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sacred geometry

sacred geometryThe 9 workbooks
8 Geometry and music
8.1
Using the square as unity with both its side and area equal to 1, by crossing the Ö2 with the (Ö5)/2 and leading a perpendicular from the point of interesection up to the side, we divide unity into 1/3 and 2/3.

Arithmetic proportion:
1/3, 2/3, 1

Have a go!

Please enable Java for an interactive construction (with Cinderella).
8.2
Use the square for unity and by means of an arc from the lower left corner,,, bring the length of side 1 down to intersect with the diagonal Ö2. Then lead an arc from the upper right corner back up to the upper side of the square.

Harmonc proportion:
(Ö2-1), (2 - Ö2), 1

Have a go!

Please enable Java for an interactive construction (with Cinderella).
8.3
Lead an arc from the point of intersection of the half-side with the semi-diagonal and the arc with radius equal to the half-side to the upper side of the square.

Geometric progression:
1/f², 1/f, 1

Have a go!
Please enable Java for an interactive construction (with Cinderella).