Islamic & arabic contributions to mathematics

ISLAMIC /
ARABIAN
Contribution to Math/Science:
Its History & DiscoveryPRESENTED BY:
TRUDI FERNANDEZ
JUWAN PALACIO
TONY GUERRA

The Power Of Mathematics
Mathematics helped bring about…
Geometric Art & Architecture
Astronomy
Geography
Physics
Cryptography

FOOD FOR THOUGHT:
There were:
• Over 260
Muslim
Scientist in the
golden age.
There was:
• 1001
inventions
exhibited in
Abu Dhabi in
2011.
Prophet
Mohammed:
• Invented the
toothbrush.
Al-Khwarizmi
• Invented the
number zero.

The Concept of Zero:
 One concept of how zero came about was from counting rocks in the sand,
when you remove or take away something, a space stayed in the form of a
circular crater, representing that something was there and thus taking its
value as nothing.
 For some it’s a symbol of inifity, since 1/infinity is equivalent to zero.
 For others it’s the infinite revolution that the earth orbits in space.
 Also what inspired the search engine google is the number 1-followed by a
hundered zeros, and a google plex is ten raised to the power of a google.

Islamic / Arabian Empire & The Golden Ratio

• India had a glorious past in every walks of knowledge.
• However, the Indian contribution to the field of mathematics are not so well known.
• Mathematics took its birth in India before 200 BC,ie the Shulba period.
• The sulba sutras were developed during Indus valley civilization.
• There were seven famous Sulbakars (mathematicians of indus valley civilization) among
which Baudhyana was the most famous. There works were mainly based on geometry and
includes enunciation of today’s Pythagoras theorem and obtaining square root of 2 correctly
up to 5 decimals.
Arabic Mathematics

The classic period: 400AD-1200AD.
• This period is often known as the golden age of Indian Mathematics, with
mathematicians such as: Aryabhata, Varahamihira, Brahmagupta, Bhaskara
I, Mahavira, and Bhaskara II.
• Their contributions would spread to Asia, the Middle East, and eventually to Europe,
leading to further developments that now form the foundations of many areas in
mathematics.
• Their works also gave contribution to the fields of astronomy and science.
Arabic Mathematics

The Islamic world: 622AD-1600AD.
• Most scientists in this period were Muslims and Arabic was the dominant language.
• Arabic was used as the chosen written language of most scholars throughout the
Islamic world at the time.
• Contributions were made by people of different ethnic groups (Arabs, Persians,
Berbers, Moors, Turks, etc.) and sometimes different religions (Muslims, Christians,
Jews, etc.).
• Islamic science and mathematics flourished under the Islamic Empire, established
across the Middle East, Central Asia, North Africa, Sicily, the Iberian Peninsula, and
in parts of France and India in the 8th century. The center of Islamic mathematics was
located in Persia, but expanded to the west and east over time. They were able to fuse
together the mathematical development of both Greece and India.
Islamic Mathematics

• During the 1st century, there were barely any mathematical achievements or
knowledge since the other empires had no intellectual drive, not until the 2nd half of
the 18th century.
• The Muslim Abbasid caliph al-Mamun (809-833) supposedly had a vision where
Aristotle appeared to him, and as a consequence al-Mamun ordered that Greek works,
such as Ptolemy’s Almagest & Euclid’s Elements, be translated into Arabic.
• The House of Wisdom was set up in Baghdad around 810, and work started almost
immediately on translating the major Greek and Indian mathematical and astronomy
works into Arabic.
Islamic Mathematics

• These works were given to the Muslims in the Byzantine Empire in exchange for
peace between the two empires.
• It is through the work of Islamic translators that many ancient Greek texts have
survived throughout history, translations into Arabic at the time were made by
scientists and mathematicians, not by language experts ignorant of mathematics. The
translating was not done for its own sake, but was done as part of the current research
effort.
• In many respects the mathematics studied today is far closer in style to that of the
Arabic/Islamic contribution than to that of the Greeks.
Islamic Mathematics

• The Qu’ran encouraged the accumulation of knowledge.
• The Qur'an says: "They ask you about the waxing and waning phases of the crescent
moons, say they are to mark fixed times for mankind and Hajj.“
• In order to observe holy days on the Islamic calendar, astronomers initially used
Ptolemy's method to calculate the place of the moon and stars.
• Islamic months do not begin at the astronomical new moon, instead they begin when
the thin crescent moon is first sighted in the western evening sky.
Religion & Mathematics

• It led Muslims to find the phases of the moon in the sky, leading to new mathematical
calculations. Predicting just when the crescent moon would become visible was a test
for the Islamic mathematical astronomers.
• To predict the first visibility of the moon, it was essential to express its motion
according to the horizon, and this problem demands pretty complicated spherical
geometry.
• However, finding the direction of Mecca and knowing the specific times for prayer
(by looking @ constellations/stars) motivated the Muslims to study and develop
knowledge of spherical geometry.
Religion & Mathematics

Religion / Mathematics / Architecture
The Dome Of The Rock. The first Muslim
masterpiece, was built in 687 A.C. by Caliph
Abd al-Malik, half a century after the death of
the Prophet Muhammad (s). The rock marks the
site from where Prophet Muhammad (s) made
his Miraaj or Night Journey into the heavens
and back to Makkah (Qur'an 17:1). The Dome
of the Rock presents the first example of the
Islamic world-view and is the symbol of the
oneness and continuity of the Abrahamic, i.e.
Jewish, Christian and Muslim faith.

Religion / Mathematics / Architecture
The Taj Mahal in India was built
by a grief-stricken emperor Shah
Jahan. His wife Mumtaz Mahal
died in 1631 while giving birth to
their 14th child. Construction of the
Taj Mahal began one year later and
it was built to be the final resting
place of Mumtaz Mahal.

• First pharmacy & drug store open in Islamic world
• First library named “Baith-ul-Hikma” open in Islamic world
• First hospital open in Islamic world name “Bimeristan”
• First telescope was invented
• Declared that Earth is sphere
• Algorithm was founded
8th Century Accomplishments

• First attempt on flight was made
• Windmill was invented
• First university open in Islamic world
• Clock was invented

• Graph paper was invented
• First sugar refinery mill was made
• Base of modern surgery was led
• The circumference, diameter and radius of earth was determined

• Speed of light is finite
• Speed of light is faster than sound
• The first globe was made
• First mechanical clock
• Gun powder was invented
• Blood circulatory system of human body
• Largest hospital of that time was built

• Al-Hassār, developed the modern symbol for fractions in the 12th century.
• Abū al-Hasan ibn Alī al-Qalasādī, developed an algebraic notation which affected the
rise towards the introduction of algebraic symbols in the 15th century.
12th – 15TH Century Accomplishments

• Aryabhata - Astronomer who gave accurate calculations for astronomical constants, 476AD-
520AD
• Aryabhata II
• Bhaskara I
• Brahmagupta - Helped bring the concept of zero into arithmetic (598 AD-670 AD)
• Bhāskara II
• Mahavira
• Pavuluri Mallana - the first Telugu Mathematician
• Varahamihira
• Shridhara (between 650-850) - Gave a good rule for finding the volume of a sphere.
Classical Mathematicians (5thC to 11thC

Banū Mūsā (c. 800 – 873)
three brothers in Baghdad; most famous mathematical treatise: The Book of the
Measurement of Plane and Spherical Figures;
The eldest, Ja’far Muḥammad (c. 800) specialized in geometry and astronomy;
Aḥmad (c. 805) specialized in mechanics and wrote On mechanics;
The youngest, al-Ḥasan (c. 810) specialized in geometry and wrote The elongated
circular figure.
Ikhwan al-Safa' (first half of 10th century)
group wrote series 50+ letters on science, philosophy and theology. The first letter is
on arithmetic and number theory, the second letter on geometry.

Labana of Cordoba (Spain, ca. 10th century)
Islamic female mathematicians & secretary of the Umayyad Caliph al-Hakem II;
could solve the most complex geometrical and algebraic problems known in her time.
Al-Hassar (ca.1100s)
Developed the modern mathematical notation for fractions and the digits he uses for
the ghubar numerals also cloesly resembles modern Western Arabic numerals.
Ibn al-Yasamin (ca. 1100s)
first to develop a mathematical notation for algebra
Abū al-Hasan ibn Alī al-Qalasādī (1412-1482)
Last major medieval Arab mathematician; Pioneer of symbolic algebra

• Narayana Pandit
• Madhava of Sangamagrama some elements of Calculus
• Parameshvara (1360–1455), discovered drk-ganita, a mode of astronomy based on
observations, Madhava's Kerala school
• Nilakantha Somayaji,1444-1545 - Mathematician and Astronomer, Madhava's Kerala
school
• Mahendra Suri (14th century)
• Shankara Variyar (c. 1530)
• Raghunatha Siromani, (1475–1550), Logician, Navadvipa school
Medieval to Mughal period Mathematicians

• Aryabhatta was born in 476A.D in Kusumpur, India.
• Is the first well known Indian mathematician.
• Born in Kerala, completed his studies at the university of Nalanda.
• Was the first person to say that Earth is spherical and it revolves around the sun.
• He gave the formula(a + b) ² = a² + b² + 2ab
Aryabhata

Aryabhata worked on the approximation for pi , and may have come to the conclusion
that is irrational.
"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference
of a circle with a diameter of 20,000 can be approached."
This implies that the ratio of the circumference to the diameter is
((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to
five significant figures.
Aryabhata

He was born at Bori, in Parbhani district of Maharashtra state in India in 7th century.
He was the first to write Hindu-Arabic numerals and with zero with a circle.
He gave importance to sine function
Bhaskara 1

He was born in 1114 A.D. at Bijjada Bida (Bijapur, Karnataka) in the Sahyadari Hills.
He was the first to declare that any number divided by zero is infinity and that the sum of
any number and infinity is also infinity.
Bhaskara can also be called the founder of differential calculus. He gave an example of
what is now called "differential coefficient" and the basic idea of what is now called
"Rolle's theorem".
Unfortunately, later Indian mathematicians did not take any notice of this. Five centuries
later, Newton and Leibniz developed this subject.
Introduced chakrawal, or the cyclic method, to solve algebraic equations. Six centuries
later, European mathematicians like Galois, Euler and Lagrange rediscovered this method
and called it "inverse cyclic".
Bhaskara 2

He has written a lot about zero, surds, permutation and combination.
He wrote, “The hundredth part of the circumference of a circle seems to be straight. Our
earth is a big sphere and that’s why it appears to be flat.”
He gave the formulae like sin(A ± B) = sinA.cosB ± cosA.sinB
Suggested simple methods to calculate the squares, square roots, cube, and cube roots of
big numbers.
The Pythagoras theorem was proved by him in only two lines. Bhaskara's 'Khandameru'is
the famous Pascal Triangle.
Bhaskara 2

He was an Indian mathematician and astronomer who wrote many important works on
mathematics and astronomy.
Born in 598 AD in Bhinmal city in the state of Rajasthan. Renowned for introduction of
negative numbers and operations on zero into arithmetic.
Gave the formula for the area of a cyclic quadrilateral as where s is the semi perimeter.
explained how to find the cube and cube-root of an integer and gave rules facilitating the
computation of squares and square roots.
gave rules for dealing with five types of combinations of fractions. He gave the sum of the
squares of the first n natural numbers as n(n + 1)(2n + 1)⁄ 6 and the sum of the cubes of the first n
natural numbers as (n(n + 1)⁄2)².
Brahmagupta

He gave the solution of the indeterminate equation Nx²+1 = y².
Founder of the branch of higher mathematics known as "Numerical Analysis".
The statement a negative integer multiplied by a negative integer give a positive integer and
many other fundamental operation first appeared in his treatise Bhramasphutasiddhanta.
But how he came to the conclusion was unknown.
Furthermore, he pointed out, quadratic equations (of the type x2 + 2 = 11, for example)
could in theory have two possible solutions, one of which could be negative, because 32 = 9
and -32 = 9.
Brahmagupta

In addition to his work on solutions to general linear equations and quadratic equations,
Brahmagupta went yet further by considering systems of simultaneous equations (set of
equations containing multiple variables), and solving quadratic equations with two
unknowns, something which was not even considered in the West until a thousand years
later, when Fermat was considering similar problems in 1657.
Brahmagupta

Mahavira was a 9th-century Indian mathematician from Gulbarga who asserted that the
square root of a negative number did not exist.
He gave the sum of a series whose terms are squares of an arithmetical progression and
empirical rules for area and perimeter of an ellipse.
He separated Astrology from Mathematics.
Expanded on the same subjects on which Aryabhata and Brahmagupta contended, but he
expressed them more clearly.
establishment of terminology for concepts such as equilateral, and isosceles triangle;
rhombus; circle and semicircle.
Mahabira

Born 10th-century Indian physist.
He suggested the damming of the Nile river.
Scientifically explained the rainbow in detail.
Founder of optics.
Excellent studies on the reflection and refraction of light.
Ibn Al Haytham

The term algebra is derived from the Arabic term al-jabr in the title of Al-Khwarizmi's
Al-jabr wa'l muqabalah.
Originally used the term al-jabr to describe the method of "reduction" and "balancing",
referring to the transposition of subtracted terms to the other side of an equation.
Before the fall of Islamic civilization, the Arabs used a fully abstract algebra, where the
numbers were spelled out in words.
They later replaced the words with Arabic numerals, but the Arabs never developed a
symbolic algebra until the work of Ibn al-Banna al-Marrakushi (13th cent) & Abū al-
Hasan ibn Alī al-Qalasādī (15th cent)
Algebra

There were 4 stages in the development of Algebra :
Geometric Stage : where the concepts of algebra are largely geometric
Static equation-solving stage : find #s satisfying certain relationships
Dynamic function : where motion is a primary idea
Abstract Stage : where mathematical structure plays an essential role
Algebra

Omar Khayyám (c. 1050-1123) wrote a book on Algebra that went beyond Al-Jabr.
Omar Khayyám gave both arithmetic & geometric solutions for quadratic equations, but
only gave geometric solutions for general cubic equations (he thought that arithmetic
solutions were impossible).
His method of solving cubic equations by using intersecting conics had been used by
Menaechmus, Archimedes, and Alhazen. However, Omar was about to generalize the
method using only positive roots and didn’t go past the 3rd degree.
He also saw a strong relationship between Geometry and Algebra
Geometric Algebra

Successors of Muhammad ibn Mūsā al-Khwārizmī (born 780) undertook a organized
application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to
the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was
how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the
numerical solution of equations, the new elementary theory of numbers, and the
geometric construction of equations arose.
Al-Mahani (born 820) conceived the idea of reducing geometrical problems to problems
in algebra. Al-Karajii (born 953) completely freed algebra & geometrical operations and
replaced them with the arithmetical type of operations.
Thabit ibn Qurra (born 836)  positive #s, real #s, intergral calculus, theorems in
spherical trigonometry, analytic geometry, and non-Euclidean geometry. He also wrote a
book on the composition of ratios. Thabit started a trend which led eventually to the
generalization of the number concept. Thabit also made a generalization of the
Pythagorean theorem, which he extended to all triangles in general
Thabit was critical of the ideas of Plato & Aristotle (especially motion)
Geometry

Around 1000 AD, Al-Karaji (using mathematical induction), found a proof for the sum of
integral cubes. Al-Karaji was praised for being "the first who introduced the theory of
algebraic calculus.
Shortly afterwards, Ibn al-Haytham, an Iraqi mathematician, was the first to derive the
formula for the sum of the fourth powers/degree, and came close to finding a general
formula for the integrals of any polynomials.
This was fundamental to the development of infinitesimal and integral calculus
Calculus

Arabic Numerals
In the Arab world (until early modern times) the Arabic numeral system was often
only used by mathematicians
Decimal Fractions
decimal fractions were first used five centuries before by the Baghdadi mathematician
Abu'l-Hasan al-Uqlidisi as early as the 10th century.
Real Numbers
In Middle Ages acceptance of zero, negative, integral and fractional numbers, first by
Indian and Chinese, and then by Arabic mathematicians, who were also the first to
treat irrational numbers as algebraic objects, which was made possible by the
development of algebra. Arabic mathematicians merged the concepts of "number" and
"magnitude" into a more general idea of real numbers, and they criticized Euclid's
idea of ratios, developed the theory of composite ratios, and extended the concept of
number to ratios of continuous magnitude
Arithmetic

Number Theory
Ibn al-Haytham solved problems involving congruences.
In his Opuscula, he considers the solution of a system of congruences, and gives two
general methods of solution. His first method (canonical method) involved Wilson's
theorem, while his second method involved a version of the Chinese remainder
theorem.
Another contribution to number theory is his work on perfect numbers. In his
Analysis and synthesis, was the first to discover that every even perfect number is of
the form 2n−1(2n − 1) where 2n − 1 is prime, but he was not able to prove this result
successfully (Euler later proved it in the 18th century).
14th century, Kamāl al-Dīn al-Fārisī made a number of important contributions to
number theory. His most impressive work in number theory is on amicable numbers.
In Tadhkira al-ahbab fi bayan al-tahabb introduced a major new approach to a whole
area of number theory, introducing ideas about factorization and combinatorial
methods. In fact, al-Farisi's approach is based on the unique factorization of an
integer into powers of prime numbers.
Arithmetic

Number Theory
14th century, Kamāl al-Dīn al-Fārisī made a number of important contributions to
number theory.
His most impressive work in number theory is on amicable numbers.
In Tadhkira al-ahbab fi bayan al-tahabb introduced a major new approach to a whole
area of number theory, introducing ideas about factorization and combinatorial
methods.
In fact, al-Farisi's approach is based on the unique factorization of an integer into
powers of prime numbers.
Arithmetic

50 : 50
There were Over ………. Muslim scientists
in the golden age
A: 200 B: 206
D: 2c: 201
10,000 Rupee
100,000 R
1,000,000 R
100 Rupee

50 : 50
There was ………. Exhibition in 2011
at Abu-Dhabbi
A: 2011 B: 1011
D: 2000c: 1001
100 Rupee
100,000 R
1,000,000 R
10,000 Rupee

50 : 50
The Prophet Mohammed invented
…………..
A: water clock B: zero
D: toothbrushc: mecca
100 Rupee
10,000 Rupee
1,000,000 R
100,000 R

50 : 50
What is the Indian word for a million
………………….
A: Lakh B: million
D: nonec: crore
100 Rupee
10,000 Rupee
100,000 R
1,000,000 R

Islamic culture played and important and undeniable role in advancing world
civilization.
Muslims carried the civilization torch during the dark ages.
preserved the advanced the treasure of culture and knowledge for humanity.
In all aspects of your daily lives, then – in our homes, offices and
universities; in religion, philosophy, science and arts – we are indebted to the
Muslim creativity, insight and scientific perseverance.
Summary

http://www.icbse.com/indian-mathematicians
http://www.mathematicianspictures.com/Mathematicians/
http://www.storyofmathematics.com/islamic.html
http://en.wikipedia.org/wiki/Mathematics_in_medieval_Islam
http://www.britannica.com/EBchecked/topic/14885/algebra/231065/Islamic-contributions
http://www.math.tamu.edu/~dallen/history/arab/arab.html
http://www.csames.illinois.edu/documents/outreach/Islamic_Mathematics.pdf
http://www.muslimheritage.com/article/muslim-founders-mathematics
http://www.famous-mathematicians.com/top-10-indian-mathematicians-contributions/
http://www.academia.edu/6645514/Muslim_Contributions_to_Mathematics_and_Astronomy
Reference

Islamic & arabic contributions to mathematics

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