I'm willing to bet you're like me in finding odd satisfaction in the simply 3x5 notecard. I use them as bookmarks, for self-notes, and the occasional for love note. They're great - thicker than regular paper, larger than a tiny sticky notes, asymmetrically lined. Ah!

But they also have a striking mathematical property: they're nearly golden. Not in color, but in shape!

Humans take fancy in lines that break at a point where the ratio of the shorter piece to the longer piece is the same as the ratio of the longer piece to the total length. 

A notecard's shorter end is 3" and its longer end is 5". The ratio of the short to long is 3/5 = 0.6, and the ratio of the long to total is 5/(3+5) = 0.625. Nearly the same!

3, 5, and 8 have a special, non-coincidental relationship: 3+5=8. This is part of the larger Fibonacci sequence. 

If we were to continue the pattern, we'd approach a length and a width that get nearer and nearer to perfectly equaling each other in their ratio. Imagine a 5x8 note card. The ratio of the short to long is 5/8 = 0.625 and the ratio of the long to total is 8/(5+8) = 0.615. Closer!

Closer and closer the humble notecard comes to perfection. But I'll close the page on this for now - and use my 3x5 notecard as a bookmark.