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Islamic Geometric Pattern Rebin Muhammad [email protected] Ohio university

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Page 1: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Islamic Geometric Pattern

Rebin [email protected]

Ohio university

Page 2: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

What is an Islamic Geometric Pattern (IGP)?

Page 3: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

What is an Islamic Geometric Pattern (IGP)?

It is a geometric shape or pattern that can be made using only compass and

straightedge.

Page 4: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

What kind of questions can we ask about IGP in

Math Circle?

Page 5: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

What kind of Question can we ask about following

IGP in Math Circle?

Page 6: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Pattern 1: 10 Loop-De-Loop Pattern

Page 7: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

First method for step by steps construction: (Only Construction Line)

Page 8: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Step 1

Page 9: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Step 2

Page 10: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Step 3

Page 11: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Step 4

Page 12: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Step 5 ( Construction line with pattern)

Page 13: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

The pattern without the construction line

Page 14: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Second method for step by steps construction: Construction Line and mathematical

guideline

Page 15: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

5

01

2

3

46

7

8

9A A+50 51 62 73 84 9

Step 1

Page 16: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

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

Page 17: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

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

Page 18: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

P P+3

P+4

P+5

Line between Points…

+ number of lines

P P+3

P+4

P+55 10

10

Page 19: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Can you Generalize the Loop-De-Loop Pattern ?

For which n are n -Loop-De-Loop is

constructible in the same way?

Page 20: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

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

Page 21: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Pattern 2: 8 -Loop-De-Loop

Page 22: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Number of Different Shape:4

Page 23: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Construction line for Pattern 2

Page 24: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Pattern 3: Khatam of Sulaiman

Page 25: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

Capplla Palatina: Palermo, Italy ( AD 1132)

Number of Different Shape:2

Page 26: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

The Koran of Rashid al-Din: Tabriz,Iran

Page 27: Islamic Geometric Patternsigmaa.maa.org/mcst/documents/ISLAMICGEOMETRY.pdf · Islamic Geometric Pattern Rebin Muhammad reben80@gmail.com Ohio university. What is an Islamic Geometric

A good Book to start doing IGP :

Islamic Geometric Patterns by Eric Broug