After seeing this video by Prof Martyn Poliakoff;
Clock also shown here: http://gizmodo.com/periodic-table-alarm-clock-lets-you-see-atomic-numbers-1603489991
He convinced me it is amazing, so I made my own version of the clock face, which is available here: http://mathewpeet.org/science/elements/
The elements are listed by atomic number (same as the number of protons in the nucleus), with 60 divisions around the clock face. To read the atomic number just read the position on the clock face. The position in ‘minutes’ is the atomic weight e.g. Fe has atomic number 26, Rh is 45, Ag is 47. For elements in the outer ring add 60, Db is 105, Th is 90, Uuo is 118.