, Raphel Moras de Vasconcellos, Raphael Durao Ato, Taff Goch, Bruce Lebel, Giovanna De Cesaris, Gianni Crovatto, Paul Winning, Enrico Tedeschi, Steve Miller.

Best Wishes,

Biagio

Biagio Di Carlo
Via Berlino 2
Villa Raspa, Spoltore
65010  PESCARA

http://www.biagiodicarlo.com
biagio...@gmail.com

Tel. 085 411588  -  3405310750

  skipename: biagiodicarlo

[TaffGoch]

Biagio,

 

I know that pseudonyms are common with authors, so I suppose that "TaffGoch" will be just fine. I suspect that more people know me as TaffGoch, rather than David Price (online, anyway.)

 

From Google searches, it seems that "taffgoch" is predominantly unique to me, so that helps, too.

 

Taff

____________________

 

(BTW, the website, ilmiolibro.kataweb.it, will not let me past the welcome page.)

[Biagio Di Carlo]

Try with this one

http://ilmiolibro.kataweb.it/categorie.asp?searchInput=biagio+di+carlo&act=ricerca&genere=tutte&scelgoricerca=nel_sito

or

digit my name  on  ilmiolibro.kataweb.it

bdc

On 20ago 2010, at 03:14, TaffGoch wrote:

Biagio,

 

I know that pseudonyms are common with authors, so I suppose that "TaffGoch" will be just fine. I suspect that more people know me as TaffGoch, rather than David Price (online, anyway.)

 

From Google searches, it seems that "taffgoch" is predominantly unique to me, so that helps, too.

 

Taff

____________________

 

(BTW, the website, , will not let me past the welcome page.)

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[TaffGoch]

 

Whichever of your links I use, I'm kicked to http://ilmiolibro.kataweb.it/default.asp every time.

 

Even when I click on a book title (any title) on the default page, all I get is a return to http://ilmiolibro.kataweb.it/default.asp

 

Perhaps it is an international problem (works there, but not in the U.S.)

 

Taff

[Richard Fischbeck]

The first 8 pages are here.

http://ilmiolibro.kataweb.it/storage2/vetrina/webprv/194649_webprv.pdf

[Biagio Di Carlo]

The problem exists here too. 

The only way to see my books is to digit my name or the titles

here http://ilmiolibro.kataweb.it/default.asp.

bdc

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[Richard Fischbeck]

Italian to English translation

1 
DCBooks Pescara 2010 
Carlo Biagi 
Geodesic structure 
PAPERS OF GEOMETRY Synergetics 
2 
Biagio Di Carlo, geodesic structure 
DC Books, 2010 Pescara 
Copyright DC Books 2010 Pescara 
http://www.biagiodicarlo.com 
No part of this publication 
can 'be stored, photocopied 
or reproduced without permission 
author 
PAPERS OF GEOMETRY Synergetics 
3 
Geodesic structure 
and 'the new, updated edition (186 pages) 
the previous book 'geodesic dome' of 2004 
(222 pages) ISBN 978-88-904581-2-5 with. Part 
the geodesic structure will Ellipsoid ' 
published later. 
Thanks to their availability ': David Anderson, Raphael 

Moras de Vasconcellos, Raphael Durao Ato, Taff Goch, 

Bruce Lebel, Joan De Cesaris, Gianni Crovatto Paul Winning, 
Enrico Tedeschi, Steve Miller. 
The digital version of the book 'DOMES GEODETICHE'e' sale 
at: http://stores.lulu.com/biagiodicarlo 
Copyright DC Books 2010 Pescara 
http://www.biagiodicarlo.com 
4 
CONTENTS 
Geodesic structures, introduction ............ 6 
Geodesic structures, definitions ............ 9 
Historical precedents .......... 10 
Fullerenes from space .................... 12 
Spherical octahedron ................... 13 
Theory of large circles ................. 14 
Polyhedra and geodesic key definitions: values face values 
ball and corners ...................... 18 
Decompositions main AC breakdown and breakdown 
Children Shall Lead ................. 21 
Generation of the rhombic dodecahedron and triacontahedron ... 26 
Dodecahedron pentakis ....................... 28 
Factors rope icosahedron ............. 30 
Geodesic dome ICOS alt 2v .......... 33 
ICOS alt 3v geodesic dome. 5 / 8 ball ......... 
David Kruschke Method ............... 37 
Good Karma Domes Award 2003 ..................... 41 
Factors rope octahedron ............ 44 
3v dome octahedron ......... 47 
4v dome octahedron ............. 49 
Octahedron 4v sectioned at 5 / 8 ............ 51 
Geodesic dome octahedron 6v ........ 52nd 
Model greenhouse octahedral ............ 54 
Collapsible dome based sull'ottaedro ........... 55 
OCTA 21 .................. 61 
Decomposition Children Shall Lead icosahedron ............... 63 
Children Shall Lead a half'............... 65 
Children Shall Lead 2v ................... 66 
4v geodesic dome Children Shall Lead ............ 67 
Breakdown octahedron Children Shall Lead ........ 68 
Tetrahedron 2v and 4v .......... 69 
Tetrahedron 8v ......... 70 
Tetrahedron trunk 1v and 2v ........... 71 
Cube 1v and 2v ............... 72 
Dodecahedron 1v and 2v ............... 73 
5 
Bamboo Dome ............................ 74 
Geodesic dome bamboo'.................... 80 
Dome with cardboard tubes ............... 82 
U Dome, World Shelter .................. 83 
Geokid ...................... 89 
Cardboard model ..... 91 
Geodesic dome based sull'ottaedro ........... 93 
Geodesic dome with 20 modules rhombic ......... 94 
Tekpo Group ................. 97 
Geodetic refuge on Mount Amaro .................... 99 
Cuca, cardboard plastic dome .............. 106 
ICOS alt 2v dome with cloth hanging ............... 110 
Dome C.Coppa BDC-112 .......... 
The dome of Gianni Crovatto ........ 113 
John Zerning, DIY a gate ............ 116 
Tents Geodetic ....... 118 
Geodesic greenhouse on the principle of the great circles ........... 120 
Pacific Dome Dome in Milan .................. 122 
ZAK geodesic structure in Spello ............. 123 
Comtek 79 ............ 124 
Dome of the Company to stay in the Aeolian Islands ..... 126 
Growing Spaces UK .............. 128 
Residential complex 'Domes America' ........ 133 
Centro Solaria ............... 134 
Solaris Ctta 'Green ................ 136 
The GEODE ............... 142 
Geodetic dual layer ................. 144 
Joints .................... 149 
Vestrut system .............. 151 
Mero System ............... 153 
NCAT come ............... 155 
Spherical and hemispherical structures ................ 159 
Bibliography ........... 180-183 
6 
Geodesic Structures 
Introduction 
Born initially as a notebook on the geometry 
Synergetics, often written and drawn by hand, sometimes 
inevitably repetitive, "geodesic structure is the 
result of over 35 years of translations, conferences, seminars, 
lectures, workshops, study tours, experiences 
and recent surfing on the teaching of Richard 
Buckminster Fuller, the Nobel Peace Prize, described by many 
Leonardo da Vinci of our age. " 
A study on geodesic is also a study of polyhedra. 
A study of polyhedra can expand toward understanding 
the dynamic quality of space. The transition from 
micro to the macro scale, is from the world of atomic structures 
(Eg fullerenes) in the world of structures built 
man, revealed in the Crystal Palace an illustrious predecessor. 
From Crystal Palace today to technological innovation 
in architecture can be seen in terms of transparency, 
lightness, interpenetration of space, lighting, optimization 
shape, dematerialization of architecture. 
Joseph Paxton in 1851 showed not a building, but a way of 
build a universally valid, because referring to the natural laws. 
"Architecture is not space but the space ( 
G.C. Argan). 
The exploration of the biological world reveals obvious similarities with 
various lightweight structures used in architecture and radiolarian 
geodesic tensegrali atoms and structures, the chemistry of carbon and 
the tetrahedron, the viruses and their polyhedral shape. 
Modern scientific research has confirmed long-standing intuitions 
once based on the simple vision and perception. ( 
In 1936 Linus Pauling showed that metals are coordinated 
tetrahedron). 
7 
In this sense be considered the fundamental principles of 
natural world to establish a mutual benefit between people, 
ecofatti and artifacts. 
The origin of the polyhedral shapes is very old. Almost 
Egyptians certainly knew the tetrahedron, the cube and 
the octahedron. Objects are known to form dodecahedral 
Celtic and Etruscan. 
The 5 Platonic solids symbolized the four elements (earth, fire, 
air, water) and the universe. 
Plato had already suggested that the area had its 
existence and its strict rules. Modern research 
science has validated the ancient theory of Plato. 
"Space is not a passive vacuum; That it has properties constrain the pattern 
That exist whithin it " 
(A. Loeb) 
More historical background can be identified: 
• in studies of five regular solids of Euclid 
¯ in seeking the Golden Section of Leonardo, and Kepler 
• in studies on the exoskeletons of Haeckel's radiolarian 
· In grid space and the giant kites of A. G. Bell 
· To structural chemistry J. Van't Hoff and L. Pauling 
· Architecture of Frei Otto. 
The dome shape has always been present in natural structures 
and in primitive shelters made of branches, leaves, clay, snow or 
stone is historical memory, and together promise of new 
potential space. 
The polyhedra and geodesic representing the voltage to the 
perfectly spherical shape. 
In the transition from micro to macro scale, the shape begins 
with point and ends with the ball (new section) passing 
through a multitude of forms in space. The methods used by 
Kandinsky in art, are scientific tests 
8 
theories on the aggregation of compact ball (close-packing) and 
in structural chemistry. 
Point, line, surface and volume are not stand-alone units 
but the result of an ongoing process whereby after 
you get the point: the line joining two points, the 
surface, joining three points and volume, joining 
four points in space. 
The curved surfaces are more resistant than flat. The shape 
ellipsoids egg is very light but also very 
resistant. 
The scope and dome enclosing the maximum area with minimum 
use of material, also retain heat well inside 
offer little surface to the external climatic difficulties. 
Despite its lightness, the dome can withstand loads 
very heavy. The geodetic spatio-standing 
open and flexible, without partitions or beams and 
easily transportable by air. The person who lives 
within a spherical space the feeling of being at 
center of things. The geometry of geodesics Recalls 
ancient magical appeal of the mandala. 
All natural forms, Fuller notes, tend to form 
curvilinear, nature does not use the greek and even more axles 
Cartesian xyz, but instead uses the value of the golden section 
this eg. nell'icosaedro. 
A major review of these topics has occurred during 
60-70 years: The pioneers of cultural renewal indicated 
a new paradigm based on principles of J. Lovelock on 
Gaia Mother Earth and related to the size of holistic-synergetics 
Fuller. In Italy most of these arguments have been described 
F. Pivano in his anthologies about the other America. 
The first geodesic dome was built in Jena in Germany 
1922 on behalf of the firm of Zeiss optics on the project 
designer Walter Bauerfeld, but Fuller was then the character 
most developed of all the contents of the geodesic 
observing the natural world, the radiolarians and perhaps even the great 
circles deftly woven by artisans in Thailand.

[Biagio Di Carlo]

Thank you very much  Richard !

bdc

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[Richard Fischbeck]

No problem, Biagio.  My pleasure. Your next book might include a RanDome!

Dick

http://randome.info/

Freedom, Maine

[TaffGoch]

Thanks, guys.

 

(The problem I was having was resolved, by opening Firefox, instead of IE.)

[Biagio Di Carlo]

Dear Richard  Fischbeck,

my next  'book on demand'  probably will be published in september and will be about ellipsoidical geodesic domes. It will be very interesting to post some work of yours about  ellipsoidical randomes suitable for childrens for example, or a simple paperboard model. 

Obviously the call for participation in this publication is extended to all the friends of 'Geodesic Help Group'.  For private correspondence write to biagio...@gmail.com.

Best wishes,

bdc

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[TaffGoch]

Biagio,

 

Don't forget super-ellipsoid domes. "Domebook 2" is the first place I recall seeing a graphic reference to such domes. (Image attached)

 

-Taff

[Blair Wolfram]

Taff;

 

Do you know what an elliptical dome is called when it has two different foci?

 

Blair

--

[Richard Fischbeck]

And the punch line is ...?

[Biagio Di Carlo]

OK Taff, Thank you.

Several years ago 

I made  a model of mine about  the 

SUPER ELLIPSE.

bdc

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[TaffGoch]

Uhm - Let's see...

 

An ellipsoid?

 

An elipsogeodesic dome?

 

-Taff

[TaffGoch]

 

Here's the math for the ellipsoid geodesic:

http://mathworld.wolfram.com/EllipsoidGeodesic.html

 

Same for an oblate sphere geodesic:

http://mathworld.wolfram.com/OblateSpheroidGeodesic.html

 

-Taff

[Richard Fischbeck]

We can also design an ellipsoid or oblate dome by using unit area sheet elements with varying curvatures. (yes, I am standing on my soapbox again)  -_-

[Biagio Di Carlo]

In 2003 I have built this model of the super ellipse

with  data from Shelter, 1973. 

Now I have only the photo.

bdc

SUPER ELLISSE (BDC)

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[Richard Fischbeck]

John Rich was way into ellipsoid and prolate domes on the old geodesic listserv. 

http://crash.ihug.co.nz/~jw.rich/people.htm

http://crash.ihug.co.nz/~jw.rich/about.htm

http://crash.ihug.co.nz/~jw.rich/index.htm

[Biagio Di Carlo]

Thank you.

I was in contact with JR.

BDC

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[Blair Wolfram]

I don't think 'ellipsoid' is a word. Well, not a word from this planet. It's ellipse or elliptical dome. A sphereoid is a shape that approaches a sphere but is elongated on at least one axis. Dividing a sphere into geodesic triangle facets doesn't make it a sphereoid, it's a triangulated sphere.

 

Blair

 

.

--

[Richard Fischbeck]

It is is word if not a good word.

ellipsoid |iˈlipsoid|nouna three-dimensional figure symmetrical around each of three perpendicular axes, whose plane sections normal to one axis arecircles and all the other plane sections are ellipses.

[Richard Fischbeck]

But elipsoidical? Not so sure.

On Tue, Aug 3, 2010 at 6:07 AM, Biagio Di Carlo 

[Gerald de Jong]

Ellipsoidal, that would be. I love ellipsoids because of their focus
properties. Everything emanating from one focus in any direction ends
up at the other focus and vice versa.

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--
Gerald de Jong
Beautiful Code BV
http://www.twitter.com/fluxe
http://www.beautifulcode.eu
skype: beautifulcode
ph: +31629339805

[Blair Wolfram]

Dick,

 

Why isn't this an ellipse?

I realize it is a word, i.e. "I discovered an ellipsoid near the brown spot and had it lanced."

 

Blair

 

 

--

[Blair Wolfram]

Again I ask for your help. Why do you call this an ellipsoid instead of an ellipse?

 

Blair

[Richard Fischbeck]

Volume compared to no volume?

[Blair Wolfram]

That doesn't apply to sphere v. sphereoid.

A sphereoid is  an irregular sphere. Ellipsoid should define an irregular elliptical sphere. Gerald's description of emminating foci describes an elliptical sphere with nothing irregular in the model.

 

Blair

[Richard Fischbeck]

Hi Blair

Okay. I follow. I admit I am bringing up the irregular structure. 

An oval dome profile and a elliptical dome profile are not the same. One question I have is, does an elliptical dome have great circles, and does that matter in the first place? If a dome is triangulated, isn't that enough to make it strong as long as the edges are geodesic ? Of course, nothing beats a sphere for strength.

I am, as usual, talking about a more general shape, one not necessarily defined by an equation. Structuring-as-we-go. Estimating. Distribution varying degrees of curvature around the dome.

Here's a link to another common shape, the football, which technically is definitely not elliptical in cross section.

"The Rugby Ball shape was dictated by the pig's bladder that was inserted into a hand stitched leather casing which was used as the ball."

http://wiki.answers.com/Q/Where_did_they_get_the_shape_of_the_football

Dick

[Biagio Di Carlo]

I have found this definition     http://en.wikipedia.org/wiki/Ellipsoid  (An ellipsoid is a closed type of quadric surface that is a higher dimensional analogue of an ellipse)

Le 'strutture ellissoidiche' never apply the general principle of expansion along two axes, but rather  along one axis and are therefore inscribed in   a   'ellissoide di rotazione'. 

So we have a monoiaxial deformation.   An   italian term  close to  ellissoide  could be 'ellissoidica'   (that I translated in ellipsoidical).

Domebook 2 calls them ELLIPTICAL DOMES  but ellipse is on the plane and  ellipsoid is 3D.

bdc

[Gerald de Jong]

An ellipse is two-dimensional, while an ellipsoid is
three-dimensional. If you spin an ellipse on its long axis you trace
a 3d ellipsoid.

[Biagio Di Carlo]

I have found this definition     http://en.wikipedia.org/wiki/Ellipsoid  (An ellipsoid is a closed type of quadric surface that is a higher dimensional analogue of an ellipse)

Le 'strutture ellissoidiche' never apply the general principle of expansion along two axes, but rather  along one axis and are therefore inscribed in   a   'ellissoide di rotazione'. 

So we have a monoiaxial deformation.   An   italian term  close to  ellissoide  could be 'ellissoidica'   (that I translated in ellipsoidical).

Domebook 2 calls them ELLIPTICAL DOMES  but ellipse is on the plane and  ellipsoid is 3D.

A book with  the term GEODETICA ELLISSOIDICA

http://www.springerlink.com/content/q1114n2t6186g000/

BDC

[Blair Wolfram]

Nowthen...

 

A sphere is a 3D symmetrical shape. According to Mathematica, a spheroid is an irregular sphere:

 

"A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted and , and the spheroid is oriented so that its axis of rotational symmetric is along the -axis, giving it the parametric representation"

 

A ellipse is two dimensional, and voids into a 3D ellipsoid:

"The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by where the semi-axes are of lengths , , and . If the lengths of two axes of an ellipsoid are the same, the figure is called a spheroid (depending on whether or , an oblate spheroid or prolate spheroid, respectively), and if all three are the same, it is a sphere. Tietze (1965, p. 28) calls the general ellipsoid a "triaxial ellipsoid."

Then an elliptical sphere = ellipsoid. A sphere is not a spheroid, but a spheroid is an ellipsoid. An irregular ellipsoid has three semi axis of different length. Two dimensionally, it would be an ellipse with two different foci:

"In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other. "

Blair

[Gerry in Quebec]

Hi Blair et al,
I’m repeating some of what you said, but here’s how I envisage the
various shapes....

I’ve found the cardinal points and other geographical terms to be
quite useful in trying to understand ellipsoids. Oblate and prolate
spheroids are members of the ellipsoid family. Each of these two
shapes can be thought of as having a circular circumference at the
equator and an elliptical circumference around the north and south
poles. The oblate’s polar radius, diameter and circumference are
smaller than its equatorial radius, diameter and circumference. In the
case of the prolate, it’s the opposite: the polar dimensions are
greater than the equatorial dimensions. The earth is technically an
oblate spheroid, a ‘squashed’ sphere, but very close to spherical.

While oblate and prolate spheroids are ellipsoids, a sphere is not an
ellipsoid since a circle can be drawn around each pair of
perpendicular axes (all axes are equal in length). And a triaxial
ellipsoid, also known as a scalene ellipsoid, is not a spheroid
because you can’t draw a circle around any two of three perpendicular
axes (all of which have different lengths). In the case of the oblate
and prolate spheroids, two of the three axes are the same length and
so you can draw a circle around them.

Twenty years ago when I was vacationing in Maine I collected smooth
stones along the Atlantic coast. And three summers ago I did the same
on the southern shore of Bristol Channel, which lies between England
and Wales. The Maine stones are pretty big, some more than 2 kg. The
UK stones are quite small, generally less than 100 grams. Both sets of
stones contain the three kinds of ellipsoids: prolates, oblates and
scalenes (or pretty close). Oddly, the scalenes and oblates
predominate, with very few prolates. I guess it has to do with the
dynamics of water erosion. In any case, the stones are very smooth to
the touch, nice to hold in your hand.

Cheers,
Gerry in Quebec

On Aug 5, 12:30 pm, Blair Wolfram <thedome...@gmail.com> wrote:
> Nowthen...
>
> A sphere is a 3D symmetrical shape. According to Mathematica, a spheroid is
> an irregular sphere:
>
> "A spheroid is an ellipsoid

> <http://mathworld.wolfram.com/Ellipsoid.html>having two axes of equal

> length, making it a surface

> of revolution <http://mathworld.wolfram.com/SurfaceofRevolution.html>. By

> convention, the two distinct axis lengths are denoted [image: a] and [image:
> c], and the spheroid is oriented so that its axis of rotational symmetric is
> along the [image: z]-axis, giving it the parametric representation"
>
> A ellipse is two dimensional, and voids into a 3D ellipsoid:
>
> "The general ellipsoid, also called a triaxial ellipsoid, is a quadratic

> surface <http://mathworld.wolfram.com/QuadraticSurface.html> which is given
> in Cartesian coordinates<http://mathworld.wolfram.com/CartesianCoordinates.html>by

> where the semi-axes are of lengths [image:
> a], [image: b], and [image: c]. If the lengths of two axes of an ellipsoid
> are the same, the figure is called a

> spheroid<http://mathworld.wolfram.com/Spheroid.html>(depending on

> whether [image:
> c<a] or [image: c>a], an oblate

> spheroid<http://mathworld.wolfram.com/OblateSpheroid.html>or prolate
> spheroid <http://mathworld.wolfram.com/ProlateSpheroid.html>, respectively),

> and if all three are the same, it is a

> sphere<http://mathworld.wolfram.com/Sphere.html>.

> Tietze (1965, p. 28) calls the general ellipsoid a "triaxial ellipsoid."
>
> Then an elliptical sphere = ellipsoid. A sphere is not a spheroid, but a
> spheroid is an ellipsoid. An irregular ellipsoid has three semi axis of
> different length. Two dimensionally, it would be an ellipse with two
> different foci:
>
> "In two dimensions, the curve known as an "egg' is an

> oval<http://mathworld.wolfram.com/Oval.html>with one end more pointed
> than the other. "
>
> Blair

>
> On Wed, Aug 4, 2010 at 6:10 PM, Biagio Di Carlo <biagiodica...@gmail.com>wrote:
>
>
>
> >   I have found this definition    http://en.wikipedia.org/wiki/Ellipsoid

> >   (An *ellipsoid* is a closed type of quadric surface<http://en.wikipedia.org/wiki/Quadric> that
> > is a higher dimensional <http://en.wikipedia.org/wiki/Dimension> analogue
> > of an ellipse <http://en.wikipedia.org/wiki/Ellipse>)

> > Le 'strutture ellissoidiche' never apply the general principle of expansion
> > along two axes, but rather  along one axis and are therefore inscribed in
> > a   'ellissoide di rotazione'.
> > So we have a monoiaxial deformation.   An   italian term  close to
> >  ellissoide  could be 'ellissoidica'   (that I translated in ellipsoidical).
> > Domebook 2 calls them ELLIPTICAL DOMES  but ellipse is on the plane and
> >  ellipsoid is 3D.
>
> > A book with  the term GEODETICA ELLISSOIDICA
> >http://www.springerlink.com/content/q1114n2t6186g000/
>
> > BDC
>
> >  On 50ago 2010, at 00:10, Gerald de Jong wrote:
>
> >  An ellipse is two-dimensional, while an ellipsoid is
> > three-dimensional.  If you spin an ellipse on its long axis you trace
> > a 3d ellipsoid.
>

> > On Wed, Aug 4, 2010 at 2:39 PM, Blair Wolfram <thedome...@gmail.com>

> > wrote:
>
> > Again I ask for your help. Why do you call this an ellipsoid instead of an
>
> > ellipse?
>
> > Blair
>

> > On Wed, Aug 4, 2010 at 12:01 PM, Gerald de Jong <geralddej...@gmail.com>

>
> > wrote:
>
> >  Ellipsoidal, that would be.  I love ellipsoids because of their focus
>
> >  properties.  Everything emanating from one focus in any direction ends
>
> >  up at the other focus and vice versa.
>
> >  On Wed, Aug 4, 2010 at 12:46 PM, Richard Fischbeck
>

> >  <dick.fischb...@gmail.com> wrote:
>
> >  But elipsoidical? Not so sure.
>
> >  On Tue, Aug 3, 2010 at 6:07 AM, Biagio Di Carlo
>
> >   my next  'book on demand'  probably will be published in september and
>
> >   will be about ellipsoidical geodesic domes.
>
> >  --
>
> >  You received this message because you are subscribed to the "Geodesic
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> >  --
>
> >  Gerald de Jong
>
> >  Beautiful Code BV
>
> >  http://www.twitter.com/fluxe
>
> >  http://www.beautifulcode.eu
>
> >  skype: beautifulcode
>

> >  ph:              +31629339805        +31629339805

>
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>
> > --
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> > Beautiful Code BV
> >http://www.twitter.com/fluxe
> >http://www.beautifulcode.eu
> > skype: beautifulcode

> > ph:              +31629339805        +31629339805

>
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>
> >    Biagio Di Carlo
> > Via Berlino 2
> > Villa Raspa, Spoltore
> > 65010  PESCARA
>
> >http://www.biagiodicarlo.com

> > biagiodica...@gmail.com

> > Tel. 085 411588  -  3405310750
> >   skipename: biagiodicarlo
>
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> > --
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> > --

> > For more options, visithttp://groups.google.com/group/geodesichelp?hl=en- Hide quoted text -
>
> - Show quoted text -

[Biagio Di Carlo]

I translated ellissoidica  with ellipsoidical, but I made a mistake.  The exact translation is  ELLIPSOIDAL, as you can see in this book of  Carlo Bernasconi      http://www.springerlink.com/content/q1114n2t6186g000/

Riassunto  L'Autore presenta un procedimento per la ricerca dell'azimut di una geodetica ellissoidica passante per due punti molto lontani fra loro. Istituisce dapprima una corrispondenza fra la geodetica ed un arco di cerchio massimo, corrispondenza definita con l'imporre uguali coordinate agli estremi dei due archi e la latitudine sferica normale uguale a quella ellissoidica. Sviluppa poi la longitudine ellissoidicaw in funzione di quella sferical, e poichè l fra gli estremi dell'arco di cerchio deve essere uguale a w, ne deduce una equazione per ricavare l'azimut.

---

Summary  The Author outlines a procedure to research the azimuth of an ellipsoidal geodesic, which passes through two points far distant from another. A corrispondence is first instituted between the geodesic and a bow of maximum circle; this correspondence may be defined by imposing the same coordinates to the extreme parts of the two bows and the spherical normal latitude equal to the ellipsoidal one. The ellipsoidal longitudew is next developed as a function of the spherical onel and, as l between the extreme parts of the circle bow must equal w, an equation is hereby deduced to find out the azimuth.

[Gerry in Quebec]

I uploaded a pdf file showing three views of a 4v octahedral dome
which is half of a triaxial ellipsoid. There's also a webcam photo of
a triaxial beach stone.
Cheers,
Gerry Toomey

On Aug 5, 12:30 pm, Blair Wolfram <thedome...@gmail.com> wrote:

> Nowthen...
>
> A sphere is a 3D symmetrical shape. According to Mathematica, a spheroid is
> an irregular sphere:
>
> "A spheroid is an ellipsoid

> <http://mathworld.wolfram.com/Ellipsoid.html>having two axes of equal

> length, making it a surface

> of revolution <http://mathworld.wolfram.com/SurfaceofRevolution.html>. By

> convention, the two distinct axis lengths are denoted [image: a] and [image:
> c], and the spheroid is oriented so that its axis of rotational symmetric is
> along the [image: z]-axis, giving it the parametric representation"
>
> A ellipse is two dimensional, and voids into a 3D ellipsoid:
>
> "The general ellipsoid, also called a triaxial ellipsoid, is a quadratic

> surface <http://mathworld.wolfram.com/QuadraticSurface.html> which is given
> in Cartesian coordinates<http://mathworld.wolfram.com/CartesianCoordinates.html>by

> where the semi-axes are of lengths [image:
> a], [image: b], and [image: c]. If the lengths of two axes of an ellipsoid
> are the same, the figure is called a

> spheroid<http://mathworld.wolfram.com/Spheroid.html>(depending on

> whether [image:
> c<a] or [image: c>a], an oblate

> spheroid<http://mathworld.wolfram.com/OblateSpheroid.html>or prolate

> spheroid <http://mathworld.wolfram.com/ProlateSpheroid.html>, respectively),

> and if all three are the same, it is a

> sphere<http://mathworld.wolfram.com/Sphere.html>.

> Tietze (1965, p. 28) calls the general ellipsoid a "triaxial ellipsoid."
>
> Then an elliptical sphere = ellipsoid. A sphere is not a spheroid, but a
> spheroid is an ellipsoid. An irregular ellipsoid has three semi axis of
> different length. Two dimensionally, it would be an ellipse with two
> different foci:
>
> "In two dimensions, the curve known as an "egg' is an

> oval<http://mathworld.wolfram.com/Oval.html>with one end more pointed
> than the other. "
>
> Blair

>
> On Wed, Aug 4, 2010 at 6:10 PM, Biagio Di Carlo <biagiodica...@gmail.com>wrote:
>
>
>
> >   I have found this definition    http://en.wikipedia.org/wiki/Ellipsoid

> >   (An *ellipsoid* is a closed type of quadric surface<http://en.wikipedia.org/wiki/Quadric> that
> > is a higher dimensional <http://en.wikipedia.org/wiki/Dimension> analogue
> > of an ellipse <http://en.wikipedia.org/wiki/Ellipse>)

> > Le 'strutture ellissoidiche' never apply the general principle of expansion
> > along two axes, but rather  along one axis and are therefore inscribed in
> > a   'ellissoide di rotazione'.
> > So we have a monoiaxial deformation.   An   italian term  close to
> >  ellissoide  could be 'ellissoidica'   (that I translated in ellipsoidical).
> > Domebook 2 calls them ELLIPTICAL DOMES  but ellipse is on the plane and
> >  ellipsoid is 3D.
>
> > A book with  the term GEODETICA ELLISSOIDICA
> >http://www.springerlink.com/content/q1114n2t6186g000/
>
> > BDC
>
> >  On 50ago 2010, at 00:10, Gerald de Jong wrote:
>
> >  An ellipse is two-dimensional, while an ellipsoid is
> > three-dimensional.  If you spin an ellipse on its long axis you trace
> > a 3d ellipsoid.
>

> > On Wed, Aug 4, 2010 at 2:39 PM, Blair Wolfram <thedome...@gmail.com>

> > wrote:
>
> > Again I ask for your help. Why do you call this an ellipsoid instead of an
>
> > ellipse?
>
> > Blair
>

> > On Wed, Aug 4, 2010 at 12:01 PM, Gerald de Jong <geralddej...@gmail.com>

>
> > wrote:
>
> >  Ellipsoidal, that would be.  I love ellipsoids because of their focus
>
> >  properties.  Everything emanating from one focus in any direction ends
>
> >  up at the other focus and vice versa.
>
> >  On Wed, Aug 4, 2010 at 12:46 PM, Richard Fischbeck
>

> >  <dick.fischb...@gmail.com> wrote:
>
> >  But elipsoidical? Not so sure.
>
> >  On Tue, Aug 3, 2010 at 6:07 AM, Biagio Di Carlo
>
> >   my next  'book on demand'  probably will be published in september and
>
> >   will be about ellipsoidical geodesic domes.
>
> >  --
>
> >  You received this message because you are subscribed to the "Geodesic
>
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>
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>
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>
> >  For more options, visit
>
> >  http://groups.google.com/group/geodesichelp?hl=en
>
> >  --
>
> >  Gerald de Jong
>
> >  Beautiful Code BV
>
> >  http://www.twitter.com/fluxe
>
> >  http://www.beautifulcode.eu
>
> >  skype: beautifulcode
>

> >  ph:              +31629339805        +31629339805

>
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> > Beautiful Code BV
> >http://www.twitter.com/fluxe
> >http://www.beautifulcode.eu
> > skype: beautifulcode

> > ph:              +31629339805        +31629339805

>
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>
> >    Biagio Di Carlo
> > Via Berlino 2
> > Villa Raspa, Spoltore
> > 65010  PESCARA
>
> >http://www.biagiodicarlo.com

> > biagiodica...@gmail.com

> > Tel. 085 411588  -  3405310750
> >   skipename: biagiodicarlo
>
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[Gerry in Quebec]

Oh.... and the file name of the trixial images is triaxial-4v-octa-
ellipsoid.pdf.
Gerry

> > >  ph:                            +31629339805        +31629339805                      +31629339805        +31629339805

> > > ph:                            +31629339805        +31629339805                      +31629339805        +31629339805

> > > For more options, visithttp://groups.google.com/group/geodesichelp?hl=en-Hide quoted text -
>
> > - Show quoted text -- Hide quoted text -

[Biagio Di Carlo]

Thank you Gerry.

I will include your triaxial ellipsoidal beach stone 

in my book. 

I send you the PDF pages when they are ready
What address should I send?
Also, if you want, please  send me a short biography

at  biagio...@gmail.com

bdc

biagio...@gmail.com

[biagiodicarlo]

Hi Taff, for my book Strutture Geodetiche Ellissoidiche,
I woulld like to make a paper model of the Jim Hooker Home, on page
53 of DOME BUILDER'S HANDBOOK N.2 by William Yarnall.
I cannot find chord factors for an oblate icosa alt 4v, 0,618.
Maybe we can use SU for getting the peel pattern, 3d drawing and chord
factors?
bdc

On Aug 7, 7:46 pm, Biagio Di Carlo <biagiodica...@gmail.com> wrote:
> Thank you Gerry.
> I will include your triaxial ellipsoidal beach stone
> in my book.
> I send you the PDF pages when they are ready
> What address should I send?
> Also, if you want, please  send me a short biography

> at  biagiodica...@gmail.com

> >>>> %2Bunsubscribe@google groups.com>

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>
> >>>>    Biagio Di Carlo
> >>>> Via Berlino 2
> >>>> Villa Raspa, Spoltore
> >>>> 65010  PESCARA
>
> >>>>http://www.biagiodicarlo.com
> >>>> biagiodica...@gmail.com
> >>>> Tel. 085 411588  -  3405310750
> >>>>   skipename: biagiodicarlo
>
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[TaffGoch]

Biagio,

I know I have a copy of the "Domebuilder's Handbook" somewhere, but
can't easily lay my hands on it. (Much of my library is still in
boxes, from my last move.)

Can you attach a copy of the page? Or, perhaps describe more?

Is it a "squashed" (oblate) sphere, where the scaled vertical
dimension is squashed to 61.8 percent?

(And, yes, this should be an easy task in SketchUp, if only vertical
scaling is required.)

-Taff

[Biagio Di Carlo]

Probably it is the same dome that we have on  page 40 of DB2:

THE ASPEN DOME.   FE=0,618 is the expansion factor (E) by Peter Calthorpe

on page 36 of DB.

[TaffGoch]

Biagio,

 

The model, scaled on the z-axis to 0.618, looks right, but the chord factors don't match those you provided.

 

I don't know what to think about which is erroneous. Perhaps the domes don't share the same radius? The model is unit radius (1.0) on the ground plane.

 

(I've attached images and the SketchUp model.)

 

-Taff

[TaffGoch]

 

Image of Carey Smoot's oblate dome, provided by Biagio:

[Biagio Di Carlo]

Dear Taff thank you very much for the beautiful drawings!

I will include your work  in my book. 

I will send you a pdf copy of the final work.

The radius is the same.

For Carey Smoot  there are 23 CF.

In wich way I can get the  23 measurements?

Please can you draw the peel pattern too?

bdc

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Biagio Di Carlo
Via Berlino 2
Villa Raspa, Spoltore
65010  PESCARA

http://www.biagiodicarlo.com

biagio...@gmail.com

[TaffGoch]

Biagio,

 

From examination of the "peel," there appears to be 29 chord factors:

[TaffGoch]

Biagio,

 

Make that 28 chord factors....

[TaffGoch]

Biagio,

 

Here's the chord factors.

 

The ground-plane chord factors are all the same (0.312869). Any unlabeled strut is a mirror-image of another labeled strut (28 count.)

 

The peel pattern can be printed from SketchUp. The chord-factor labels can be turned off by unchecking the "Labels" layer.

[TaffGoch]

Biagio,

 

This version depicts the mirror lines:

[Biagio Di Carlo]

Great !!!

I  begin to make the  paper model

Thank you very much Taff.

bdc

[Biagio Di Carlo]

Dear Taff,

this is the paper model of the 

Oblate Icosa 4v.

Thank you for all.

bdc

[TaffGoch]

[TaffGoch]

Biagio,

Your paper model looks good! (I've never liked oblate domes, but this one is attractive.)

I oriented the model perspective, to register to the Carey Smoot photo, and it looks like they correlate well. I think we got it right.

 

I've also posted the model in the SketchUp 3D Warehouse:

http://sketchup.google.com/3dwarehouse/details?mid=1aca88c08929849c2137e32e8ebf2b1

 

-Taff

[TaffGoch]

This image shows the model perspective registered, to the photo, a little bit better, should you want it for your book:

[Biagio Di Carlo]

Incredible!

Thank you very much Taff. 

I will use it for my book.

bagio

On 160ago 2010, at 01:32, TaffGoch wrote:

This image shows the model perspective registered, to the photo, a little bit better, should you want it for your book:

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[TaffGoch]

Biagio,

Be sure you mention that Smoot used the Golden Ratio, 0.6180339887...
for the vertical scale factor.

(I knew I recognized that number from somewhere.)

-Taff

[Biagio Di Carlo]

OK

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[biagiodicarlo]

Hi all
probably during this week I wil publish my book in
http://ilmiolibro.kataweb.it/categorie.asp?searchInput=biagio+di+carlo&act=ricerca&genere=tutte&scelgoricerca=in_vetrina
I would like to thank all the friends of the Geodesic Help Group
bdc

> > For more options, visithttp://groups.google.com/group/geodesichelp?hl=en

>
> Biagio Di Carlo
> Via Berlino 2
> Villa Raspa, Spoltore
> 65010  PESCARA
>
> http://www.biagiodicarlo.com

> biagiodica...@gmail.com

[TaffGoch]

Biagio,
 
Grande notizia!

 

-Taff