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Front page > Geometry based on Silver Ratio and Golden Ratio > Logarithmic spiral is the basic structure of galaxies
Geometry based on Silver Ratio and Golden Ratio

Logarithmic spiral is the basic structure of galaxies

In case of the following galaxies, the angle between the line drawn from the center of the galaxy and the tangent to the sriral is measured to be 72.8 degrees:

Great Bear Galaxy M101

— Great Bear [brightness: magnitude 8.2; distance: 19 million light-years]

— Pisces [brightness: magnitude 9.8; distance: 37 million light-years]

— Canes Venatici [brightness: magnitude 9.0; distance: 21 million light-years],

These measurements were made by Mr. Tanimura with his special software “Spiral”.  This angle, 72.8 degrees, is about the same as the one of the logarithmic spiral derived from the golden rectangle and the golden rhombas.  Please refer to the paper “Logarithmic Spirals based on the Golden Ratio, Golden Square Ratio, Silver Ratio, and Silver Square Ratio” posted in this website under the category “Geometry Study based on the Silver Ratio and the Golden Ratio”.  In Table 1 of Page 5, you will find  b=o.405376 π (72.9 degrees).

According to Mr. Tanimura, ,two different kinds of spiral are noticed in case of the The Milky Way Galaxy that includes the solar system and their such angles are approx. 78 degrees and 75 degrees, respectively.  If  you refer to the aforementioned Table 1,  you wiill find that  78 degrees correspond to b  of the spiral derived from the silver rectangle/silver rhombas (0.430877 π=77.6 degrees) and 75 degrees correspond to b of the spiral derived from the acute golden triangle (0.420438 π=75.7 degrees).  While investigation on the other galaxies is not conducted yet,  it is inferred from these data that their respective basic structure is also based on either of the six kinds of logarithmic spiral shown in Table 1.

The angle b of DNA spiral structure is yet to be investigated.  It is inferred, however, that the DNA spiral structure also corresponds to either of the six kinds of logarithmic spiral in Table 1.  In general, DNA consists of two chains held together by hydrogen-bonding that are spirally-coiled.  Partial molecular configuration of such dual spiral structure is equivalent to the regular tetrahedron.  Namely, the bond angle between the carbon atom in the center and the other atoms and atom group is equal to 109.47 degrees.  This angle corresponds to the obtuse angle of the silver rhombas and it is called the “regular tetrahedron angle” in the field of crystallography.  This fact indicates that the Silver Ratio is hidden in the molecular configuration of DNA.

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