math presentation 2011 final

8/10/2019 Math Presentation 2011 FINAL

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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
http://en.wikipedia.org/wiki/File:Arabic_numerals-en.svg


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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


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
http://cuip.net/~dlnarain/golden/mattdamon.htm


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GOLDEN RATIO
http://cuip.net/~dlnarain/golden/mattdamon.htm


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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


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


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


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
http://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpghttp://en.wikipedia.org/wiki/File:Abu-Rayhan_Biruni_1973_Afghanistan_post_stamp.jpg


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Wrote one of his masterpieces, the Kitab al-Tafhim in

both Persian and Arabic

CONTRIBUTIONS


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Expressed the formula by means of chords

2

120

c chord Aa

u


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CONTRIBUTIONS


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Calculated the circumference of the earth

Gave the procedure to solve trigonometric problems

CONTRIBUTIONS


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Accurate determination of latitudes and longitudes

CONTRIBUTIONS


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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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