Posts tagged 'field-pentagonal-hexagonal'

GC-05.04 · Tran Quang Hung’s Shared-Base Regular Pentagon & Hexagon

Erect regular hexagon ABCDEF and regular pentagon AMNPF on the same side AF. The perpendiculars MQ and PR to diagonal MP at M and P intersect upper hexagon sides BC and DE at Q and R such that \(|CQ|/|QB| = |DR|/|RE| = \phi\).

GC-05.06 · Tran Quang Hung’s Fivefold Wu Xing Equilateral Star

Arrange five congruent equilateral triangles OV1W1 … OV5W5 of unit side with fivefold rotational symmetry around shared vertex O. The pentagram star joining outer vertices V1 … V5 cuts the radial sides of the equilateral triangles in the golden ratio, e.g. chord V2V5 cuts OW1 at F with \(|OF|/|FW1| = \phi\).