Who Made The First Geodesic Dome?

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.

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

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/

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

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?)...

"...flat triangles..."

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

Oh the monotony.

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"...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.

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

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...)

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.

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.

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.

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.

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...

...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?

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.

"...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...."

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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?

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

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

If it's dynamite, I suppose.

Sticks , or . . . (?)

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

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.

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.

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

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.

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.

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

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

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...

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

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

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

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

So it would seem.

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

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...

"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

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

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

You have natural rock formations....

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

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

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.

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.

I should have said successive line segments. Oops.

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.

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?...)

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.

...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?...

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.

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.

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 ? ...

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.

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.

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

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.

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

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

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.

Only Frank Gehry.

Hmmmm. Stainless steel Cheetos!

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.

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".

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.

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.)

Even when surrounded with gooey jalapeno cheddar goodness?

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.

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

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.

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.

triangles don't warp. Your imagination might warp.

"...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..."

He is obviously referring to a non-Euclidean triangle.

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"

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

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+

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.

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.

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It is easy to understand why you posted anonymously.

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.

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?

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?

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.

This is quite a useful structure.

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.

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?

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.

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

"..may be stable..."

Sure, maybe.

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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?

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

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.

That is the answer I was hoping for. Thank you.