[THE eXchanger]

The two squares, the drawn and the projection square, form an octagram Pell's series are the progressions that approximate the geometry of proportions originating from the octagram The first of Pell's series is:


1 - 2 - 5 - 12 - 29 - 70 - 169 ...

Both main numbers 24 (2x12) and 29 are members of this series. Leonardo used this progression to rationalise irrational geometry of square root of 2 that rules the geometry of the octagram. As a proof, all other numbers are derived as a combination of the members of the series. The distance between the two centers, the navel and Phallos, is according to rationalized geometry 2,5 palms, and it seems that the position of palms touching the square in Thau formation of the figure equals 9,5 palms, again the measure derived from rational approximation of the geometry of the octagram by means of Pell series. Also the diagonal of the square is calculated from the series as 2x(5+12) = 34 palms.

The composition founded in octagram is one of the most spread cannons of proportions in ancient and classical architecture clearly presented by enormous opus of research done by Prof. Tine Kurent of Ljubljana School of Architecture, Slovenia. Almost every important christian church has dome placed on an octagram, and gematric value of Greek spelling for Jesus, ΙΗΣΟΥΣ = 888 associates the number 8 (octagram) with Jesus Christ.
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