I'm afraid I don't know of the other rectangle you remember reading about. I am in love with the golden rectangle and golden proportions. I advocate the use of the value of phi (1.618) to determine good proportions for quilt sizes and especially border widths. Do a search on the Internet for "phi" and you will find many mathematics and art references. It's fascinating. Phi relates to the Fibonacci numbers, and the Fibonacci numbers relate to the Golden Rectangle and lots of other natural things. It relates to beauty as perceived by the eye as being perfectly proportioned.
I really can't imagine that some quilters have found a "better" rectangle for quilts that beats the Golden Rectangle.
If you find the reference you remember, please come back here and let us know!
How I would use phi:
1. Figure the length of the short side of your quilt. Multiply by 1.618 and you'll have a perfect rectangle size for the length.
2. If you have a quilt that is made up primarily of, for example, 10" blocks. Multiply the size of that 10" block by 1.618 for a wider border or by .618 for a narrower border. It looks great! I used to size the border by half the size of the block, and many other quilters I know went by that "rule." When you compare a border sized by half the block with one sized by phi, the one sized by phi has a more pleasing appearance. Really. Set examples of the two in EQ6 and compare them side-by-side in the Sketchbook. I hope you will agree.
3. If you have a series of borders to apply to a quilt, you can size them using Fibonacci numbers. OR add one border. then use phi to size the next border and so on. You'll be generating the same proportion that Fibonacci numbers offer.
It's really fun.