Harry Lindgren’s Book Improvements

Recreational Problems in Geometric Dissections and How to Solve Them (1972)

The following list of improvements to Harry Lindgren’s book is in book order. The lists are not complete.

Figure DissectionDescriptionOld
#pieces		New
#pieces
2.11 {6}–{8} Hexagon to Octagon 9 8
3.6 {5}–{8} Pentagon to Octagon 9 8
6.1 {4}–{7} Square to Heptagon 9 7
6.5 {4}–{5/2} Square to Pentagram 8 7
7 end {4}–2×{10} Square to two Decagons 1310
12.6 {4}–{4−} Square to Truncated Square 5 4
12.6 {4}–{4+} Square to Augmented Square 5 4
15.1 {7}–{3} Heptagon to Triangle 9 8
15.7 {7}–{8} Heptagon to Octagon 1310
15.8 {7}–{5} Heptagon to Pentagon 11 9
15.9 {7}–{6} Heptagon to Hexagon 11 8
15.10 {7}–{6/2} Heptagon to Hexagram 11 9
15.11 {7}–{L} Heptagon to Latin Cross 12 8
15 end {7}–{4} Heptagon to Square 9 7
16.3,
16.5 		{9}–{3} Enneagon to Triangle 9 8
16.8 {9}–{4} Enneagon to Square 12 9
16.9 {9}–{6} Enneagon to Hexagon 1410
16.10-14 {9}–{3} Enneagon to Triangle 9 8
17.2 {4}–{10} Square to Decagon 8 7
17 end {8}–{G} Octagon to Greek Cross 9 8
19.2 {5/2}–{6} Pentagram to Hexagon 10 9
19.3 {5/2}–{3} Pentagram to Triangle 9 7
20.3 {10/2}–{5} Decagram to Pentagon 8 7
21.14 {3}–7×{3} Triangle to seven Triangles 1311
21.27 {5}–2×{5} Pentagon to two Pentagons 11 9
21.34 {6}–2×{6} Hexagon to two Hexagons 9 8
D6 {8}–{6/2} Octagon to Hexagram 9 8
D10 {6/2}–{L} Hexagram to Latin Cross 9 8
D13 {6}–{6/2} Hexagon to Hexagram 7 6
D18 {3}–{8} Triangle to Octagon 8 7
D19 {5}–{8} Pentagon to Octagon 9 8
D25 {6}–{8} Hexagon to Octagon 9 7
D26 {12}–{6/2} Dodecagon to Hexagram 10 9
D27 {4}–{7} Square to Heptagon 9 7
D28 {7}–{Rϕ} Heptagon to Golden Rectangle 9 7
D29 {6}–{7} Hexagon to Heptagon 1110
D30 {7}–{G} Heptagon to Greek Cross 12 9
D31 {4}–{9} Square to Enneagon 12 9
D32 {9}–{Rϕ} Enneagon to Golden Rectangle 12 9
D35 {6}–{10} Hexagon to Decagon 9 8
G4 {10}–{5} Decagon to Pentagon 10 9
G5 {10}–{3} Decagon to Triangle 8 7
G6 {10}–{Rϕ} Decagon to Golden Rectangle 7 6
G7-8 {10}–{8} Decagon to Octagon 1210
H1 {10}–{7} Decagon to Heptagon 1311
H7 {4}–{12/3} Square to Dodecagram 10 8

This list of improvements is in dissection order.

Figure DissectionDescriptionOld
#pieces		New
#pieces
21.14 {3}–7×{3} Triangle to seven Triangles 1311
15.1 {3}–{7} Triangle to Heptagon 9 8
16.3,
16.5 		{3}–{9} Triangle to Enneagon 9 8
D18 {3}–{8} Triangle to Octagon 8 7
16.10-14 {3}–{9} Triangle to Enneagon 9 8
G5 {3}–{10} Triangle to Decagon 8 7
19.3 {3}–{5/2} Triangle to Pentagram 9 7
6.1 {4}–{7} Square to Heptagon 9 7
15 end {4}–{7} Square to Heptagon 9 7
D27 {4}–{7} Square to Heptagon 9 7
16.8 {4}–{9} Square to Enneagon 12 9
D31 {4}–{9} Square to Enneagon 12 9
7 end {4}–2×{10} Square to two Decagons 1310
17.2 {4}–{10} Square to Decagon 8 7
6.5 {4}–{5/2} Square to Pentagram 8 7
H7 {4}–{12/3} Square to Dodecagram 10 8
12.6 {4}–{4−} Square to Truncated Square 5 4
12.6 {4}–{4+} Square to Augmented Square 5 4
21.27 {5}–2×{5} Pentagon to two Pentagons 11 9
15.8 {5}–{7} Pentagon to Heptagon 11 9
3.6 {5}–{8} Pentagon to Octagon 9 8
D19 {5}–{8} Pentagon to Octagon 9 8
G4 {5}–{10} Pentagon to Decagon 10 9
20.3 {5}–{10/2} Pentagon to Decagram 8 7
21.34 {6}–2×{6} Hexagon to two Hexagons 9 8
15.9 {6}–{7} Hexagon to Heptagon 11 8
D29 {6}–{7} Hexagon to Heptagon 1110
2.11 {6}–{8} Hexagon to Octagon 9 8
D25 {6}–{8} Hexagon to Octagon 9 7
16.9 {6}–{9} Hexagon to Enneagon 1410
D35 {6}–{10} Hexagon to Decagon 9 8
19.2 {6}–{5/2} Hexagon to Pentagram 10 9
D13 {6}–{6/2} Hexagon to Hexagram 7 6
15.7 {7}–{8} Heptagon to Octagon 1310
H1 {7}–{10} Heptagon to Decagon 1311
15.10 {7}–{6/2} Heptagon to Hexagram 11 9
D28 {7}–{Rϕ} Heptagon to Golden Rectangle 9 7
D30 {7}–{G} Heptagon to Greek Cross 12 9
15.11 {7}–{L} Heptagon to Latin Cross 12 8
G7-8 {8}–{10} Octagon to Decagon 1210
D6 {8}–{6/2} Octagon to Hexagram 9 8
17 end {8}–{G} Octagon to Greek Cross 9 8
D32 {9}–{Rϕ} Enneagon to Golden Rectangle 12 9
G6 {10}–{Rϕ} Decagon to Golden Rectangle 7 6
D26 {12}–{6/2} Dodecagon to Hexagram 10 9
D10 {6/2}–{L} Hexagram to Latin Cross 9 8

Square — Truncated Square (4 pieces)

Square — Truncated Square (4 pieces with 1 turned over)

These dissections use the method of completed tessellations. The first one uses curved pieces to avoid turning one over.

Square — Augmented Square (4 pieces)

Square — Augmented Square (4 pieces)

Square — Augmented Square (4 pieces)

These dissections use the method of completed tessellations. They also use curved pieces to avoid turning one over.