Phi's best-known modern association, the golden ratio, an irrational number close to 1.618 with notable mathematical properties, is a far more recent naming than many readers assume: the ratio itself was studied by ancient Greek mathematicians including Euclid, but the convention of labelling it with the letter phi dates only to the early 20th century, when the American mathematician Mark Barr proposed the symbol around 1909, reportedly to honour the sculptor Phidias, whose initial in Greek is phi and whose work at the Parthenon was believed, not entirely reliably, to embody the ratio's proportions. The golden ratio itself has attracted persistent, often exaggerated claims of appearing throughout art, architecture and nature, many of which later scholarship has questioned or rejected as invented pattern-matching rather than deliberate design.
Outside this mathematical association, physicists use phi for magnetic flux and for phase angles in wave equations, and astronomers, following the Bayer star-naming convention of 1603, use Phi for one of the fainter numbered stars in a constellation. None of these modern uses connects to phi's ancient Greek sound value, covered elsewhere in this atlas.