Generally, billiard, etc., tables have a ratio of about 1:2. For example, a standard snooker table has dimensions of 11’ 8.5" x 5’ 10" giving a ratio of 281:140. For some odd reason, last night I started thinking about the golden ratio. If you were to make a snooker table with the golden ratio (approximated to 1:1.618), then the result would be 5’ 10" x 9’ 5". (If my calculations are off, feel free to correct them; it’s been quite a while since I had to mess around with such.)
I’ve seen, and even played pool on, non-standard tables, such as round and octagonal. What’s gotten me wondering now is how the games, especially three-cushion billiards (thanks to the diamond system), would change with what seems to me to be a slight change in the ratio of the short to long sides for a rectangular table.
While I’m on the topic, has anyone here played on a kaisa or Russian billiards table with Russian billiard balls? How would you rate the difficulty of the game?
Pool/billiards/snooker tables are 2:1 in aspect ratio (actual measurements will vary ever so slightly). The diamonds divide the table into 32 equal square sections, which is possible because there are exactly twice as many diamonds at the same spacing along the long sides as there are diamonds on the short sides. If you changed the aspect ratio of the table, you would no longer be able to rely upon the diamonds creating square areas (equal spacings) if you retained the same number of markings. Thus, aiming would be different.
Notice that one common variant found in the 60s in America was the octagonal bumper pool table. It, too, makes use of the geometry of equal lengths/areas to make aiming easy.
There was also an elliptical pool table with one hole at one focus of the ellipse. If you sent a ball through the dot at the other focus in any direction (without English and with no obstructions) it would fall into the hole after one carom due to the geometry of ellipses.