Piano Keys
Piano Keys If you've ever looked closely at a piano keyboard you may have noticed that the widths of the white keys are not all the same at the back ends (where they pass between the black keys). Of course, if you think about it for a minute, it's clear they couldn't possibly all be the same width, assuming the black keys are all identical (with non-zero width) and the white keys all have equal widths at the front ends, because the only simultaneous solution of 3W=3w+2b and 4W=4w+3b is with b=0