Check out this table...  

A few thoughts...
1. Interesting, effective solution for a variable-sized, round table.
2. I'd have to see exactly how many more place settings, or gambling hands, would be facilitated before knowing how effective it is.
2. Does not solve the age-old problem of what to do with extra chairs when reduced--but then neither does any other solution I've seen.
3. I'd sure hate to get any part of me caught in the middle as those points converge, but then I'd hate to get any part of me caught between the sections of leafed tables when they converge.
4. There's something about the geometry of this table and its parts that make me think it might look more fitting if it were made out of a higher tech material than wood. I can definitely see this table being a gotta have it table in a high tech firm's executive office, if it were made of carbon fiber, or titanium even, and cost some massive amount of money and had a designer's mark visible on it.
3. Looks very heavy.

Note that
in its smaller diameter a rim rises to enclose the six pie-slice leaves; this seems designed to disguise (or correct) the fact that the outer edge of each leaf cannot simultaneously have the correct arc, at both large and small diameters, to make a perfectly circular top.
I have seen one or two other versions of this idea; one from Scandinavia has three "enlargement" leaves that tilt to vertical and store in the cylindrical base of the table. This is certainly the most elaborate and "automatic" of these.

Appears practical
but I would end up playing with it all day, kinda like those expanding ball toys. And of course whenever company comes over, I would have to show off my investment.
Looking at the video, you could conceiveably set the table for six, and then if a few extra guests arrive (or you just want to show off again), then just ch-ch-ch-ch-ch (i.e. make the sound effect from Transformers: Robots in Disquise with your mouth, as you expand the table).