Knitting Math

Have you ever  ....

So many questions and stories start with this. Knitting math falls under this category. 

Have you ever knit and knit and knit and feel like you aren't getting anywhere?

Have you ever wondered why some knitting seems to fly while others drag on and on?

Knitting math 1.  Recently I wondered why a corner-to-corner dishcloth seemed to knit more quickly while a traditional cast-on with straight sides seemed to take forever.   I did the math to first see if it was because there is actually fewer stitches. 

First the traditional dishcloth example:

10 stitches cast on 

10 rows knit 

This equals 100 stitches knit 

Bind off the 10.

Now for the corner-to-corner dishcloth example 

Cast on 1.

Increase and knit across for 10 rows.

1+2+3+4+5+6+7+8+9+10=55 stitches 

10-1=9-1=8-1=7-1=6-1=5-1=4-1=3-1=2-1=1=45 stitches.  55+45 =100 stitches 

Nope, there is not a different number of stitches.  So what is the supposed difference?  Could it be the constant turning of the short rows?  The constant turning at the beginning and end will definitely make it feel like it's going faster.