Here is the floor plan:

Making an octagon on the floor to match the tray ceiling exactly would be a great architectural feature. Tray and floor would reinforce each other. I'm sure there is an official designer term for that. But I don't know it.

Paint our hardwood floor? Seems criminal.

Here are some web pages about it:

• Country Living, including paint company floor paints.
• Behr's pages on interior floor painting is mostly about concrete.
• Another Country Living concentrating on stencils.
• Ask the Builder is very encouraging.
• American Hardwood on faux painting floors.
  

  "You don't have to strip your hardwood floors if you don't want the painted design to last forever," she says. "You may need to touch it up a little from year to year."

   

  She recommends that homeowners use water-based paint for wood floors so that it can be removed easily without harming the finish. This distinction is critical. Water-based paint won't smear if a layer of oil-based urethane is later applied over it. Oil-based paint will smear.

• Stenciling Your Hardwood Floors, another good one from American Hardwood.