What is the origin of 4K term?
According to Wikipedia ,Digital Cinema Initiatives originated the term 2K in 2002 for a digital film format of 2048 x 1080.  2048 is commonly referred to as 2K in the digital world.  It logically follows that when DCI went on to specify a resolution 2x larger in each direction, they called the 4096 x 2160 format 4K.  4096 is commonly referred to as 4K in the digital world.