Aspect Ratio

Every once in a while I try to understand aspect ratio better, and each time I get confused.

Here's some starters:

Here's my latest test set as I'm trying to figure out what HandBrake's options do:

dvd_copy 1.665.2098.TNTGO.iso/ -t 1 -c 1-1

Math:
720/480		1.5
3/2		1.5
4/3		1.3_
16/9		1.7_ (1.78)
854/480		1.779_ (1.78)		mplayer
854/480		1.779_ (1.78)		mplayer -aspect 16:9
720/480					mplayer -noaspect
720/540		1.779_ (1.78)		mplayer -aspect 4:3
720/720		1			mplayer -aspect 1:1


source.vob (widescreen):			720x480 DAR 16:9	mplayer 1.78:1
mplayer movie aspect:				854/480 (1.78)
mplayer force fullscreen:			mplayer -aspect 4:3
mplayer force widescreen:			mplayer -aspect 16:9
mplayer force scope (?):			mplayer -aspect 2.67:1

HandBrake encoding settings                     mediainfo output        mplayer display aspect ratio
none						720x480 DAR 16:9	mplayer 1.78:1
-w 720 -l 480 (all)				720x480 DAR 16:9	mplayer 1.78:1
--non-anamorphic				720x480 DAR 3:2		mplayer 1.50:1
--auto-anamorphic				720x480 DAR 16:9	mplayer 1.78:1
--loose-anamorphic				720x480 DAR 16:9	mplayer 1.78:1
--display-width 720				720x480 DAR 3:2		mplayer 1.50:1
--custom-anamorphic --display-width 720		720x480 DAR 3:2		mplayer 1.50:1
--keep-display-aspect				720x480 DAR 16:9	mplayer 1.78:1
--no-keep-display-aspect			720x480 DAR 16:9	mplayer 1.78:1
--custom-anamorphic --pixel-aspect 16:9		720x480 DAR 16:9	mplayer 2.67:1 (scope?)
--custom-anamorphic --pixel-aspect 4:3		720x480 DAR 2.00	mplayer 2.00:1 (flat?)