The Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a cylindrical projection preserving the direction from any place to another predetermined place, while avoiding some of the bizarre distortion of the Hammer retroazimuthal projection. It is sometimes known as the Mecca projection because Craig, who had worked in Egypt as a cartographer, created it to help Muslims find their Qibla. Check out the mathematical calculation used to create the map on Wikipedia.
I think it would be neat to use this cartographic projection technique to create a map that uses Washington, DC as the center.