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Who Made The First Geodesic Dome?

06/19/2017 10:39 PM

In discussing Structural Engineering, Buckminster Fuller once said, in essence, that (primitives) could not have invented the geodesic dome, becausue they didn't have the ''math'' for it...

And yet, Native Americans built (mobile homes) out of poles and animal hides; migrating Mongolian herdsmen transported their housing (yerts) on wagons from grassland to grassland; Eskimos built semi-hemisperical igloos; various peoples built similar semi-hemispherical (bamboo) huts, etc., all without a single equation...

Can anybody say who earlier (approximated a semblance) of a geodesic dome before B. F. ?

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#1

Re: Who made the first geodesic dome?

06/19/2017 11:40 PM

Although roughly hemispherical, and even ingenious, none of those structures is really equivalent to a geodesic dome.

There are various typographical glitches in your post that indicate lack of knowledge, or even authentic interest, in this topic.

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#2

Re: Who made the first geodesic dome?

06/20/2017 12:21 AM

Well the hexagon is a structure seen throughout nature in honeycombs, water crystals, diamond crystals, basalt columns, epithelial cells in the eye and many others....the hexagon is basically 6 triangles...and 5 sided figures as well....

https://www.quora.com/Geometry-Why-do-we-see-hexagons-in-nature-so-often

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#5
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Re: Who made the first geodesic dome?

06/20/2017 8:44 AM

The triangle isn't considered symmetrically attractive, and was more popular as a support structure for building domes than as a design element....

http://www.smithsonianmag.com/history/the-secrets-of-ancient-romes-buildings-234992/

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#9
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Re: Who made the first geodesic dome?

06/20/2017 1:00 PM

Here's a GA for the good link...

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#37
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Re: Who made the first geodesic dome?

06/21/2017 7:37 PM

The (raydome) configuration presented above, consisting of a frame-work of inconsistantly-sized, flat triangles, in the general shape of a dome, is sufficiently ''geodesic'' for the purpose of my question, which remains (who did it first?)...

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#39
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Re: Who made the first geodesic dome?

06/22/2017 8:31 AM

"...flat triangles..."

.

Right? I mean, that's pretty much every triangle you see these days; all flat, perfectly aligned with some plane.

Oh the monotony.

.

"...my question, which remains (who did it first?)..."

Radiolarians, as far as I can tell no one was earlier, starting about 540 million years ago.

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#42
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Re: Who made the first geodesic dome?

06/22/2017 9:27 AM

Well, aren't those old-timers just cute and darling!

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#3

Re: Who made the first geodesic dome?

06/20/2017 2:31 AM

An igloo is dome-shaped. Certain East Coast Native Americans built dome-shaped lodgings (the Wampanoag for example), as well as did other groups, but were they geodesic domes? What makes a dome geodesic?

Geodesic domes are instances of geodesic polyhedra, and that takes math. Bucky is correct.

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#10
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Re: Who made the first geodesic dome?

06/20/2017 1:12 PM

Theoretically, any people with access to bamboo could easily have improvised dome-shaped (temporary?) structures made of triangles ''sized'' on a trial-and-error basis, but are not recorded to have done so...

Here's a GA for the good link anyway...

(There is one recording of bamboo being used in the design of a working (hang-glider-apparatus), some 1200+ years ago, but that is a different question...)

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#4

Re: Who made the first geodesic dome?

06/20/2017 3:03 AM

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#7
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Re: Who made the first geodesic dome?

06/20/2017 10:21 AM

Those are not geodesic, although they are domed. That is also the reason why we normally find these in a flat heap on the ground. It takes a level of solid geometry math skill not typically found, to calculate the various (solid) angles for stress-free structural elements to result.

True, geodesics can be made with some built-in stress bending of the structural elements, but I suspect they will not last a significant amount of time.

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#18
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Re: Who made the first geodesic dome?

06/20/2017 2:30 PM

The structure in the bottom photo has a largely rectangular tiling and therefore is prone to torsional failure (think of collapsing a box open at opposite ends). Stand under the centre, grab the top, and give it a good twist.

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#19
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Re: Who made the first geodesic dome?

06/20/2017 3:17 PM

yep, but it worked for the eskimo people and the first arrivals in North America for a long time, in various locations where Mastodon tusks could be had, but little wood.

The trick is adaptability to the raw materials, climate, and other resources available at the time in a given place.

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#25
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Re: Who made the first geodesic dome?

06/20/2017 4:14 PM

Lots of things worked: a lean-to made of pine branches. Caves. Tee-pees. A hollowed-out snowbank, but we're getting far afield from the original question.

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#6

Re: Who Made The First Geodesic Dome?

06/20/2017 9:52 AM

If you count microscopic, they've been around for a long time.

https://en.wikipedia.org/wiki/Buckminsterfullerene

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#8
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Re: Who Made The First Geodesic Dome?

06/20/2017 12:58 PM

If a structure is defined as being ''geodesic'' because it is an assemblage of flat triangles into a semi-hemisherical configuration, and you connect all the interior corners of each of the pentagons and hexagons in buckminsterfullerene, then you would have a geodesic globe, but not a ''dome,'' per say.

Here's a GA anyway...

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#11
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Re: Who Made The First Geodesic Dome?

06/20/2017 1:15 PM

...but if they half the recipe? Just kidding, I think that half of a Buckyball has been made by some chemist somewhere, just saying. If you put chalk inside a Buckyball, is it now a snow globe?

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#14
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Re: Who Made The First Geodesic Dome?

06/20/2017 1:42 PM

A geodesic is the shortest path between two points in a curved space. If that curved space is the surface of sphere (or dome, which is a subset of a sphere), then the path connecting the two points is a chord of a great circle, ie, of a circle whose centre is the centre of the sphere (longitude lines, for example). A chord of any circle on the sphere that does not include the sphere's centre is not a shortest-path and is therefore not a geodesic (latitude lines excluding the equator, for example).

Primitive dome-shaped shelters are typically built using long structural members (willow branches, for instance), and herein lies the problem: such members are seldom sections of a great circle and so do not traverse the shortest distance between two points on the sphere. In other words, they are not geodesics. Triangular tessellations are no guarantee that the result is geodesic, but only when each and every edge of every polygon tiling the sphere is a great-circle chord (that is, the shortest possible path* between adjacent vertices).

So you see, the meaning of 'geodesic' refers to a very specific kind of tiling of a curved surface. Just any old tiling won't do even if it's triangular. All the polygon edges have to be shortest-paths for the dome to be considered 'geodesic.'

Does this help?

------

* an obvious result of the shortest-path criterion is that the structure is built with the minimum amount of materials for the chosen geometry.

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#16
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Re: Who Made The First Geodesic Dome?

06/20/2017 1:49 PM

That should help a lot, because it is the most conservative approach to structural members that can exist in making an enclosed space. All other designs "waste" materials.

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#35
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Re: Who Made The First Geodesic Dome?

06/21/2017 4:20 PM

"...Primitive dome-shaped shelters are typically built using long structural members (willow branches, for instance), and herein lies the problem: such members are seldom sections of a great circle and so do not traverse the shortest distance between two points on the sphere...."

.

The surface is not required to be perfectly spherical, is it? There is no requirement for constant or uniform curvature, right? Geodesic lines can be found for unusual curved surfaces, right?

Your quote above seems to suggest you have knowledge of two points on the surface of a sphere which could escape falling on a circle whose center is the center of the sphere. If you could demonstrate these on a basketball or other close to spherical object, I am very interested.

The shortest distance between two point on the surface of a sphere is a cord and that cord will always be the cord of a circle with the same center as the sphere.

Here in the real world, we, of course have no perfect spheres, nor any perfectly straight connecting members from which to make cords. As such, any physical geodesic structures we build won't be perfect geodesic structures, but you can see what they are approaching and use the term 'geodesic' without fear of being wrong, outright.

Considering prehistoric curved structures: if you agree that surfaces other than portions of perfect spheres might have geodesic lines and if you are willing to allow for less than perfectly straight support members (so just use the points of connection and forgive the meandering if the willow branches or elephant tusks); doesn't that make it more difficult to discount these support structures as geodesic?

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#70
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Re: Who Made The First Geodesic Dome?

06/26/2017 1:02 AM

Hi Andrew, you confused me for a moment there because all chords of a sphere lie on a great circle -

Chord (geometry) ... A chord of a circle is a straight line segment whose endpoints both lie on the circle.

As you say, a geodesic is "in a curved space" hence is an arc. In geometry (I think!) "line" is normally reserved for straight line (infinite), a segment of which is the [absolute] shortest path between the ends of the segment. The shortest path on the sphere between two points is an arc of a great circle of the sphere.

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#76
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Re: Who Made The First Geodesic Dome?

06/26/2017 11:48 AM

Then a tetrahedron is a geodesic. If so, then they have been around every time someone leaned three sticks together.

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#77
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Re: Who Made The First Geodesic Dome?

06/26/2017 11:55 AM

So if rubbing two sticks together can make a fire, what do you get when you rub three sticks together? An explosion? LOL.

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#84
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Re: Who Made The First Geodesic Dome?

06/26/2017 2:17 PM

If it's dynamite, I suppose.

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#85
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Re: Who Made The First Geodesic Dome?

06/26/2017 2:50 PM

Sticks , or . . . (?)

(( sorry , but you "painted a picture" , there...))

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#99
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Re: Who Made The First Geodesic Dome?

06/28/2017 1:09 AM

No, tetrahedrons are not geodesics. Fuller's patents explicitly disclaim the basic solids from which geodesics are created. Most geodesics are icosahedrons with the basic triangles further subdivided - it keeps down the number of different lengths that structural members must be cut to - but tetrahedrons have been used as a basis as well, though they require many more different strut lengths.

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#101
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Re: Who Made The First Geodesic Dome?

06/28/2017 5:26 AM

The three post structures need not be seen as tetrahedrons. These can be seen as half of triangular bipyramids which should allow a straight forward geodesic using the ground plane to begin a hemisphere circumscribing the hemi triangular bipyramid.

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#33
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Re: Who Made The First Geodesic Dome?

06/21/2017 10:12 AM

Excellent(!) [or, "Eggscellent!"] ... "...there is no new thing under the sun"

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#12

Re: Who Made The First Geodesic Dome?

06/20/2017 1:30 PM

Buckminster Fuller is much overrated. There is nothing all that special about a 'geodesic' dome. It's an extension of the notion of the Platonic solids, but doesn't qualify as one since the dome is not composed from just one repeated shape.

To say that 'the primitives' couldn't have built one implies they were unaware of the geometry of flowers, beehives, or wasps nests.

'The primitives' simply didn't need geodesic domes. Eskimoes and Inuits made igloos. Ancient peoples of the British Isles made beehive huts. American indians and ancient people of other lands made dwellings with crossed poles and furs, blankets, etc.

It's a shame that a self-promoting second-rater like him is memorialized with names like Buckyballs and Fullerines.

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#15
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Re: Who Made The First Geodesic Dome?

06/20/2017 1:47 PM

Is there anyone out there you do not consider as second-rate, or self-promoting?

It can be someone from another field, I am just curious how you will answer.

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#27
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Re: Who Made The First Geodesic Dome?

06/20/2017 7:02 PM

Why don't you get off my back? The last few times I've made comments, you attacked me for my opinions. What do you care what I think? If you don't like what I said, move along. If you have something useful to add, go ahead. I haven't attacked you. Buzz off.

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#32
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Re: Who Made The First Geodesic Dome?

06/21/2017 8:35 AM

Same, right back at ya. In the meantime, try really hard to say something positive.

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#83
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Re: Who Made The First Geodesic Dome?

06/26/2017 2:07 PM

As an Ancient, I just looked for caves..Much less work..

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#13

Re: Who Made The First Geodesic Dome?

06/20/2017 1:32 PM

As a point of clarification, Native Americans built teepees by arranging wooden poles in the configuration of an upright cone. So, in a sense, they did create geodesic cones...

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#17
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Re: Who Made The First Geodesic Dome?

06/20/2017 2:17 PM

This is true, but what does this 'clarify' exactly?

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#23
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Re: Who Made The First Geodesic Dome?

06/20/2017 3:39 PM

It could be viewed as the first step towards (geodesic-ness)...

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#24
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Re: Who Made The First Geodesic Dome?

06/20/2017 3:53 PM

A straight stick meets the geodesic criterion in flat 2D space (the surface of a sphere of infinite radius, if you will), but how does this understanding naturally lead to the construction of geodesic domes by primitives? What is missing that B.F. spoke of, something that primitives show no evidence of having mastered in their constructions? We can speak of other geometric forms, but how does this clarify your original question, one specifically about geodesic domes? We have no evidence that they built these. They built dome-shaped structures, yes, but B.F. is not speaking of just any type of dome, but of geodesic domes in particular. This distinction - of the dome's being geodesic - is critical to the entire discussion.

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#102
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Re: Who Made The First Geodesic Dome?

06/28/2017 5:30 AM

Doesn't seem like the moderns were or contemporaries are builting proper geodesics either. Fairly straight 'sticks' are used in most cases.

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#20

Re: Who Made The First Geodesic Dome?

06/20/2017 3:17 PM

So what's a pyramid? The most basic geodesic structure?

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#21
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Re: Who Made The First Geodesic Dome?

06/20/2017 3:21 PM

So it would seem.

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#22
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Re: Who Made The First Geodesic Dome?

06/20/2017 3:38 PM

Close, but not quite: the edges of its base are not geodesics. An equilateral tetrahedron fills this criterion though.

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#28
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Re: Who Made The First Geodesic Dome?

06/20/2017 7:07 PM

While this particlar structure was intended to (shelter) an (egyptian pharoah, and queen), in their (afterlives), their (remains) were to be kept in rectangular rooms, which are not domes, even if they had vaulted ceilings with stars painted on them...

And, the original posting asks ''who'' made an (earlier/proto) geodesic dome...

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#29
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Re: Who Made The First Geodesic Dome?

06/20/2017 7:39 PM

"The first geodesic dome was built in Jena, Germany in 1922 on top of the Zeiss optics company as a projection surface for their planetarium projector. R. Buckminster Fuller subsequently popularized so-called geodesic domes, and explored them far more thoroughly."

source

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#103
In reply to #20

Re: Who Made The First Geodesic Dome?

06/28/2017 7:10 AM

A pyramid with (8), not (4) sides showing.

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#26

Re: Who Made The First Geodesic Dome?

06/20/2017 5:17 PM

I think the earliest geodesic domes must be from something like radiolarians or diatoms.

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#30
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Re: Who Made The First Geodesic Dome?

06/20/2017 11:54 PM

You have natural rock formations....

Such as this "Giant's Causeway" in Northern Ireland....age 50 to 60 million years old...

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#31
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Re: Who Made The First Geodesic Dome?

06/21/2017 4:25 AM

Fossils of diatoms date back to around 180 million years ago.

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#34
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Re: Who Made The First Geodesic Dome?

06/21/2017 11:56 AM

If that's in nature, there should also be a Fibonacci sequence in there somewhere.

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#36

Re: Who Made The First Geodesic Dome?

06/21/2017 4:57 PM

Fuller used the term "geodesic" in a way that differs from correct geometric usage. Some (but only some) of the straight line segments of a "geodesic" dome actually project onto great-circle arcs, which are true geodesics.

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#38
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Re: Who Made The First Geodesic Dome?

06/22/2017 8:19 AM

How can a line segments two points on the surface of a sphere avoid projecting onto some great-circle arc?

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#40
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Re: Who Made The First Geodesic Dome?

06/22/2017 9:13 AM

My head also be scratching...

A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a small circle, the intersection of the sphere and a plane that does not pass through the center. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a great circle of exactly one sphere.-Wikipedia.

The great circle should be called the greatest circle, and all other circles drawn on the surface of a ball (sphere) should be called lesser circles. Or you could call her Margaret.

Geodesics: The shortest distance whereby surface travel on a sphere connects two points on the surface of the sphere. A segment of the greatest circle. Geodetics - same meaning. A line is not really a geodesic (since it is not a segment of the greatest circle), but B. Fuller's structures, approximate geodesics in the limit of how a linear chord of a circle may approach a geodesic arc line segment.

That should just about settle the argument. "Geodesic" domes are not geodesic in a purist sense, and neither are eskimo huts made of bones and furs. Both approximate a half-sphere (more or less), and the resemblance is similar to comparing a simple rectangular box frame house to a cracker box.

BTW- flying off the greatest circle between two points is done when the winds at altitude are favorable for a lesser circle route. It depends on wind layering perhaps, but the transit time is indeed shorter by such a route.

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#41
In reply to #38

Re: Who Made The First Geodesic Dome?

06/22/2017 9:22 AM

I should have said successive line segments. Oops.

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#45
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Re: Who Made The First Geodesic Dome?

06/22/2017 3:41 PM

Not sure many so called geodesic domes even follow that rule.

Look below at how many successive segments are at angles such that a plane on which the center of the sphere also lies cannot also contain both successive segments. Also not that five (perhaps seven) lines of successive segments near the top of the dome, running foreground to background, are pretty much parallel...until making faily abrupt turns.

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#79
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Re: Who Made The First Geodesic Dome?

06/26/2017 12:26 PM

OK, let's just say that (someone) painstakenly custom-fit a piece of (flat, plywood, say) for each different triangular opening, and then, carefully inserted the appropriate such panel to fit snuggly into its corresponding triangular opening of the geodesic structure provided above...

Then, would there not then be a geodesic dome consisting of flat, unwarped, straight, triangles?...

(at least, until the first rainfall sufficiently dampened said panels to warp them ever-so slightly?...)

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#82
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Re: Who Made The First Geodesic Dome?

06/26/2017 1:25 PM

Once warped, they are no longer triangles, but are sections of some elliptical or perhaps spherical surface, if and only if the warp has a regular curvature. A piece of plywood is not a mathematical object, and is not two-dimensional no matter how many ways or times you try to say otherwise. It is a three-dimensional object, because (1) it has a measurable thickness, and (2) we don't live in 2D land.

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#113
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Re: Who Made The First Geodesic Dome?

06/29/2017 12:48 PM

...and, if the plywood-ed geodesic dome, mentioned previously, was rained upon,

...and all its triangular panels allowed to completely dry out,

...and developed some tolerable warping during the drying process,

...then, would it not have become a slightly warped geodesic dome, with slightly warped triangular panels?...

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#114
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Re: Who Made The First Geodesic Dome?

06/29/2017 1:33 PM

Even though you are as wrong as hell, at least you are nothing if not persistent.

Points for hanging in there, although you could not be more totally wrong.

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#115
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Re: Who Made The First Geodesic Dome?

07/01/2017 4:45 AM

You are confusing a naming convention for a qualitative description. If my t-square gets hammered and warped out of square, you might call it a warped t-square, but it is not square any longer.

If you warp a triangle the verticies will form a triangle (unless the warp puts all three in a line) but that doesnt mean the non-planar connecting material can be would be properly described simply as a triangle or triangular.

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#43

Re: Who Made The First Geodesic Dome?

06/22/2017 12:41 PM

On the one hand, in between the World Wars, ''Bucky'' Fuller started extolling the structural virtues of geodesic domes in the USA. He patented them in the USA, and stood to personally profit substantially from promoting them, therein. For this, he came to be referred to as a (visionary). Today, he would probably be regarded as an enterpreneur...

On the other hand, German astronomer, Max Wolf, suggested to Walter Bauersfeld, Chief engineer of the Zeiss Corporation, to start work on the first planetarium in 1912. A small dome was built, the design was patented, and the planetarium was completed in Germany in 1923.

This would seem to make Walter Bauersfeld the original maker-of-record, but the question remains as to just how much of the structural design was suggested by Max Wolf...

...or, did some uncredited (grad student?) mathematician provide Max Wolf with enough of the math theory to show that the semblance of an interior curved surface was sufficiently approximate-able by an appropriate configuration of flat, unwarped, triangles ? ...

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#44
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Re: Who Made The First Geodesic Dome?

06/22/2017 2:11 PM

The answer to that is most likely buried in a burned up archive in Berlin, or has been otherwise lost to time. As to men, time and chance happeneth to them all, but for paper, acid and time happens sooner or later.

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#46
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Re: Who Made The First Geodesic Dome?

06/22/2017 3:54 PM

Again with these "...flat, unwarped, triangles....".

I won't make the mistake of being subtle this time:

Please show me one of these warped non-flat triangles to which you keep alluding. A triangle describes straight segments connecting three different points in space. Line segments connecting three different points in space cannot help but be on a flat plane.

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#47
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Re: Who Made The First Geodesic Dome?

06/22/2017 4:10 PM

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#49
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Re: Who Made The First Geodesic Dome?

06/22/2017 4:53 PM

When was the last time you've eaten a Dorito(R) - style chip ?...

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#50
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Re: Who Made The First Geodesic Dome?

06/22/2017 4:58 PM

Couple weeks, but those are not triangles, they are remotely triangular in shape, but clearly do not come to a point, and have curled edges. A triangle is strictly a two-dimensional object. Doritos could possibly be classified as approximating a pseudo-triangular section of a hollow sphere of corny, cheesy goodness.

Besides, who puts salt on their triangles? Really. Sheesh.

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#51
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Re: Who Made The First Geodesic Dome?

06/22/2017 5:59 PM

wouldn't touch 1 of those things with whatever length pole

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#54
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Re: Who Made The First Geodesic Dome?

06/22/2017 8:27 PM

And just how flat-surfaced, straight-edged, sharp-cornered, perfectly-triangular, are the Doritos, where ever you come from?...

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#55
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Re: Who Made The First Geodesic Dome?

06/22/2017 10:06 PM

Now that you mention it, Cheetos aren't straight-edged or sharp-cornered around my neck of the woods either.

Good thing that much like Doritos, not many people confuse Cheetos for triangles or try to build geodesic structure from them.

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#56
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Re: Who Made The First Geodesic Dome?

06/22/2017 11:10 PM

Only Frank Gehry.

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#57
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Re: Who Made The First Geodesic Dome?

06/23/2017 12:25 AM

Hmmmm. Stainless steel Cheetos!

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#63
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Re: Who Made The First Geodesic Dome?

06/23/2017 10:59 AM

So now I know who Frank Gehry is. Of all the pics on his Wikipedia page, I liked the Santa Monica home site the best. That looks entirely livable.

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#62
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Re: Who Made The First Geodesic Dome?

06/23/2017 10:56 AM

Only after they consume mass quantities of the "Weed Infused" Doritos. Heck I thought that was from pushing bong smoke through a bag of Doritos, but heck no, those things are actually green, not "green" in the sustainable sense, only in the sensimilla sense.

Sheesh and Shong. (you know what I am tokin' about, man).

Someone has been smoking too many "triangles".

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#61
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Re: Who Made The First Geodesic Dome?

06/23/2017 10:53 AM

Doritos are Doritos, and they still are not triangles, within the definition of "triangle", they may have something resembling triangular shape when viewed in projection, but even in that case, the corners are rounded, and some are broken, and thus even if they were flat with infinitely sharp corners, not rounded, they would no longer be triangular.

You can argue harder, but you are going to lose this argument, plain and simple.

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#59
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Re: Who Made The First Geodesic Dome?

06/23/2017 10:19 AM

So with those green Dorito's, you just skip the smoke and go straight to the munchies?

I guess those will only appear on shelves in States like Colorado (Rocky Mtn. high, in more ways than one.)

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#80
In reply to #51

Re: Who Made The First Geodesic Dome?

06/26/2017 12:32 PM

Even when surrounded with gooey jalapeno cheddar goodness?

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#58
In reply to #49

Re: Who Made The First Geodesic Dome?

06/23/2017 7:17 AM

As much as I love Dorito's Ranch,... You're using THAT is the example.?

We are talking about structures, a triangle is one of the most sturdy structures there are. And it establishes a plane. That is the reason 3 legged stools can stand firmly.

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#110
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Re: Who Made The First Geodesic Dome?

06/28/2017 11:16 PM

I have a 3 leg stool who's legs are at just such an angle that it will toss whoever sits on the stout and sturdy looking piece.

I've relegated it to shop duty as a single step for putting my head in other places.. (schmart!)

As it sits.. the seat is an inch or two too high in the (pyramid).. creating an unnoticed tipping hazard.

I suppose I could reduce leg length and seat diameter to correct it?

...or give it to a pub as a seat 'offer' to someone who just needs to sit and calm down for a few minutes.

A short spill later dignity's restored

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#53
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Re: Who Made The First Geodesic Dome?

06/22/2017 8:03 PM

I guess your confusion must stem from not being familiar with 'alluding'. '

'Alluding', as I used it, means to suggest, hint at, or otherwise bring to mind without directly mentioning.

By describing 'flat, unwarped triangles' an unambiguous suggestion is being made that triangles exist which are not flat and are warped.

Three points in space cannot describe more than a flat surface, neither can the line segments connecting those points, which describes a triangle.

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#64
In reply to #53

Re: Who Made The First Geodesic Dome?

06/23/2017 11:28 AM

as for me - Doritos or not - I have never had ANY problem envisioning warped triangles. Sort of like the kid in The Last Mimzy, I can see them everywhere! Look REALLY close.

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#65
In reply to #64

Re: Who Made The First Geodesic Dome?

06/23/2017 12:36 PM

triangles don't warp. Your imagination might warp.

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#67
In reply to #64

Re: Who Made The First Geodesic Dome?

06/24/2017 2:26 AM

"...Do not try and bend the triangle, that's impossible. Instead, only try to realize the truth...there is no triangle. Then you'll see it is not the triangle that bends, it is only yourself..."

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#96
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Re: Who Made The First Geodesic Dome?

06/27/2017 3:07 PM

He is obviously referring to a non-Euclidean triangle.

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#97
In reply to #96

Re: Who Made The First Geodesic Dome?

06/27/2017 6:50 PM

non-Euclidean -

sort of related to but dif'rent than in post number 64 above

Sometimes (as once waxed poetically) "...things are not what they seem"

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#100
In reply to #97

Re: Who Made The First Geodesic Dome?

06/28/2017 4:22 AM

If so, then, would things that aren't, be what they don't seem?

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#104
In reply to #100

Re: Who Made The First Geodesic Dome?

06/28/2017 12:21 PM

Most indubitably, the things which are seen are made from things which are unseen (in more ways than one can count!).

(Can) "things that aren't, be what they don't seem?"

't all depends on how much of the kool-aid one has swallowed.

Once one has bought-into "Lie#1", it is inevitable that they will happily swallow "Lie#2", "Lie#3", etc etc.

George Santayana's axiomatic aphorisms {engraved on public-placards in Germany} should be taught to one-and-all ('round this globe, at the elementary level).

Did not he, as others, consider matter to be something that we mere humans could only 'know' metaphorically?

A coupla hours well spent+

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#107
In reply to #104

Re: Who Made The First Geodesic Dome?

06/28/2017 3:30 PM

I've always found that during a presentation or sales pitch, the presenter asks,"Does that make sense?".

This means that the salesman has hit a potential dead end and you have to buy in to the seller's proposition. I always say no and the sales pitch falls apart.

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#108
In reply to #104

Re: Who Made The First Geodesic Dome?

06/28/2017 10:25 PM

Uhg, your first and third links are so tediously drawn out, pedantic and downright illogical.

Just because some aspect is not yet thoroughly understood does not mean it is necessary to invoke a whispy judgemental voyeur floating in the sky.....and even if that is going to be your position, please get to it a little faster. Jeeze, at least go fast enougb that your speaker isn't totally bored with him lines and falling asleep. Colossal waste of time.

.

It is easy to understand why you posted anonymously.

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#111
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Re: Who Made The First Geodesic Dome?

06/29/2017 10:09 AM

It is true that such posts have side effects, mostly the poor blokes that attempt to completely follow the drivel through its twists and turns of pointless rhetoric, and end up banging forehead to edge of desk, as they nod off to sleep, perhaps the endless sleep. Beware of the weeping angels.

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#48
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Re: Who Made The First Geodesic Dome?

06/22/2017 4:51 PM

Why not would he have merely stated: "Triangles"

Not all "geodesic" domes use triangles. I think some use a combination of pentagons and squares, perhaps the less distorted, the stronger the structure, less strain in the segments. Am I right? Can I have a gold star, please?

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#52
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Re: Who Made The First Geodesic Dome?

06/22/2017 7:41 PM

It could certainly be done with other than triangles, but once you exceed three sides on your most simple polygon, much more would be required of the members and joints.

.....and the would also be more useful... as in providing an example of a polygon that actually could be warped and not flat....useful structurally and argumentatively.

Tried to give you a gold star....could only find a GA ....Gold Astral?

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#60
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Re: Who Made The First Geodesic Dome?

06/23/2017 10:22 AM

OOOO, thank you, thank you, uncompromising one of the truth!

Strictly speaking, any distorted polygon is no longer a 2D object, and therefore not a polygon.

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#66
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Re: Who Made The First Geodesic Dome?

06/24/2017 2:18 AM

Hmmm. Skew polygons are real thing....though they do require a minimum of 4 verticies....and as such a triangle can never be a skew polygon.

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#71
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Re: Who Made The First Geodesic Dome?

06/26/2017 5:26 AM

This is quite a useful structure.

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#86
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Re: Who Made The First Geodesic Dome?

06/27/2017 12:08 AM

Yes, but the common embodiment of that structure is based on a pressurized thin shell/inflatable membrane. That is very different from (as is the embodiment made of stiff panels of polyhedrons joined at the edges) a space frame.

These structures are viewed by some to have note worthy utility.

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#87
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Re: Who Made The First Geodesic Dome?

06/27/2017 6:27 AM

If you say so, but it would be helpful to have an explanation. Why is it so different from an embodiment made of stiff panels of polyhedrons joined at the edges and why is it so different from a space frame made of appropriately dimensioned rods?

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#88
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Re: Who Made The First Geodesic Dome?

06/27/2017 9:03 AM

How is a derigible different from a truss bridge?

How is a wacky crazy inflatable arm waving man different from the Eiffel tower?

How is a balloon different from as egg shell?

Comparing the shapes sewn together that will be inflated to form a soccer ball has very in common structurally with an object constructed by connecting struts or struts and ties...even though you might see similarities in the prominent lines of both objects.

The inflated ball has essentially all the material (comprised of sheets) under tangential tension. Those lines that resemble the layout of struts in geodesic domes are not compression bearing members just seams joining sheets in tension.

Even when building your object from rigid panels, it is still fundamentally different than using struts or struts and ties. With rigid panels, the shape of the polygon will resist deformation of angles whatever shape is used. Using struts, the stability of the polygons formed depends on the structure, typically not on the ability of connectors to maintain specific angles.

It is somewhat backwards to ask me to expound on why the similar patterns in different objects is not evidence of a likeness of structure from which useful analogies might easily be generated. The more direct route would be to ask what makes you think the structures are sufficiiently similar as to function as useful analogies structurally.

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#90
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Re: Who Made The First Geodesic Dome?

06/27/2017 12:43 PM

So we agree that a football-shaped structure made up of rigid polyhedral panels may be stable?

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#92
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Re: Who Made The First Geodesic Dome?

06/27/2017 12:52 PM

"..may be stable..."

Sure, maybe.

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#105
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Re: Who Made The First Geodesic Dome?

06/28/2017 2:41 PM

So we agree that a football-shaped structure made up of rigid polyhedral panels can be stable?

The next stage is to drill a hole in the centre of each panel. Does this make it unstable?

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#106
In reply to #105

Re: Who Made The First Geodesic Dome?

06/28/2017 3:26 PM

Only if this is an inflatable structure, and you are messing with the structure of the Universe again.

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#109
In reply to #105

Re: Who Made The First Geodesic Dome?

06/28/2017 10:33 PM

I think I understand where you are going with this, and it isn't anything I disagree with.

The whole point is that using triangles, the joints only have to keep things connected and the struts/ties are subject to compression/tension almost exclusively at any time.

If you use a hexagonal pattern or if you drill out your rigid hexagonal panels, then the 'joints' at the verticies can't just keep the long members connected, the joints must resist bending to new angles. The long members are also no longer under just compression or tension.

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