Golden Rectangle Dissections

Author : Gavin Theobald

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The golden rectangle {Rϕ} is a rectangle of proportions 1:(1+√5)/2 or approximately 1:1.6180. If a square is removed from one end of the rectangle then the remainder will have the same proportions as the original.

{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{9} Enneagon
{10} Decagon
{12} Dodecagon
{5/2} Pentagram
{6/2} Hexagram
{8/2} Octagram
{8/3} Octagram
{10/2} Decagram
{12/2}  Dodecagram
{R√2} Silver Rectangle
{R2} Domino
{G} Greek Cross
{L} Latin Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
4 3 6 5 7 6 9 6 10 7


5/2 6/2 7/2 7/3 8/2 8/3 9/2 9/3 9/4 10/2 10/3 10/4 12/2 12/3 12/4 12/5
7 5 8 7 10 9

Triangle — Golden Rectangle (4 pieces)

The dissection is hingeable.

Square — Golden Rectangle (3 pieces)

The dissection is translational.

Pentagon — Golden Rectangle (6 pieces)

Hexagon — Golden Rectangle (5 pieces)

The dissection is translational.

Heptagon — Golden Rectangle (7 pieces)

Octagon — Golden Rectangle (6 pieces)

Enneagon — Golden Rectangle (9 pieces)

Decagon — Golden Rectangle (6 pieces)

Dodecagon — Golden Rectangle (7 pieces)

Discovered by Harry Lindgren (1964).

Golden Rectangle — Pentagram (7 pieces)

Golden Rectangle — Hexagram (5 pieces)

Discovered by Harry Lindgren (1964).

The dissection is translational.

Golden Rectangle — Octagram {8/2} (8 pieces)

Golden Rectangle — Octagram {8/3} (7 pieces)

The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Golden Rectangle — Decagram {10/2} (10 pieces)

Golden Rectangle — Dodecagram {12/2} (9 pieces)

Silver Rectangle — Golden Rectangle (3 pieces)

The dissection is translational and hingeable.

Golden Rectangle — Domino (3 pieces)

The dissection is translational and hingeable.

Golden Rectangle — Greek Cross (5 pieces)

The dissection is translational.

Golden Rectangle — Latin Cross (5 pieces)

Discovered by Harry Lindgren (1964).

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