Al-Khwarizmi fileAl-Khwarizmi Contribution 2. Numeral System: “Western scholars are of the opinion...
Transcript of Al-Khwarizmi fileAl-Khwarizmi Contribution 2. Numeral System: “Western scholars are of the opinion...
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History of mathematics Done by
Reem Isa (20110429)
Dalal Mohammed (20111454)
Dalal khalid(20123336)
Fatima Mubark (20123106)
Aisha Saleh (20123627)
Section 4
Al-Khwarizmi Father of algebra
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General information
• Full Name : Abu Ja'far Muhammad ibn Musa Al-Khwarizmi • Born: about 780 in Khwarezm (now in Iran). • Died: about 850 • Called : 'father of algebra'
He was : mathematician astronomer geographer historian
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1. Algebra : a mathematical text he published in about 830 called “Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala”. was contain 3 Parts : First part: discusses the equations of the first and second
degrees. Second part: Deals with practical mensuration by giving rules for
finding the area of various plane figures including the circle, and for finding the volume of a number of solids including cones and pyramids.
Third part : concerns legacies as well as inheritance. It consists entirely of solutions to problems which arise out of legacies.
Al-Khwarizmi Contribution
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“al-Jabr wa al-Muqabalah” book
contains chapters which cover various topics:
i. Operations of multiplication, addition, subtraction and division.
Ones tens hundreds thousands
1 2
4 5
3
2 3
4
9 7 5 3
Until NOW
We still use Al-Khwarizmi ways in
ii) Equations iii) Survey iv) Problems in sale and purchase and commercial transactions v) Division/Distribution of currency vi) Weights and Measures vii) Measurement of a flat plane viii) Surface area of circle and triangle ix) Volume of pyramid and cone x) Wills and inheritance property distribution
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(الجبر)
algebra
Solving equations of the issues that faces Muslims
• Distribution of property. توزيع األمالك • Inheritance. الميراث • Zakat. الزكاة • Qibla direction. اتجاه القبلة
Was referring to
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اخلوارزيم
اخلوارزمية
Algorithm
It is mean solving equations using Al-Khwarizmi way.
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Al-Khwarizmi Contribution
2. Numeral System: “Western scholars are of the opinion that zero is one of the
greatest mathematical invention or innovations in the world contributed by a Muslim scholar”.
3. Trigonometry:
Al-Khawarizmi was the first person to introduce the theory of
jib (sine), tajjib (cosine), dhill (cotangent) and tadhill
(tangent)
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3. Geometry:
• the area of triangle. • the area of parallelogram. • the area of circle
Al-Khwarizmi Contribution
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What did he do?!
Most important contribution to algebra
Ever heard of completing square?
Al-Khwarizmi Method Let us see the example problem..!
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X²+10X = 39
Step 1:-
Square side = X
Area = X.X= X²
Step 2:-
Add (10X).how? Add rectangle to each side,
width= 5
2 , length= X
Area=5𝑥
2
Total area= 4.5𝑥
2 = 10 X
x 5
2
5𝑥
2
39
Step 3:- 𝟐𝟓
𝟒
Complete the square by adding 4 small square to the gap.
Area= (5
2)²=
25
4
Total area for = 4.25
4= 25
39 + 25 = 64 Each side of large square = 8 Side of original square =
8- 5
2 . 2 = 3
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Step to CTS X²+ 12X +4 = 0
STEP 1: (X²+12X+ -------) _ ------ + 4 = 0 STEP 2: ( B/2)² , add the answer to B and C (X²+12X+ ---36---) _ --36-- + 4 = 0 STEP 3: (X+6)² _ 32 = 0 STEP 4: (X+6)² = 32 STEP 5: X+6 = ± 32 STEP 6: X = -6 ± 32 X= -6 ±4 2
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The end
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References
https://www.youtube.com/watch?v=xkAQDEhmPYc
http://www.muslimheritage.com/article/contribution-al-khwarizmi-mathematics-and-geography
http://www-history.mcs.st-and.ac.uk/Biographies/Al-Khwarizmi.html
http://www.storyofmathematics.com/islamic_alkhwarizmi.html
https://www.youtube.com/watch?v=58aUrD0FnDM. http://www.andyborne.com/math/downloads/AL-Kwarazmi.pdf https://www.youtube.com/watch?v=SWtyswqulg0 http://www.aensiweb.com/old/anas/2012/324-330.pdf