Phi spirals are the proportions of the 5 sided pentagon the geometry of which is nested within the icosahedron, dodecahedron, DNA and the human body.

Phi spirals are the proportions of the 5 sided pentagon the geometry of which is nested within the icosahedron, dodecahedron, DNA and the human body.

4 circle golden ratio (down about a dozen pictures at the website): AB/AG = PHI & AG'/AB = PHI The solution twists your brain around.

4 circle golden ratio (down about a dozen pictures at the website): AB/AG = PHI & AG'/AB = PHI The solution twists your brain around.

Proporción Aúrea. Capilla de los Pazzi, año 1441 fue su última obra.:

Proporción Aúrea. Capilla de los Pazzi, año 1441 fue su última obra.:

Draw a line from the intersection points of the two smaller circles at A to the intersection point of the two larger circles at G. The ratio of the length of segment AG to segment AB is Phi, or 1.618 0339 887 … Proof:  AB/AG = ( 2 Ö 3 ) / ( Ö15 + Ö3)  =  2 / ( Ö5 = Ö1)  =  2 / ( Ö5 = Ö1)  = Phi

Draw a line from the intersection points of the two smaller circles at A to the intersection point of the two larger circles at G. The ratio of the length of segment AG to segment AB is Phi, or 1.618 0339 887 … Proof: AB/AG = ( 2 Ö 3 ) / ( Ö15 + Ö3) = 2 / ( Ö5 = Ö1) = 2 / ( Ö5 = Ö1) = Phi

Portrait Class - WetCanvas Portrait Class - WetCanvas www.wetcanvas.com447 × 600Search by image OK, if that's what you SEE, draw it that way! Front face proportions:

Portrait Class - WetCanvas Portrait Class - WetCanvas www.wetcanvas.com447 × 600Search by image OK, if that's what you SEE, draw it that way! Front face proportions:

Golden Ratio (an example of the two golden triangles and how they describe a pentagram).

Golden Ratio (an example of the two golden triangles and how they describe a pentagram).

Whoever wants to understand much must play much. –Gottfried Benn.   The Golden Ratio has an interesting property: Its square is only one more than itself.  For large numbers, given any Fibonacci number, you can approximate the next Fibonacci number by multiplying the current one by (1+√5)/2, that is F(n+1)≈φF(n).

Fibonacci Findings

Whoever wants to understand much must play much. –Gottfried Benn. The Golden Ratio has an interesting property: Its square is only one more than itself. For large numbers, given any Fibonacci number, you can approximate the next Fibonacci number by multiplying the current one by (1+√5)/2, that is F(n+1)≈φF(n).

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