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Topic: Squaring the circle with equal areas and the ratio 1.12783848556170 (which = sqrt (sqrt Phi))

We know that the square root of the Golden ratio (the Golden Ratio being 1.6180339887) is 1.2720196495141. The square root of the Golden ratio (1.2720196495141) is also called the Golden root. Are you are(?? aware) of the ratio 1.1278384855617?   1.1278384855617 is the ratio of the diameter of a circle divided by the edge of a square that has the same surface area as the circle.  Also if a circle and a square have the same surface area, then if the perimeter of the square is divided by the circumference of the circle the ratio is also 1.1278384855617.  1.1278384855617 is also the square root of the Golden root (the Golden root being 1.2720196495141).  We already know that the Golden root   (1.2720196495141) is the square root of the Golden ratio (1.6180339887…) and that Cosine ( 36) multiplied by 2 = 1.6180339887… .   The purpose of this message is to bring attention to the role of the square root of the Golden root (1.1278384855617) in creating a circle and a square with equal areas, Squaring the circle.

Response by Harry Lear

Mr. Liddz is correct in his above assertions.  Plugging in my values for the squared area of a circle to the squared area of a rectangle and then obtaining the side of a square with the same area (see my Pi Math Proof, Squaring the Area on Measuring Pi Squaring Phi) Mr. Liddz’s assertions are true.  Let me add that those asserted relationships are only true precisely because Pi = 4 / sqrt Phi = 3.144605511… and NOT 3.141592654… .  There are many universal constant relationships between the parameters comprising various geometric figures (sides, circumf, perimeter, diameter, diagonal, etc.).  Read my results on Measuring Pi Squaring Phi entitled Five More Universal Constants for my newly discovered universal constants involving Pi and Phi.  Pi is only one of many universal constants related to Phi.


Carlos Hernandez

Topic:  The true value of Pi = 4 / sqrt Phi = 3.144605511…

Response by Harry Lear

Visit Carlos Hernandez’s Facebook web site for some very interesting scientific discussions including the true value of Pi at:   Real Number Pi –

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