Confused about PAR(Pixel Aspect Ratio) in video

Part1

According to Here

SAR_x   DAR_x * height
----- = --------------
SAR_y   DAR_y * width

for example: width x height = 704x576, DAR = 4:3 ==> SAR = 2304:2112 or 12:11

So we can derive

SAR_x    width      DAR_x              width
----- x -------- = -------  ==> SAR x -------- = DAR
SAR_y    height     DAR_y              height

According to here, we can get: SAR × PAR = DAR.

Which means

       width
PAR = -------
       height

Part2

According to here

main_dar, mdar : The main input video’s display aspect ratio. Calculated from (main_w / main_h) * main_sar.

we can derive

            main_w                        width
main_dar = -------- x main_sar ==> DAR = -------- x SAR
            main_h                        height

Again proof that:

       width
PAR = -------
       height

Part3

But from here, we can get 2 images

Which means PAR(Pixel Aspect Ratio) is the ratio of single pixel, apparently this definition of PAR is not the same as the result that we get from above(part1 & part2).

So I'm confused about this, anyone who can explain this?

Edit

Search "Non-square aspect ratios of common video formats" within this page, you can see a table which I already take a screenshot below