Yoshiro Nakamatsu
Nakamatsu claims IBM reached licensing agreements with him in the late 1970s. He also claims to have licensed his floppy disk to IBM in 1979, but that the details are "confidential". An IBM spokesman, Mac Jeffery, confirmed that the company did license some of his patents, but claimed they were not for the floppy disk, which he claimed IBM invented on its own. Another IBM spokesman, Brian Doyle, said they licensed 14 patents from Nakamatsu, but also claimed that they do not have anything to do with the floppy disk.
History of the floppy disk
Like the -inch, the -inch disk underwent an evolution of its own. When Apple introduced the Macintosh in 1984, it used single-sided -inch disk drives with an advertised capacity of 400 kB. The encoding technique used by these drives was known as GCR, or Group Coded Recording (similar recording methods were used by Commodore on its -inch drives and Sirius Systems Technology in its Victor 9000 non-PC-compatible MS-DOS machine). 
Somewhat later, PC-compatible machines began using single-sided -inch disks with an advertised capacity of 360 kB (the same as a double-sided -inch disk), and a different, incompatible recording format called MFM (Modified Frequency Modulation). GCR and MFM drives (and their formatted disks) were incompatible, although the physical disks were the same. In 1986, Apple introduced double-sided, 800 kB disks, still using GCR, and soon after, IBM began using 720 kB double-sided double-density MFM disks in PCs like the IBM PC Convertible. IBM PC compatibles adopted it too, while the Amiga used MFM encoding on the same disks to give a capacity of 1 MB (880 KB available once formatted).