When the forefathers of the Native Americans crossed the Bering strait, the Mongolians still were shamanistic and pitched tepees, not gers. Without outside influence until Columbus rediscovered the Americas, the native Americans remained shamanistic and kept on pitching tepees, whereas Mongolians went through a number of religions and at some point traded the tepee for the ger.
I don’t remember reading whether the ger is a Mongolian or a Turkic invention. What is more amazing is that at some point, someone decided that a different kind of tent was needed and proceeded to completely re-invent the wheel. And not only that, over time, that new type of tent, the ger, proved to be so much better that everyone pitching tents in central Asia moved to the ger as their favorite dwelling.
Gers are very easy to set up, it taking only about two hours to build one from scratch. Several layers of felt, depending on the time of year, form the outer layers of the tent, the roof being carried by 100 to 200 wooden beams, resting on the top of the outside wall and supporting a wooden open hole in the top of the ger (although in Erdene Zuu the monks used a ger that was supported by no less than 1500 beams). A ger also has two large beams supporting the roof from the ground, but they are not strictly necessary, the ger being strong enough to support itself without them. The open hole in the middle can be covered if needed, but also generally allows for the chimney of a stove to go through to let out smoke.
Gers keep the inhabitants warm in winter and cool in summer and is also relatively cheap to produce. Depending on the amount of decoration in the wood used, a regular ger costs between 250 and 500 euros.

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