Tiling L-Shape With Squares
7
∗ b × h B × H B × H − b × h b × h B × H ∗
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Transcript of Tiling L-Shape With Squares
8/10/2019 Tiling L-Shape With Squares
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∗
b × h
B × H
B × H − b × h
b × h
B × H
∗
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H h b
B
B×H −
b × h
BH
= M
bh
M
Q
|M | = 1, M ij ≥ δ ij, M ij ∈ Q
Q
< b, h >=< B, H >
< b, h >= 1
dim < b,h >= 2 M
α1, α2 < b,h >
b = α1b1 + α2b2 h = α1h1 + α2h2 bh
=
b1 b2h1 h2
α1
α2
BH
=
B1 B2H 1 H 2
α1α2
B1 B2
H 1 H 2
α1
α2
= M
b1 b2h1 h2
α1
α2
α1 α2
[α1, α2]T
M =
B1 B2
H 1 H 2
b1 b2h1 h2
−1
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M = 1
b ∧ h
B ∧ h b ∧ BH ∧ h b ∧ H
∧
< α1, α2 >
L1 L2
L1 L2
M
B1 B2
H 1 H 2
= M
b1 b2h1 h2
|M | = 1, M ij ≥ δ ij, M ij ∈ Q
M
M
M
B × H − b × h
M
|M | = 1, M ij ≥ δ ij, M ij ∈ Q
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BH
= M
bh
B × H − b × h
B × H − b × h
b ×h
G
• X a a ∈ Q
b × h
(b + ha) × h
h
b
X a−→ h
b ah
• Y a a ∈ Q
b × h
b × (h + ba)
h
b
Y a−→ h
ba
G
h
b
X a2Y a1−→
b × h [b, h]T
X a Y a R2 R2
Q
X a =
1 a0 1
Y a =
1 0a 1
G
X a
Y a
G ∈ G ⇐⇒ G = X a1Y a2 · ·X aK−1Y aK
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• P 1
B × H
•
P 3
B × H
• P 2 R = h/b
P 1
P 2
b × h
R
b P 1 P 3 B
R
h
P 1
P 3
H
h/b
P 1, P 2, P 3
P 0 P 1 P 2
P 3
• P 1 P 0 R1
•
P 2 P 0
R2
• P 3 P 0 R3
R1, R2, R3
P 1
P 2
P 3
R1, R2, R3 ∈ Q
R
P 1
P 2
V P 1 P 3
V
I
=
R1+R3
R1
1
R1
R1R2+R1R3+R2R3
R1
R1+R2
R1
vRiR
V = H I = B vR = h iR = b BH
=
R1+R2
R1
R1R2+R1R3+R2R3
R1
1
R1
R1+R3
R1
bh
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|M | = 1
