They have not changed much since Archimedes' time.
June 14 is apparently International Bath Day, celebrating the anniversary of the day (one week before the beginning of summer according to Greek legend) when Archimedes tried to figure out the density of a crown to determine if it was gold or something else less valuable, like silver. According to Wikipedia:
While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!"
Baths have not changed much over the years; in 1904 Charles Rennie Mackintosh put this one in the Hill House near Glasgow. It might be a little more comfortable than Archimedes, who basically was in a big barrel.
Many people do their best thinking in the bath. Instead of "Eureka!" the screenwriter Dalton Trumbo, who did much of his writing submerged, might be yelling "I AM SPARTACUS" while writing the movie screenplay. He at least set himself up right, with a place to work, a big cigar and a whiskey.
Today, baths are not a whole a whole lot different than they used to be. Free-standing tubs are all the rage again, sitting free of the wall. They do not appear to be designed for comfort, but more as architectural objects. In his 1966 classic, the Bathroom Book, Alexander Kira noted that bathtubs were ridiculously uncomfortable.
The first and most obvious (and also the most ignored) criterion is that the user be able to lie back and stretch out comfortably....most modern baths are totally inadequate in these respects, as indicated by the postures illustrated.
Kira determined that tubs should be longer (but not too long for short people) and have contoured backs.
Then there is the issue of safety; hundreds of people are injured and even killed getting in and out of bathtubs. People are putting all their weight onto one leg on a curving slippery surface and lifting the other. The fancy new tubs have no ledge to sit on so they are particularly dangerous, and being away from the wall, no place to put a safety rail. It is almost as if they are designed to make it difficult to get in and out of.
Kira acknowledged that the bath is about relaxation and not about cleanliness, because you don't actually get very clean in a tub; you just soak in your own dirt. That's why the Japanese way of bathing makes so much sense; you sit on a stool and shower with a hand shower or a bucket that runs when you need it (saving water) and then you soak in a hot tub; since you are already clean, the water can be shared with the whole family.
Or, you could be like Margot Robbie in "The Big Short," who has a big tub, great views, and champagne while you explain how subprime mortgages work. Nice tub, big sills to sit on and hold the champagne.
In the end, if you are going to celebrate International Bath Day, your Eureka moment should come when you pick a tub that is comfortable, long enough to stretch out in, with a big sill that you can sit on and swing over. Think about using it as you age, and plan for effective grab bars. (I put blocking in the walls behind my tile so that I could add bars later) Think about a quick shower first so that you can share it and not waste so much water and energy, and if you can, use the water after as gray water in your garden or toilet tank. And Happy International Bath Day!