and many pleasant facts about the square of the hypotenuse

Via TYWKIWDBI, we discover that a century of study and conjecture mathematicians have teased the secrets from a thirty-seven-hundred-year old Babylonian clay tablet and revealed that not only were the fundamental principles of the Pythagorean theorem known and applied earlier than expected, that indispensable ratio among the sides of a right-triangle providing that c²=a²+b², but moreover the artefact represents not only the world’s first trigonometric table and also the only completely accurate one—owning to the way the Babylonians counted in base-sixty instead of base-ten number-systems, which we retain in the way we reckon time and the degrees and minutes of longitude and latitude. This anonymous tablet predates the work of Hipparchus of Nicaea by more than a millennium, whom history has called the father of the branch of mathematics and credits with the invention of such preternaturally useful navigation and surveying tools like the astrolabe and the first star charts. The discovery is not just a revelatory in that it shows that these underlining principles were known to architects and astronomers far earlier than we believed, but there’s also the insight that these triads, the values of the sides of triangles, were derived ratiometrically—that is without inscribing a right-triangle in a circle.