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So here's the background: there's an adventurer who is looking for a golden hat made by an extraterrestrial civilization as a gift for one of his ancestor in the 18th century.

Is it technically possible to braid a panama-like hat with some kind of pure gold fiber and it still be usable (malleable and no so heavy)?

When he found the hat, he starts wearing it until the story end.

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closed as off-topic by Mołot, wetcircuit, L.Dutch, Burki, Frostfyre Jan 31 '18 at 13:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about worldbuilding, within the scope defined in the help center." – Mołot, wetcircuit, L.Dutch, Burki, Frostfyre
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Welcome to the site, Peretto. Please note that the Worldbuilding SE is dedicated to providing detailed answers to specific questions a user has while developing his/her fictional world. Discussions about real-world objects are off-topic for us. Thus, this question is likely to be put on hold until an edit is made identifying how this is a worldbuilding question. Feel free to take the tour to get a better understanding of the site. $\endgroup$ – Frostfyre Jan 31 '18 at 13:02
  • $\begingroup$ This is a situation where you don't need to justify or describe your worldbuilding efforts. If you want to make a world where people wear hats of gold, then any other background information is useless in the context of the question here. This question looks on-topic, adequately scoped, and answerable to me. Nominating for re-opening. $\endgroup$ – kingledion Jan 31 '18 at 13:21
  • $\begingroup$ This is a story about an adventurer who is looking for a golden hat made by an extraterrestrial civilization as a gift for one of his ancestor in the 18th century. $\endgroup$ – Peretto Jan 31 '18 at 13:32
  • $\begingroup$ Adding "it was aliens" to the backstory doesn't make this question about worldbuilding, but if you'd added this detail earlier you might have gotten different answers. As it stands the answer is "no", unless you are now saying the hat was made in some special alien way with a "pure gold" jipijapa palm plant that grows on their gold planet…. $\endgroup$ – wetcircuit Jan 31 '18 at 13:47
  • $\begingroup$ A few prehistoric gold "hats" made of sheet gold, not woven out of gold thread, have been found in Europe. en.wikipedia.org/wiki/Golden_hat And for an example of the kind of artistic decorations which can be made in sheet gold and worn on the head see the four reliefs on the miter of the imperial crown of Rudolph II, en.wikipedia.org/wiki/Imperial_Crown_of_Austria $\endgroup$ – M. A. Golding Feb 2 '18 at 4:55
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Gold is extremely malleable and ductile. Gold has been drawn into thin wires and woven into fabrics since the deep antiquity; much more commonly, a core of silk is spun with gold strips, because gold alone is almost unusably soft.

It is certainly possible to weave gold into the material of which the hat is made; you could in principle make it of only gold, but gold is very soft and very dense -- but yes, definitely, you could make it of pure gold as long as you intend to wear the hat only during special ceremonies.

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If you make the hat entirely out of gold then it's going to be really quite heavy, but that doesn't mean it can't look largely gold. It would probably look better with a woven pattern or embroidery but that's a matter of taste.

https://en.wikipedia.org/wiki/Goldwork_(embroidery)

Goldwork is the art of embroidery using metal threads. It is particularly prized for the way light plays on it. The term "goldwork" is used even when the threads are imitation gold, silver, or copper. The metal wires used to make the threads have never been entirely gold; they have always been gold-coated silver (silver-gilt) or cheaper metals, and even then the "gold" often contains a very low percent of real gold. Most metal threads are available in silver and sometimes copper as well as gold; some are available in colors as well.

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First answer is no. Gold density is $19300 kg/m^3$ while the heaviest straw, from winter cereals is $65 kg/m^3$. So even doubling it will result in weight 148 times less than using gold.

What can be done is to either apply gold to finished hat or use very small amount of gold in embossing the straws.

Modern gold foil with a thickness of $0,05 μm$ and one square meter would weight about 2-3 grams. A change in weight of final product that would go unnoticed.

Gold thread would require twisting gold over straw. Depending on straw you choose and it's diameter (or just width when folding final hat) you would add additional 5-7 grams of gold.

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