Re:
The abs are constantly worked in everyday life. They're already a six pack, but those who don't see them have too much bodyfat. Even scrawny guys who don't lift have six pack abs. Training abs boils down to a few purposes...
1. If you're attempting to build "core" strength beyond what you do in everyday life to lift more weight squatting and dead lifting.
2. If you're training specifically for a sport.
When I played a few games of flag and tackle football, my abs were killing from the jumping and tossing around, as I can handle the squats and deads, but not the intensity for over an hour that football placed on my abs. It's rare a person would end up expanding their waste and diminish any V they might attain, unless they're on drugs to do it. Growing abs, like calves, is a bit tougher, and any sizeable gains aren't likely to be seen easily since they're don't represent much, like a growing chest, thighs, glutes, biceps, triceps, back, or traps would. Any growth in those areas will stretch a shirt in some fashion.
When you say waist, you're referring to your abs, as they plug right down to your pelvis and genitals. And no muscle would be added to the abs, not under a normal diet with normal genetics. Abnormal genetics or abnormal dieting plus juice "might" do it, even then, a guy would want toned muscles, but not bigger toned muscles on the stomach as it would diminish the protruding chest you've worked so hard to achieve.
I see lots of people do hanging leg curls, and leg raises, and that's fine. It keeps you fit, it builds core strength so you can improve your athletic ability, and possibly gain in lifts. It doesn't spot reduce. And it doesn't ab alot of definition. Any perceived definition is the reduction of fat all over, the last of which is stripped from the midsection. I haven't done any, but I do 'different' ab stretches...like standing stretches, where I arch far back and contract my abs, or I do vacuums, something Arnold did, and also back bridges, that stretch it the opposite direction. I own a book by Matty Furey called combat abs. Probably the best book to alternative ab exercises that doesn't require weights or machines, and gets your abs tough enough to handle most sports fatigue.
A-Unit