Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric...
Transcript of Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric...
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What is an Islamic Geometric Pattern (IGP)?
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What is an Islamic Geometric Pattern (IGP)?
It is a geometric shape or pattern that can be made using only compass and
straightedge.
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What kind of questions can we ask about IGP in
Math Circle?
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What kind of Question can we ask about following
IGP in Math Circle?
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Pattern 1: 10 Loop-De-Loop Pattern
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First method for step by steps construction: (Only Construction Line)
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Step 1
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Step 2
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Step 3
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Step 4
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Step 5 ( Construction line with pattern)
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The pattern without the construction line
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Second method for step by steps construction: Construction Line and mathematical
guideline
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5
01
2
3
46
7
8
9A A+50 51 62 73 84 9
Step 1
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5
01
2
3
46
7
8
9A A+4
0 4
1 5
2 6
3 7
4 8
5 9
6 6+4=0
7 7+4=1
8 8+4=2
9 9+4=3
Steps 2,3
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5
01
2
3
46
7
8
9A A+3
0 3
1 4
2 5
3 6
4 7
5 8
6 9
7 7+3=0
8 8+3=1
9 9+3=2
Steps 4
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P P+3
P+4
P+5
Line between Points…
+ number of lines
P P+3
P+4
P+55 10
10
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Can you Generalize the Loop-De-Loop Pattern ?
For which n are n -Loop-De-Loop is
constructible in the same way?
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P P+2
P+3
P+48
P P+2
P+3
P+55 7
7
4
8
8 -Loop-De-Loop7 -Loop-De-Loop
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Pattern 2: 8 -Loop-De-Loop
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Number of Different Shape:4
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Construction line for Pattern 2
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Pattern 3: Khatam of Sulaiman
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Capplla Palatina: Palermo, Italy ( AD 1132)
Number of Different Shape:2
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The Koran of Rashid al-Din: Tabriz,Iran
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A good Book to start doing IGP :
Islamic Geometric Patterns by Eric Broug