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2. A property of ellipses. Source of diagram: ref. [3.1] and [5.3]. 

2. A property of ellipses. Source of diagram: ref. [3.1] and [5.3]. 

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The paper is an updated version of the December 2, 2017 paper under an identical title by this author. It incorporates in it exact measurements of the ring (received by the author on December 3, 2017). The paper strengthens and expands on the findings of the previous paper, as well as it amends and extends the prior analysis. Editorial corrections...

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This is an update of the paper under the same title by the author. It contains editorial corrections and the formal permission by the University of Cincinnati Dept. of Classics to use the image of the ring.

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Article
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A new class of ellipses is discussed in this paper, with the bezel ellipse of the Minoan 5-priestess signet ring from the 1450 BC Pylos’ tomb of the Mycenaean Griffin Warrior acting as the springboard to this new classification. The ellipse carries a strong mathematical interest. The elementary theorems governing ellipses that obey the condition that the ratio of their major to minor axes is at a Golden Ratio are stated, and to that end nine sets of mathematical theorems are proven. Following the mathematical exposition of the Golden Ratio Ellipse, the ring from Pylos is examined as to whether its maker was aware of any of these Mathematics. It is concluded that although, and on purely Aesthetics grounds, the maker gravitated and tried to approximate the making of a true Golden Ratio Ellipse, (s)he was only partially aware of the underlying Mathematics. The findings are based on a detailed analysis of the ring’s iconography. This is an updated version of a previous article by the author under the same title, of December 7, 2017. In this version the formal permission by the department of Classics, University of Cincinnati, to use the ring's image is included
Article
Full-text available
A new class of ellipses is discussed in this paper, with the bezel ellipse of the Minoan 5-priestess signet ring from the 1450 BC Pylos’ tomb of the Mycenaean Griffin Warrior acting as the springboard to this new classification. The ellipse carries a strong mathematical interest. The elementary theorems governing ellipses that obey the condition that the ratio of their major to minor axes is at a Golden Ratio are stated, and to that end nine sets of mathematical theorems are proven. Following the mathematical exposition of the Golden Ratio Ellipse, the ring from Pylos is examined as to whether its maker was aware of any of these Mathematics. It is concluded that although, and on purely Aesthetics grounds, the maker gravitated and tried to approximate the making of a true Golden Ratio Ellipse, (s)he was only partially aware of the underlying Mathematics. The findings are based on a detailed analysis of the ring’s iconography