Who propounded the principle of Golden Section?

Question

Accepted Answer

The correct option is 3:

Euclid, the renowned ancient Greek mathematician, is credited with first rigorously defining and propounding the geometric principle now known as the Golden Section. He documented this fundamental concept around 300 BCE in his seminal work, *Elements*, which remains one of the most influential mathematical texts in history. In his book, Euclid refers to the Golden Section as the division of a line "in extreme and mean ratio." This definition precisely describes the ratio where the whole line is to the larger segment as the larger segment is to the smaller one, forming the irrational number Phi ($\phi$), approximately 1.618. Although the term "Golden Section" was coined much later, it is Euclid's original mathematical formalization that established the principle.

The incorrect option is 1:

Jan Van Eyck was a highly influential Flemish painter of the Early Netherlandish Renaissance (c. 1390–1441). He is celebrated for his revolutionary mastery of oil painting, which allowed for unprecedented realism, luminosity, and minute detail in works like *The Ghent Altarpiece*. While his paintings are sometimes analyzed by art historians who suggest the presence of Golden Ratio proportions, his historical role was as a pioneering artist and diplomat, not as the mathematician who propounded this ancient geometric theorem. The principle was established over 17 centuries before Van Eyck's birth.

The incorrect option is 2:

J. C. French is not a figure recognized in the history of mathematics or classical geometry as the originator of the Golden Section principle. The Golden Section is an ancient concept with its formal documentation dating back to the Hellenistic period. The individuals associated with its mathematical, philosophical, or aesthetic documentation are primarily ancient Greeks, Renaissance scholars, or 19th-century German mathematicians who named the ratio. Therefore, J. C. French is not a name associated with propounding this fundamental mathematical law.

The incorrect option is 4:

R. G. Collingwood (1889–1943) was a 20th-century English philosopher, historian, and archaeologist. He is primarily known for his significant contributions to the philosophy of history, particularly his work *The Idea of History*. Collingwood's scholarly domain was speculative philosophy and historical analysis, and he did not work in the field of classical mathematics or geometry. The mathematical foundation of the Golden Section was firmly established by Euclid more than 2,000 years before Collingwood's time, making him historically too late to have propounded the principle.