In 5 or 6-way intersections like the examples above, roundabouts can actually be rather difficult to implement. If all legs of the intersection are equally arranged around the circle it's easier, but still can be a problem. The main issue is that to accommodate the proper entry and exit geometries of the approach legs, the circle itself needs to be enlarged. That's a big no-no in modern roundabouts because it encourages higher speeds around the circle and thus makes it more difficult to merge into it.
In the UK, people don't seem to have that much of a problem with roundabouts with high circulatory speeds. There's quite a few, normally at freeway intersections, or in new build towns, where you can get up to 30-40mph easily (there's one in Skelmersdale which is a mile around and you can easily do the 60mph speed limit, but also no traffic), but the merging is normally OK on these big roundabouts, depending on traffic levels. The
Pyebush roundabout in Beaconsfield has a large radius (by no means the largest) and traffic heads round it at 40mph, it's fairly heavily trafficked, but people don't seem to have trouble getting onto it.
OK, many large roundabouts have been signalised, like the turbo roundabout, only with less channelisation (one or two have colour coding to make it easier to follow the spiral pattern, and u-turns aren't too difficult, or having 5 or 6 exits), or have been turned into magic roundabouts, like the example I gave. Of course, I never suggested a roundabout for 5- or 6-way junctions, I suggested magic roundabouts for them.
Here's a turbo roundabout, UK style. It's in a place that ought to have some kind of stack and it struggles with traffic levels, but it has also (unlike almost everywhere) got colour-coding for the right turns - red for E to N, green for S to E, yellow for W to S and grey (lighter than the tarmac) for N to W.
Here's a version with 7 roads, and no colour coding - this (1.3 miles around, IIRC) didn't use to be signal controlled, but it, again, ought to have some free-flow ramps due to traffic levels and the roundabout doesn't give enough capacity without signals. One of the entrances is still a yield. There's probably a better example than that second one, but it shows a couple of points - that you can have more than 4 entrances, and you can have yields onto high speed roundabouts and not have much problem.
What's an old roundabout? Traffic Circle? I'm just confused as modern roundabout seems to just be a plain vanilla, small roundabout - nothing modern about them, just that they are only 30 years old in America.
what is the difference? and, while we're at it, what's a rotary?
Traffic circles are yield to traffic entering, Roundabouts are yield on entrance. That is the difference, not geometry or size. Unless this is a US English/UK English discrepancy.