### Islamic Mathematicians

```Mathematics of Islamic
Art & Geometric Design
‫رياضيات الفن اإلسالمي‬
‫والتصميم الهندسي‬
Learning Objectives:
• To raise awareness of
Islamic contribution to
Mathematics
• To inspire Mathematics
through the study of
Islamic Geometric Designs
• To have fun with Islamic
Geometric Designs
• To create works of art
Formative Assessment to Determine
Knowledge Base to Track Progress
1.
After which Muslim Mathematician is the term “algorithm” named?
A. al-Karaji
2.
B. al Jurjani
C. ibn Haytham
D. al Firnas
B. ibn Battuta
C. Hasan Selebi
D. al Kindi
Which Muslim Mathematician, philosopher, musician and physicist
has been described as one of the “Twelve great minds of history”?
A. ibn Haytham
5.
D. al Jazari
Which Muslim Polymath is regarded as the first aviator?
A. ibn Firnas
4.
C. al Biruni
Which Muslim Mathematician is regarded as the “Father of Optics”?
A. al-Mawsili
3.
B. al Khawrizmi
B. al Wafa
C. al Rammah
D. al Kindi
Which Italian Mathematician played a major role in promoting the
use of Arabic numbers in Europe?
A. Galileo
B. de Vinci
C. Fibonacci
D. di Capprio
Thabit bin Qurra:
Greatest Muslim geometer
Kamal al-Din al-Farisi’s work
ibn al-Haytham
Algebra, Geometry
‫أشهر علماء الرياضيات المسلمين‬
Famous Muslim mathematicians
Omar Khayyam: Poet,
Mathematician, Astronomer
Al-Khwarizmi
The “Father of Algebra”
Al-Khwarizmi
The “Father of Algebra”
• The best known of the Islamic
Mathematicians
• Considered one of the greatest
Mathematicians of all times
• His books were studied long into
the Renaissance
• To him we owe the words:
Algebra and Algorithm
Al-Karaji
• Al-Karaji was the first to
use mathematical
induction to prove the
binomial theorem
– He proved that if the
first statement in an
infinite sequence of
statements is true,
then so is the next one.
He proved that: If (13 + 23) = (1 +2)2
Then (13 + 23 + 33) = (1 +2 + 3)2 and so on and so on
Omar Al Khayyam
• Famous poet and the writer of
the “Rubaiyat”, but an
important mathematician and
astronomer in his own right
The Moving Finger writes, and, having
written,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
Nasir Al-Din Al-Tusi
• The first to treat trigonometry as
a separate math discipline,
distinct from astronomy
• Gave the first extensive account
of spherical trigonometry
• One of his major mathematical
contributions was the
formulation of the famous law of
sine for plane triangles:
a⁄
b⁄
c⁄
=
=
(sin A)
(sin B)
(sin C)
ibn Al-Haytham
• Systemized conic sections
and number theory on
analytic geometry
• Worked on the beginnings of
geometry
• This in turn had an influence
on the development of René
Descartes' geometric analysis
and Isaac Newton's calculus.
Kamal Al-Din al-Farisi
• Applied the theory of
conic sections to solve
optical problems
• Pursued work in number
theory such as on
amicable numbers (e.g.,
220 & 284)
• Factorization of
an integer into powers
of prime numbers
Thabit bin Qurra
• Greatest Muslim geometer
• Played an important role in
preparing the way for
mathematical discoveries:
– extension of the concept of
number to (positive) real
numbers, integral calculus,
theorems in spherical
trigonometry, analytic and nonEuclidean geometry
• Was one of the first to create a
new proof for the Pythagorean
Theorem
Astrolabe
• The Astrolabe was highly
developed in the Islamic
World by 9th Century
• It was introduced to
Europe from Islamic
Spain (Al Andalus) in the
early 12th Century
• It was the most popular
astronomical instrument
What is Taught and What Should be Taught?
What is Taught:
What Should be Taught:
Francois Vieta was
the first to utilize
algebraic symbols.
Muslim mathematicians
invented algebra.
In early 9th century, they
In 1591, he wrote an introduced the concept
algebra book
of using letters for
describing equations unknown variables in
with letters.
equations.
What is Taught and What Should be Taught?
What is Taught:
What Should be Taught:
In 1614, John
Napier invented
logarithms and
logarithmic tables.
Islamic Mathematicians
invented logarithms and
produced logarithmic
tables.
These were common in
the Islamic world as early
as the 13th Century.
What is Taught and What Should be Taught?
What is Taught:
What Should be Taught:
The use of decimal
fractions in
mathematics was
first developed by
a Dutchman, Simon
Stevin, in 1589.
Al-Kashi's book, Key to
Arithmetic, was the
stimulus for the application
of decimals to whole
numbers and fractions.
It was written at the
beginning of the 15th
century.
What is Taught and What Should be Taught?
What is Taught:
What Should he Taught:
The concept that
numbers could be
less than zero was
unknown until 1545
when Cardano
introduced the idea.
Muslim mathematicians
introduced negative
numbers for use in
arithmetic functions at
least 400 years prior to
Cardano.
Mathematics of Islamic
Art & Geometric Design
Islamic art explores the geometric
systems of the regular division of
the circle
Islamic Art increases appreciation
and understanding of geometry
Working only with a ruler and
compass, students can discover
how to create and study many of
the geometric designs
Circles, Squares & Octagons
The eight-points star, made of two overlapping
squares in a circle, is the basis of many Islamic patters
Seven overlapping circles
Discovering Patterns with Triangle Grid
Discovering Patterns with Five Overlapping
Circle Grids
Discovering Patterns with the Diagonal Grid
Activities based on geometric Islamic
shapes, spaces and measures
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In Primary, students can learn to draw
and recognise circles, triangles,
squares, hexagons and octagons
Create pictures using 2-D shapes
Learn to identify lines of symmetry
Recognise reflective and rotational
symmetry
Upper Primary and Middle school
students can study symmetric
patterns to produce tessellations.
High school students can look at
molecular & crystal shapes and
calculate spaces occupied
Work of AAM Students
http://cmcuworkshops.net/?page_id=13
http://www.dynamicgeometry.com/
Review of Math topics using Jigsaws and
Islamic Geometric Designs
Formulator Tarsia is designed for Teachers of Mathematics to create
activities in a form of jigsaws for use in a class. It includes the powerful
equation editor for building the math-expressions for the activities.
3-D Applications (G&T Projects)
A few References on Islamic Art & Math
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Islamic Art and Geometric Design: Activities for Learning Copyright ©2004 by The
Metropolitan Museum of Art, New York:
http://www.metmuseum.org/~/media/Files/Learn/For%20Educators/Publications%20for%2
0Educators/Islamic_Art_and_Geometric_Design.pdf
Mathematics, Geometry and the Arts Resources (under: Islamic Art and the Sciences)
http://cmcuworkshops.net/?page_id=13 ; http://www.dynamicgeometry.com/
Islamic Art & Culture: A resource for Teachers
The connection between Islamic art and Mathematics
http://www.dartmouth.edu/~matc/math5.pattern/lesson5A&M.connection.html
Using Technology to investigate mathematics in Islamic Art:
http://cmcuworkshops.net/?page_id=13
Formulator Tarsia known earlier as Formulator Jigsaw is an editor designed for Teachers of
Mathematics creating the activities in a form of jigsaws or dominos etc for later use in a
class. It includes the powerful equation editor for building the math-expressions for the
mid=10
Book of Curiosities of the Sciences and Marvels of the Eyes
http://cosmos.bodley.ox.ac.uk/store/Teacher_s-Pack-Inside-pages.pdf
Geometric Concepts in Islamic Arts by El-Said
Islamic Design: A Genius for Geometry (Wooden Books) by Daud Sutton
Learning Objectives:
• To raise awareness of
Islamic contribution to
Mathematics
• To inspire Mathematics
through the study of
Islamic Geometric Designs
• To have fun with Islamic
Geometric Designs
• To create works of art
LOLOLO
```