Al-Khwarizmi презентация по теме Общие темы

  • Al-Khwarizmi
The Father of Algebra
  • By Ibrahim B. Syed, Ph.D., D.Sc., F.A.C.R.
Clinical Professor of Medicine
University of Louisville School of Medicine
And  
President 
ISLAMIC RESEARCH FOUNDATION INTERNATIONAL, INC.
Louisville, KY 40242
  • Al-Khwarizmi
A Portrait    	   of 
Al-Khwarizmi
  • Portrait of Al-Khwarizmi
This is taken from a stamp from the former USSR
  • MUHAMMAD BIN MUSA AL-KHWARIZMI (Algorizm) (770 - 840 C.E.)
Abu Abdullah Muhammad Ibn Musa al-Khwarizmi was born at Khwarizm (Kheva), a town south of the river Oxus in present day Uzbekistan.
  • LEARNING ALGEBRA
RESEARCH ON BRAIN shows Algebra concepts can be taught -as early as in Kindergarten
Second graders at The School at Columbia Univ. are learning  algebra
Other countries: To 6th or 7th graders
US: 25% of middle graders get algebra
In California, Algebra is taught-beginning of the 8th grade
  • WHAT IS ALGEBRA?
Algebra is a branch of Maths.
Describes relationships between things that vary over time
Variables denoted by letters and symbols.
Algebra is a study in logic.
  • WHY LEARN ALGEBRA?
Careers today demand skills like problem solving, reasoning, decision-making, and applying solid strategies etc.
Algebra provides one with a wonderful grounding in those skills.
Colleges require it and some employers demand it.
  • WHY LEARN ALGEBRA?
Algebra is a very unique discipline. It is very abstract.
The abstract-ness of algebra causes the brain to think in totally new patterns.
Algebra builds a better brain.
  • Abu Jafar Muhammad Ibn Musa al-Khwarizmi

21st Century is the age of Information Technology (IT)
Modern Computers are indispensable in everyday life.
Al-Khwarizmi is the grandfather of Computer Science.
He is the Father of Algebra.
  • BAYT AL-HIKMA-Center for Study and Research
    Abu Jafar Muhammad ibn Musa al-Khwarizmi lived in Baghdad(Gift of God) in the early ninth century. Baghdad at that time was at cultural crossroads, and, under the patronage of the Abbasid caliphs, the so-called House of Wisdom at Baghdad,  produced a Golden Age of Arabic science and mathematics. In Baghdad, scholars encountered and built upon the ideas of ancient Greek and Indian mathematicians
  • BAYT AL-HIKMA
There, al-Khwarizmi encountered the Indian numeral system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and he wrote a treatise on what we call Arabic numerals. It was translated into Latin in the twelfth century as Algoritmi de numero Indorum (that is, Al-Khwarizmi on the Hindu Art of Reckoning) and was crucial in the introduction of Arabic numerals to medieval Europe. It may well represent the first use of zero as a positional place holder. From that title, we have the word "algorithm."
  • ALGEBRA- A Practical System for solving problems in
 Cases of Inheritance
Contracts
Surveying
Tax collection
Legacies
Partition
Lawsuits and
Trade
  • Algebra-A Practical System for solving real life  Problems in the Islamic empire at that time 
In all their dealings with one another.
Where the measuring of lands.
The digging of canals.
Geometrical computations.
Other objects of various sorts and kinds are concerned.
  • LAWS OF ALGEBRA
Distributive: x(y+z) = xy+xz, (x+y)z = xz+yz 
Associative: (x+y)+z = x+(y+z) 
                        (xy)z = x(yz)
 Commutative: x+y = y+x
                              xy = yx 
Identity:  x+0 = 0+x = x x 1 = 1x = x 
Inverse: x+(-x) = (-x)+x = 0 
x(x-1) = (x-1)x = 1
  • Some Problems-Formal
"If from a square, I subtract four of its roots and then take one-third of the remainder, finding this equal to four of the roots, the square will be 256. "
He explained it in the following manner:
"Since one-third of the remainder is equal to four roots, one knows that the remainder itself will equal 12 roots. Therefore, add this to the four, giving 16 roots. This (16) is the root of the square. The above can also be stated in terms of modern notation as 
1/3 (x2 - 4x ) = 4x." Therefore x = 16.
  • "A man is hired to work in a vineyard 30 days for 10 Dollars. He works six days. How much of the agreed price should he receive?"
It is evident that since days are one-fifth of the whole time; and it is also evident that the man should receive pay having the same relation to the agreed price that the time he works bears to the whole time, 30 days. The month, i.e., 30 days, represents the measure, and ten represents the price. Six days represents the quantity, and in asking what part of the agreed price is due to the worker you ask the cost. Therefore multiply the price 10 by the quantity 6, which is inversely proportional to it. Divide the product 60 by the measure 30, giving 2 Dollars.
  • SOLUTIONS OF EQUATIONS
  • The Geometric Proof
Al-Khwarizmi starts with a square of side x,
 which therefore represents x2 (Figure 1).
To the square we must add 10x
 and this is done by adding four rectangles 
each of breadth 10/4 and length x to the square (Figure 2). 
Figure 2                             has area  x2 + 10 x 
    which is equal to 39.
  • Geometric Proof
We now complete 
the square by adding the four little squares
 each of area.  5/2x5/2 = 25/4. 
Hence the outside square in Fig 3  has area 4 x 25/4 + 39 = 25 + 39 = 64. 
The side of the square is therefore 8.
 But the side is of length 5/2 + x + 5/2 
so x + 5 = 8, giving x = 3.
  • GEORGE   SARTON(1884-1956) Author of Introduction to History of Science             (3 Volumes)
Former Prof. At Harvard Univ. 
Wrote on Al-Khwarizmi as
... the greatest mathematician
      of the time, and if one takes
   all the circumstances into                                 account,
 one of the greatest of all time....
  • Al-Khwarizmi wrote on
Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu Art of Reckoning) gave ALGORITHM deriving from his name in the title of the book.
He explained the use of ZERO
He developed the decimal system
Developed several arithmetical procedures including operations on fractions.
He developed in detail Trigonometric tables containing Sine functions and tangent functions
Developed calculus of two errors, which led him to the concept of differentiation
  • ASTRONOMY
Al-Khwarizmi wrote on
Calendars
True positions of the sun, moon, and planets
Spherical astronomy
Parallax and eclipse calculations
Visibility of the moon (21ST CENTURY Muslims are confused on the sighting of the moon)
Wrote a book on Astronomical Tables-A SIGNIFICANT CONTRIBUTION TO THE SCIENCE OF ASTRONOMY
  • GEOGRAPHY
Supervised 70 geographers to 
 create a map of the then known world which shows the pacific coast of South America –about 700 years before Columbus discovered America.
Measured volume and circumference of the earth.
Wrote Kitab al-Tarikh and Kitab al-Rukhmat (on sundials)
  • Satellite Photo Vs Piri Map
  • MUSLIM IMPACT ON EUROPE
Baghdad, Damascus, Cairo and Cordoba were the centers of civilization. Here Muslim scientists made tremendous progress in applied & theoretical science and technology.
While Europe festered in the Dark Ages.
  • Muslim Impact on Europe
Scholars and students from various parts of the world and Europe came to Cordoba to study.
In the 9th century the library of the monastery of St. Gall was  the largest in Europe with 36 volumes. At that time, that of  Cordoba contained over 500,000 volumes.
  • Arabic Maths Worldwide
Muslim mathematicians invented geometrical algebra, solved third and fourth degree equations.
The world witnessed a new stage in the development of mathematical science, driven by the numerous translated works from Arabic into European languages.
  • Advancement of Sciences in Europe
The sciences, with Arab mathematics as their essence, flourished and developed in the disciplines we know today.
Without the number zero and Arabic numerals in Europe, the world as we know today would have been different.
  • NUMBER ZERO
Muslim mathematical study concentrated in three areas: ongoing progress in algebra, the development of arithmetic algorithms, and the increasing complexity in geometry.
The number zero and decimal system in Europe was the  basis for the Scientific revolution.
Problems that took days (using Roman Numerals) to solve could now be solved in minutes (using Arabic numerals).
  • From EAST TO EUROPE
Europe would have been a lot poorer-economically, culturally and scientifically-had it resisted the globalization of mathematics, science and technology at that time.
Today Western science and technology are flowing to many parts of the world. (Our Ulama are resisting them)
  • Breaking the Boundaries
The Renaissance, the Enlightenment and the Industrial Revolution were great achievements. These developments drew on the experience of the Muslim world, India and China.
Today a mathematician in Boston invokes algorithm to solve a difficult computational problem, then he/she is commemorating Al-Khwarizmi
  • The square root of math itself
Al-Khwarizmi is one of many whose works influenced the European Renaissance, the Enlightenment and the Industrial Revolution.
Modern prosperity is due to science and technology, which have delivered better lives for people, longer lives, and for larger populations.
  • CONCLUSION
Algebra and algorithms are enabling the building of computers, and the creation of encryption. 
The modern technology industry would not exist without the contributions of Muslim mathematicians like Al-Khwarizmi.
  • Ms. Carly Fiorina
We are unaware of our indebtedness to this other (Islamic) Civilization, its gifts are very much part of our heritage.
.   Sufi poet-philosophers like Rumi challenged our notions of self and truth.
Leaders like Suleiman the Magnificent contributed to our notions of tolerance and civic leadership based on MERITOCRACY, NOT INHERITANCE.
It was leadership that harnessed the full capabilities of a very diverse population-that included Christian, Islamic and Jewish traditions."
  • THE END
THANK YOU FOR YOUR ATTENTION!
  • THE END
THE END
THANK YOU FOR YOUR ATTENTION!
  • THE END
THANK YOU FOR YOUR ATTENTION!
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Al-Khwarizmi The Father of Algebra

By Ibrahim B. Syed, Ph.D., D.Sc., F.A.C.R. Clinical Professor of Medicine University of Louisville School of Medicine And President ISLAMIC RESEARCH FOUNDATION INTERNATIONAL, INC. Louisville, KY 40242

Al-Khwarizmi A Portrait of Al-Khwarizmi

Portrait of Al-Khwarizmi This is taken from a stamp from the former USSR

MUHAMMAD BIN MUSA AL-KHWARIZMI (Algorizm) (770 - 840 C.E.) Abu Abdullah Muhammad Ibn Musa al-Khwarizmi was born at Khwarizm (Kheva), a town south of the river Oxus in present day Uzbekistan.

LEARNING ALGEBRA RESEARCH ON BRAIN shows Algebra concepts can be taught -as early as in Kindergarten Second graders at The School at Columbia Univ. are learning algebra Other countries: To 6th or 7th graders US: 25% of middle graders get algebra In California, Algebra is taught-beginning of the 8th grade

WHAT IS ALGEBRA? Algebra is a branch of Maths. Describes relationships between things that vary over time Variables denoted by letters and symbols. Algebra is a study in logic.

WHY LEARN ALGEBRA? Careers today demand skills like problem solving, reasoning, decision-making, and applying solid strategies etc. Algebra provides one with a wonderful grounding in those skills. Colleges require it and some employers demand it.

WHY LEARN ALGEBRA? Algebra is a very unique discipline. It is very abstract. The abstract-ness of algebra causes the brain to think in totally new patterns. Algebra builds a better brain.

Abu Jafar Muhammad Ibn Musa al-Khwarizmi 21st Century is the age of Information Technology (IT) Modern Computers are indispensable in everyday life. Al-Khwarizmi is the grandfather of Computer Science. He is the Father of Algebra.

BAYT AL-HIKMA-Center for Study and Research Abu Jafar Muhammad ibn Musa al-Khwarizmi lived in Baghdad(Gift of God) in the early ninth century. Baghdad at that time was at cultural crossroads, and, under the patronage of the Abbasid caliphs, the so-called House of Wisdom at Baghdad, produced a Golden Age of Arabic science and mathematics. In Baghdad, scholars encountered and built upon the ideas of ancient Greek and Indian mathematicians

BAYT AL-HIKMA There, al-Khwarizmi encountered the Indian numeral system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and he wrote a treatise on what we call Arabic numerals. It was translated into Latin in the twelfth century as Algoritmi de numero Indorum (that is, Al-Khwarizmi on the Hindu Art of Reckoning) and was crucial in the introduction of Arabic numerals to medieval Europe. It may well represent the first use of zero as a positional place holder. From that title, we have the word "algorithm."

ALGEBRA- A Practical System for solving problems in Cases of Inheritance Contracts Surveying Tax collection Legacies Partition Lawsuits and Trade

Algebra-A Practical System for solving real life Problems in the Islamic empire at that time In all their dealings with one another. Where the measuring of lands. The digging of canals. Geometrical computations. Other objects of various sorts and kinds are concerned.

LAWS OF ALGEBRA Distributive: x(y+z) = xy+xz, (x+y)z = xz+yz Associative: (x+y)+z = x+(y+z) (xy)z = x(yz) Commutative: x+y = y+x xy = yx Identity: x+0 = 0+x = x x 1 = 1x = x Inverse: x+(-x) = (-x)+x = 0 x(x-1) = (x-1)x = 1

Some Problems-Formal "If from a square, I subtract four of its roots and then take one-third of the remainder, finding this equal to four of the roots, the square will be 256. " He explained it in the following manner: "Since one-third of the remainder is equal to four roots, one knows that the remainder itself will equal 12 roots. Therefore, add this to the four, giving 16 roots. This (16) is the root of the square. The above can also be stated in terms of modern notation as 1/3 (x2 - 4x ) = 4x." Therefore x = 16.

"A man is hired to work in a vineyard 30 days for 10 Dollars. He works six days. How much of the agreed price should he receive?" It is evident that since days are one-fifth of the whole time; and it is also evident that the man should receive pay having the same relation to the agreed price that the time he works bears to the whole time, 30 days. The month, i.e., 30 days, represents the measure, and ten represents the price. Six days represents the quantity, and in asking what part of the agreed price is due to the worker you ask the cost. Therefore multiply the price 10 by the quantity 6, which is inversely proportional to it. Divide the product 60 by the measure 30, giving 2 Dollars.

SOLUTIONS OF EQUATIONS

The Geometric Proof Al-Khwarizmi starts with a square of side x, which therefore represents x2 (Figure 1). To the square we must add 10x and this is done by adding four rectangles each of breadth 10/4 and length x to the square (Figure 2). Figure 2 has area x2 + 10 x which is equal to 39.

Geometric Proof We now complete the square by adding the four little squares each of area. 5/2x5/2 = 25/4. Hence the outside square in Fig 3 has area 4 x 25/4 + 39 = 25 + 39 = 64. The side of the square is therefore 8. But the side is of length 5/2 + x + 5/2 so x + 5 = 8, giving x = 3.

GEORGE SARTON(1884-1956) Author of Introduction to History of Science (3 Volumes) Former Prof. At Harvard Univ. Wrote on Al-Khwarizmi as ... the greatest mathematician of the time, and if one takes all the circumstances into account, one of the greatest of all time....

Al-Khwarizmi wrote on Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu Art of Reckoning) gave ALGORITHM deriving from his name in the title of the book. He explained the use of ZERO He developed the decimal system Developed several arithmetical procedures including operations on fractions. He developed in detail Trigonometric tables containing Sine functions and tangent functions Developed calculus of two errors, which led him to the concept of differentiation

ASTRONOMY Al-Khwarizmi wrote on Calendars True positions of the sun, moon, and planets Spherical astronomy Parallax and eclipse calculations Visibility of the moon (21ST CENTURY Muslims are confused on the sighting of the moon) Wrote a book on Astronomical Tables-A SIGNIFICANT CONTRIBUTION TO THE SCIENCE OF ASTRONOMY

GEOGRAPHY Supervised 70 geographers to create a map of the then known world which shows the pacific coast of South America –about 700 years before Columbus discovered America. Measured volume and circumference of the earth. Wrote Kitab al-Tarikh and Kitab al-Rukhmat (on sundials)

Satellite Photo Vs Piri Map

MUSLIM IMPACT ON EUROPE Baghdad, Damascus, Cairo and Cordoba were the centers of civilization. Here Muslim scientists made tremendous progress in applied & theoretical science and technology. While Europe festered in the Dark Ages.

Muslim Impact on Europe Scholars and students from various parts of the world and Europe came to Cordoba to study. In the 9th century the library of the monastery of St. Gall was the largest in Europe with 36 volumes. At that time, that of Cordoba contained over 500,000 volumes.

Arabic Maths Worldwide Muslim mathematicians invented geometrical algebra, solved third and fourth degree equations. The world witnessed a new stage in the development of mathematical science, driven by the numerous translated works from Arabic into European languages.

Advancement of Sciences in Europe The sciences, with Arab mathematics as their essence, flourished and developed in the disciplines we know today. Without the number zero and Arabic numerals in Europe, the world as we know today would have been different.

NUMBER ZERO Muslim mathematical study concentrated in three areas: ongoing progress in algebra, the development of arithmetic algorithms, and the increasing complexity in geometry. The number zero and decimal system in Europe was the basis for the Scientific revolution. Problems that took days (using Roman Numerals) to solve could now be solved in minutes (using Arabic numerals).

From EAST TO EUROPE Europe would have been a lot poorer-economically, culturally and scientifically-had it resisted the globalization of mathematics, science and technology at that time. Today Western science and technology are flowing to many parts of the world. (Our Ulama are resisting them)

Breaking the Boundaries The Renaissance, the Enlightenment and the Industrial Revolution were great achievements. These developments drew on the experience of the Muslim world, India and China. Today a mathematician in Boston invokes algorithm to solve a difficult computational problem, then he/she is commemorating Al-Khwarizmi

The square root of math itself Al-Khwarizmi is one of many whose works influenced the European Renaissance, the Enlightenment and the Industrial Revolution. Modern prosperity is due to science and technology, which have delivered better lives for people, longer lives, and for larger populations.

CONCLUSION Algebra and algorithms are enabling the building of computers, and the creation of encryption. The modern technology industry would not exist without the contributions of Muslim mathematicians like Al-Khwarizmi.

Ms. Carly Fiorina We are unaware of our indebtedness to this other (Islamic) Civilization, its gifts are very much part of our heritage. . Sufi poet-philosophers like Rumi challenged our notions of self and truth. Leaders like Suleiman the Magnificent contributed to our notions of tolerance and civic leadership based on MERITOCRACY, NOT INHERITANCE. It was leadership that harnessed the full capabilities of a very diverse population-that included Christian, Islamic and Jewish traditions."

THE END THANK YOU FOR YOUR ATTENTION!

THE END THE END THANK YOU FOR YOUR ATTENTION!

THE END THANK YOU FOR YOUR ATTENTION!

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