Center of a Golden Rectangle
Center of a Golden Rectangle
The center of a golden rectangle (GR), shown as the small gold sphere in the figure, is defined as the intersection of the diagonal of a GR formed by a square with a smaller attached GR and the diagonal of the smaller GR.
S
The square in is the top face of a cube on which an infinite series of cubes is constructed, connected edge to edge.
S
Each cube in the series is reduced by (the golden ratio) relative to the previous one.
ϕ
Suppose the side of the initial cube is 1. The extended red diagonal of the small GR intersects the far vertex of the black square with side . That vertex and the center of the GR are on circle 3, which is traced by the vertex when the series of cubes is folded back into the GR.
2
ϕ
The circles placed on the vertices of the squares also pass through the center of the GR.