Coins come in all sorts of shapes, including hexagons and octagons, some with holes in the middle, some made from two different shades of metal, etc. If you look them up, there have been coins in just about every sort of shape you can think of. These days, increasingly. A rounded edge is easiest when considering the use of vending machines, so there has been a trend in that direction.
A round shape gets wear on all sides, keeping a round shape even after circulation. Everything else degrades into a circle (or sphere, I guess) over time, as the corners stick out and get caught on stuff.
Holes in the middle used to be more common so they could be carried on strings, but that’s not been common for a while, hence the shape that holds across currencies by now
While vending machine theory sounds good ( and there were vending machins 2000 years ago). The real answer is following:
Round shape with little teath was best to reduce frauds. The most major was to grind some gold from side. If grinding was done uneven than shape was clearly not round. And it was quite hard to grind round coin evenly. Things become even more harder when theath was introduced around edge. The made distinguish between grinded and non grinded coins much easier.
Tradition is very important in money. A big part of the value of money comes from the fact that it’s _perceived_ to have value, and a big part of that perception is “looking like” money.
Regardless of any other useful aspects of round currency, the _real_ reason it’s round is that previous coins were round, and people making new coins wanted them to match the old coins. Those coins were round because they matched older coins, going all the way back to the earliest coins that were created around the ancient Mediterranean (other parts of the world had other traditions).
So why round? The very first Lydian coins were made by placing blobs of electrum onto an anvil containing a pattern and whacking them with a hammer. This naturally produced a flattish, roundish shape with an embossed picture. That shape became traditional and was carried on and refined. All those other reasons to have coins were just later discoveries, the first reason is that’s just the shape you get when you stamp a blob of metal flat so you can stick an image on it.
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