Trigonometry.

I have five colors of post-it notes, and I want to make a post-it-coaster.  The first time I did this, I did it by eye, and it didn't work so well.  Last time, I realized that I actually know math.

The base post-it.

 Five post-its means I'm making a pentagon.  The sum of interior angles of a polygon is 180 * (n-2) or 540.  There are five such angles, so each one is 108.  The excess from the 90 corner of a post it is 18.  Converting this to radians tells us that q = pi/10, so tan(q) ~ 1/3 (due to small angle formula).  The triangle formed from this has to meet the triangle from the opposite corner halfway across the base post-it (due to symmetry).  This means that the intersection point is 1/6 the height of the post-it.

Make a mark there.

 Now all the remaining post-its can be placed, keeping that angle in common.

And you get a tiny corner that isn't totally correct, but it's close enough.