Conclusion

A Landap Design

Muslim Mathematician

Mathematical Analysis

Suggested patterns

Introduction One creativity of mathematics can

be found on Muslim crafts. Though one would doubt of the word creativity together with math but it fits best on Muslim crafts.

As we can see on their crafts, our Muslim brothers and sisters have created a wide range of styles, forms and patterns which were definitely produced by mathematical knowledge. A pattern, whether in nature or art, relies upon three characteristics: a unit, repetition, and a system of organization.

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Mathematical Analysis

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Muslim mathematician

al-Khwārizmī, Muhammad ibn Mūsā(780-850 CE)

“FATHER OF ALGEBRA”

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ContributionsAl’Khwarizmi also gave a classification system for

quadratics. He devotes a chapter to each chapter in his treatise and gives methods in solving each differently.

Six Types of Quadratics:1. Squares equal to roots (x² = square root of 2) 2. Squares equal to numbers (x² = 2) 3. Roots equal to numbers (square root of x = 2) 4. Squares and roots equal to numbers (x² + 3x = 25) 5. Squares and numbers equal to roots (x² + 1 = 9) 6. Roots and numbers equal to squares (3x + 4 = x²)

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Contributions  Al’Khwarizmi also gives geometric proofs of these methods. In 1145, Savasorda published Liber embadorum that gave the complete solution of the quadratic equations. In 1494, the first edition of Summa de arithmetica, geometrica, proportioni et proportionalita was published. It sets out equation systematically and algebraically, as in the following translated equations:

(6 + square root of 10)(18 - square root of 90) = (108 - square root of 3240 +

square root of 3240 - square root of 900) which is 78

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Muslim Mathematician

Mathematical Analysis

Suggested patterns

A Landap design

Conclusion

A Landap Design

Muslim Mathematician

Mathematical Analysis

Suggested patterns

The yellow lines are made using translation.

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Mathematical Analysis

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The curved patterns are made using reflection.

line of reflection

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MathematicalAnalysis

• When a figure is translated, each point of the figure is moved the same distance.

Translation (or slide)

rigid motion with repetition

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Mathematical Analysis

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MathematicalAnalysis

Properties of Line Reflection 1. When a figure is reflected in a line, the

image is congruent to the original figure.2. A reflection line is perpendicular to each

segment that joins an original point to its image. The reflection line divides each of these segments into two equal halves.

rigid motion with repetitionacross a line (axis)

Reflection

glide reflection

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Suggested Patterns

By simply the use of letter F for presenting patterns, the following outcomes are presented each of are of the different geometric patterns:

reflections +glide reflections

rotations +glide reflections

rotations +reflections + reflections

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Muslim Mathematician

Mathematical Analysis

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Suggested Patterns

reflections +rotations

rotations

reflections +rotations

Conclusion

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Muslim Mathematician

Mathematical Analysis

Suggested patterns

Conclusion

Mathematics has the ability to define every figure. Every mathematical concept is a great help to learn mathematics as it defines this idyllic and challenging world of ours.

Conclusion

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Muslim Mathematician

Mathematical Analysis

Suggested patterns

References

Books• Allan Bellman, Sadie Chaves Bragg et. al.

Advanced Algebra Tools for a Changing World Prentice Hall Needham, Massachusetts New Jersey , 1998.

• Gordon Fuller et. al. Analytic Geometry Addison Wesley Publishing Co. NY 1992.

Internethttp://www.algebra.com/algebra/about/history/