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Muslim contribution to Mathematics - YouTube_mpeg4.mp4
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INTRODUCTION
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Plato Aristotle
INTRODUCTION
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INTRODUCTION
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INTRODUCTION
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INTRODUCTION
Tadabbur - DeliberationTafakkur - Thinking
Tavaqual - Reasoning
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MATHEMATICALREASONING
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AIM
To highlt the contributions of
Muslims in Mathematics
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SEQUENCE
PART-I
Contributions of Muslims in Algebra
Maj Muhammad Zafar
PART-II
Contributions of Muslims in Geometry
Capt Muhammad SaeedPART-III
Contributions of Muslims in Trigonometry
Capt Tahir Imran
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ACHIEVEMENTS OF MUSLIMS IN ALGEBRA
http://ebookee.org/go/?u=http://gigaimg.com/images/190590 -
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ALGEBRA
In Balance Out of Balance In balance again
Add 2 to left side Add 2 to right side
Describes relationships between things that vary over
time
It is a study in logic
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BRANCHES OF ALGEBRA
Elementary Algebra
Abstract Algebra
Linear Algebra
Universal Algebra
Algebraic Number Theory
Algebraic Geometry
Algebraic Combinatory
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MUHAMMAD IBN MUSA AL-KHWARIZMI
Born - c. 780Died - c. 850
Ethnicity - Persian
First to use zero as a place holder in positional
base notation
Algorithmhas been derived from his name
The word algebra is derived from his book
Hisab al-jabr w'al-muqabala(first book to be
written on algebra)
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CONTRIBUTIONS
First to use ZERO as place holder in positional based
notation
Introduced use of zero to Europe
00000001
10000000
10000001
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CONTRIBUTIONS
Provided base for Computer Algorithm
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CONTRIBUTIONS
Introduction of Arabic numerals based on place-value
decimal system
Arabic numerals provided a pivotal advance over the
cumbersome Roman numerals and assisted progress inscience and accounting
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CONTRIBUTIONS
Developed the decimal system
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CONTRIBUTIONS
Developed several arithmetical procedures including
Operations on fractions
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CONTRIBUTIONS
Provided procedure for solving linear and quadratic
equations
Squares equal roots (ax2= bx)
Squares equal number (ax2= c)
Roots equal number (bx = c)
Squares and roots equal number (ax2+ bx = c)
Squares and number equal roots (ax2+ c = bx)
Roots and number equal squares (bx + c = ax2)
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CONTRIBUTIONS
Developed Calculus of two errors, which led him to the
concept of differentiation
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BOOKS
Al-Jabr wa-al-Muqabilah from whose title came the nameAlgebra
Kitab al-Jama wal-Tafreeq bil Hisab al-Hindi
Kitab Surat-al-Ard
Istikhraj Tarikh al-Yahud (about the Jewish calendar)
Kitab al-Tarikh
Kitab al-Rukhmat (about sun-dials)
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THABIT IBN QURRA
Born - 826 CE, Harran
Died - February 18, 901, Baghdad
Era - Islamic Golden Age
Region - Islamic civilization
Main interest - Mathematics, Mechanics,
Astronomy, Astrology, Number
theory
Notable ideas - Early reformer of the Ptolemaic
system, A founder of statics,
Length of the sidereal year
http://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpg -
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CONTRIBUTIONS
Discovered an equation for determining the amicable
Numbers
(220, 284), (1184, 1210), (2620, 2924),
(5020,5564), (6232, 6368)
Established a rule for finding amicable numbers
a = (3 x 2n) 1
b = (3 x 2n-1) 1
c = (32 x 22n-1) 1
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CONTRIBUTIONS
Calculated the solution to a chessboard problem
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ABU KAMIL SHUJA IBN ASLAM
Born - c. 850
Died - c. 930
Era - Islamic Golden Age
Region - Egypt
Main interests - Algebra, Geometry
Major works - The Book of Algebra
Influenced - Al-Khawarizmi, Al-Karaji,
Fibonacci
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CONTRIBUTIONS
Contributions to algebra and geometry
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CONTRIBUTIONS
Considered the first mathematician to systematically use
accept irrational numbers
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CONTRIBUTIONS
Mathematical techniques were later adopted by
Fibonacci
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CONTRIBUTIONS
First Islamic mathematician to work easily with algebraic
Equations
Solved sets of non-linear simultaneous equations with
three unknown Variables
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BOOKS
Book of Rare Things in the Art of Calculation
Described a number of systematic procedures for finding
integral solutions for indeterminate equations
Book of Rare Things in the Art ofCalculation
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BOOKS
On Measurement and Geometry Wrote manual of geometry for non-
mathematicians, like land surveyors and other
government officials
Measurement and Geometry
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IBN AL-HAYTHAM
Born - July 1, 965 (age 1045) Basra
Died - Circa July 1, 965 (aged -75) Egypt
Fields - physicist and Mathematician
Known for - Book of Optics, Doubts Concerning
Ptolemy, On the Configuration of
the World, The Model of the
Motions,Treatise on Light, Treatise
on Place, scientific method,experimental science,
experimental physics,
Influences - Aristotle, Euclid, Ptolemy
Influenced - Averroes, Roger Bacon, Kepler
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CONTRIBUTIONS
Worked on number theory and introduced perfect
numbers and Golden Ratio
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
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Golden Ratio
Golden Ratio is an irrational number
It has an infinite number of decimal places andnever repeats itself
Rounded the Golden Ratio to 1.618
CONTRIBUTIONS
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FLORETS OF THE DAISY
34 : 21 = 1.618
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SPIRALSOF A PINECONE
13 : 8= 1.68 : 5 = 1.6
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SPIRALSOF A PINECONE
Scientists speculate that plants
that grow in spiral formation do so in
perfect numbers because this arrangementmakes for the perfect spacing for growth.
So for some reason, these numbers provide
the perfect arrangement for maximumgrowth potential and survival of the plant
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HUMAN HAND
HUMAN FOREARM
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HUMAN FOREARM
3
33
Ratio = 3/4
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GOLDEN RATIO
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a
=
Top-of-head to chin = cm
b
=
Top-of-head to pupil = cm
c
=
Pupil to nose tip = cm
d = Pupil to lip = cm
e
=
Width of nose = cmf = Outside distance
between eyes
= cm
g = Width of head = cm
h
=
Hairline to pupil = cm
i = Nose tip to chin = cm
j
=
Lips to chin = cm
k = Length of lips = cm
l = Nose tip to lips = cm
GOLDEN RATIO
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a/g = 1.6 cm
b/d = 1.6 cm
i/j = 1.6 cm
i/c = 1.6 cm
e/l = 1.6 cm
f/h = 1.6 cm
k/e = 1.6 cm
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GEOMETRY
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GEOMETRY
Geometry is a branch of mathematics that deals
with shapes and sizes
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POINT & LINE
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POINT & LINE
Point
Line
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POLYGONS
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POLYGONS
Any plane figure bounded by straight lines is a polygon
TRIANGLE
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TRIANGLE
A plane figure bounded by three straight lines
QUADRILATERAL
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QUADRILATERAL
A plane figure bounded by four straight lines
Trapezoids
Parallelograms
Rhombus
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SPHERE
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SPHERE
A surface where all points are equidistant from one
point
The equator on Earth is a great circle
POLYHEDRON
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POLYHEDRON
Polyhedron is a figure bounded by plane surfaces
PRISM & PYRAMID
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PRISM & PYRAMID
A polyhedron that has parallel and
congruent polygons
A polyhedron that has a polygon asits base and sides that consist of
triangles having a common vertex,
called the apex
GEOMETERY
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GEOMETERY
Muslim mathematicians gave the ideas in geometry
Architects
Decorators
Engineers
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GEOMETERY
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GEOMETERY
Navigators use to guide boats, planes and Space Ships
GEOMETERY
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GEOMETERY
To guide Vessels, aim Guns and Missiles by
military personnel
GEOMETERY
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GEOMETERY
Land Surveying, Navigation and Astronomy
GEOMETERY
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GEOMETERY
Architects and Engineers use geometry in planning
buildings, bridges and roads
GEOMETERY
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GEOMETERY
Reestablished boundaries of Nile river
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OMER IBN IBRAHIM AL-KHAYYAM
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OMER IBN IBRAHIM AL-KHAYYAM
Born - 1048
Died - 1131
School - Persian mathematics, Persian
poetry, Persian philosophy
Main interests - Poetry, Mathematics, Philosophy,
Astronomy
Influenced by - AbRayhn al-Brn, Avicenna
CONTRIBUTIONS
http://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPGhttp://en.wikipedia.org/wiki/File:Omar_Khayyam.JPG -
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CONTRIBUTIONS
Explained the difficulties in the postulates of Eucliden
Elements
Ratios
Modern continued fractions
Multiplication of ratios
Article of Khayyam is considered as the first treatment
of parallels axiom
CONTRIBUTIONS
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CONTRIBUTIONS
Gave the concept of Saccheri Quadrilateral
Proved the parallel postulate from Principle of the
philosopher
BOOKS
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BOOKS
Explanations of the difficulties in the
postulates of Euclidean's Elements
Risala Dar Wujud
ABU SAHL AL-QUHI
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ABU SAHL AL QUHI
Born - c. 940
Died - c. 1000
Era - Islamic
Region - Iran
Main interest - Physics, Mathematics and
Astronomy
Notable ideas - Archimedean and
Apollonian problems
CONTRIBUTIONS
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CONTRIBUTIONS
One of the greatest Muslim geometers
Many mathematical and astronomical writings are
ascribed to him
Leader of the astronomers working in 988 AD at the
observatory built by the Buwayhid
CONTRIBUTIONS
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CONTRIBUTIONS
Devoted his attention to those equations higher thanthe second degree
Solved and discussed the conditions of solvability
THABIT IBN QURRA
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THABIT IBN QURRA
Born - 826 CE, Harran
Died - February 18, 901, Baghdad
Era - Islamic Golden Age
Region - Islamic civilizationMain interest - Mathematics, Mechanics,
Astronomy, Astrology
Notable ideas - Early reformer of the Ptolemaicsystem, A founder of statics,
Length of the sidereal year
http://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpghttp://en.wikipedia.org/wiki/File:20010219-001-01.jpg -
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CONTRIBUTIONS
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CONTRIBUTIONS
Removed the difficulties of Euclideansgeometry
Duplication of the cube
Trisection of the angle
Quadrature of the circle
CONTRIBUTIONS
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CONTRIBUTIONS
Worked on Cubature, Quaderaturte and developed
integral calculus
NASIR AL-DIN AL-TUSI
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NASIR AL DIN AL TUSI
Birth - 18 February 1201
Death - 26 June 1274 (aged 73)
Ethnicity - Persian
Region - Iran
Main interests - Mathematics, Islamic Philosophy,Astronomy, Biology and Physics
Works - Rawda-yi Taslm, Tajrid al-'Aqaid,
Akhlaq-i- Nasri, Zij-i ilkhani, al-Risalah al-
Asturlabiyah, Al-Tadhkirah fi'ilm al-hay'ahInfluences - Avicenna, Fakhr al-Din al-Razi
Influenced - Ibn Khaldun, Qutb al-Din al-Shirazi, Ibn
al-Shatir
CONTRIBUTIONS
http://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpghttp://en.wikipedia.org/wiki/File:Nasir_al-Din_Tusi.jpg -
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CONTRIBUTIONS
one circle rolls inside the circumference of another
circle, periphery of first describe the diameter of second
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TRIGONOMETRY
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TRIGONOMETRY
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Deals with the relationships between the sides and
angles of a triangle
CLASSIFICATION OF TRIGONOMETRY
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SPHERICAL TRIGONOMETRY
PLANE GEOMETRY
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Deals with figures lying wholly in a single plane
Angle +ve
Clockwise rotation in the planeCounterclockwise rotation in the plane
Angle - ve
SPHERICAL TRIGONOMETRY
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Deals with triangles that are sections of the surface of a
sphere
Navigation
Astronomy
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CONTRIBUTIONS
ABU AL-WAFA BUZJANI
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Born - June 10, 940 Buzhgan
Died - 997 or 998 CE Baghdad
Era - Islamic Golden Age
Region - Islamic civilization
Main interests - Mathematics and Astronomy
Notable ideas - Tangent function Law of sines,
Several trigonometric identities
Influenced by - Al-Battani
CONTRIBUTIONS
http://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpghttp://en.wikipedia.org/wiki/File:Buzjani,_the_Persian.jpg -
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Gave Tangent function for problems involving right-
angled spherical triangle
CONTRIBUTIONS
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Developed a new technique to calculate sine tables
Graph of sine table
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CONTRIBUTIONS
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Demonstrate the set theorem for the general spherical
triangle
Introduced the theorem of the tangents for the spherical
oblique triangle
sin 2 sin cos
2 2
tansin
tan
bc
B
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CONTRIBUTIONS
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Presented definite form of secant and cosecant functions
CONTRIBUTIONS
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Almagest (Greek work on astronomy)
Solutions to determine the direction of Qibla
BOOKS
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Kitab Ilm al-Hisab
Al-Kitab al-Kamil
Kitab al-Handsa
ABU NASR MANSUR
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Born - 970, Gilan
Died - 1036, Ghazni
Fields - Astronomer Mathematician
Known for - Trigonometric Law of sines
CONTRIBUTIONS
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Well known for spherical sine law
CONTRIBUTIONS
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Focused on math, but some of his writings were on
astronomy
CONTRIBUTIONS
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Preserved and reworked many of the Greeks theorems
ARTICLES
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Properties of spherical triangles
Properties of systems of parallel circles on a sphere
Proof of Menelausstheorem
JAMSHID AL-KASHI
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Birth - 1380
Death - 22nd June, 1429
Ethnicity - Persian
Region - Iran
Main interests - Astronomy, Mathematics
Notable ideas - Pi decimal determination to
the 16th place
Works - Sullam al-Sama
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CONTRIBUTIONS
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Computed sin 1nearly equal to
Sin 10=
CONTRIBUTIONS
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Invented the following formula to determine sin10
3sin3 = 3sin - 4sin
ABU AL-RAYHAN AL-BIRUNI
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Born - September 5, 973, Persia
Died - December 15, 1048
Era - Islamic Golden Age
Region - Persia
Main interests - Physics, anthropology, comparative
sociology, astronomy, astrology,
history, geography, mathematics
Notable ideas - Founder of Indology
Major works - Tarikh al-Hind, The Masudi Canon,
Understanding Astrology
Influenced by - Aristotle, Ptolemy, Aryabhata,
Muhammad, Brahmagupta, Rhazes,
Influenced - Al-Sijzi, Avicenna, Omar Khayyam
CONTRIBUTIONS
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Wrote one of his masterpieces, the Kitab al-Tafhim in
both Persian and Arabic
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Expressed the formula by means of chords
2
120
c chord Aa
u
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Calculated the circumference of the earth
Gave the procedure to solve trigonometric problems
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Accurate determination of latitudes and longitudes
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Established the fact that the speed of light is far greater
than sound
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Q & A
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