page_title: List of works designed with the golden ratio
section_title: Early history
hierarchical_section_title: List of works designed with the golden ratio / Early history
caption_attribution_description: English: Kheops pyramid Esperanto: Piramido de Keopso Nāhuatl: Egiptopa Guizanahuac tlamanacalli
context_page_description: Many works of art are claimed to have been designed using the golden ratio.
  However, many of these claims are disputed, or refuted by measurement.
  The golden ratio, an irrational number, is approximately 1.618; it is often denoted by the Greek letter φ.
context_section_description: Various authors have claimed that early monuments have golden ratio proportions, often on conjectural interpretations, using approximate measurements, and only roughly corresponding to 1.618. For example, claims have been made about golden ratio proportions in Egyptian, Sumerian and Greek vases, Chinese pottery, Olmec sculptures, and Cretan and Mycenaean products from the late Bronze Age. These predate by some 1,000 years the Greek mathematicians first known to have studied the golden ratio. However, the historical sources are obscure, and the analyses are difficult to compare because they employ differing methods.
  It is claimed, for instance, that Stonehenge (3100 BC – 2200 BC) has golden ratio proportions between its concentric circles. Kimberly Elam proposes this relation as early evidence of human cognitive preference for the golden ratio.  However, others point out that this interpretation of Stonehenge "may be doubtful" and that the geometric construction that generates it can only be surmised. As another example, Carlos Chanfón Olmos states that the sculpture of King Gudea (c. 2350 BC) has golden proportions between all of its secondary elements repeated many times at its base.
  The Great Pyramid of Giza (constructed c. 2570 BC by Hemiunu) exhibits the golden ratio according to various pyramidologists, including Charles Funck-Hellet. John F. Pile, interior design professor and historian, has claimed that Egyptian architects sought the golden proportions without mathematical techniques and that it is common to see the 1.618:1 ratio, along with many other simpler geometrical concepts, in their architectural details, art, and everyday objects found in tombs. In his opinion, "That the Egyptians knew of it and used it seems certain."
  From before the beginning of these theories, other historians and mathematicians have proposed alternative theories for the pyramid designs that are not related to any use of the golden ratio, and are instead based on purely rational slopes that only approximate the golden ratio. The Egyptians of those times apparently did not know the Pythagorean theorem; the only right triangle whose proportions they knew was the 3:4:5 triangle.
caption: The Great Pyramid of Giza, Egypt
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