Mathematics in Islamic Society
description
Transcript of Mathematics in Islamic Society
![Page 1: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/1.jpg)
Mathematics in Islamic Society
Becca and Hank
![Page 2: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/2.jpg)
The Role of Math
• Scholars• Contributions in other areas of study• Universities• Math for the sake of Math• Some had government positions• Arabic numerals• From simple to complex concepts
![Page 3: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/3.jpg)
Islamic Mathematics
• Islamic algebra based on Greek and Hindu foundations
• Many believed that through numbers-ascend into higher world
![Page 4: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/4.jpg)
Apply Math to Science
• Astronomical table• Direction of Mecca• Schedule 5 daily prayers• Fix holy days on lunar calendar
• Navigate monsoon swept Indian Ocean
![Page 5: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/5.jpg)
Apply Math to Science
• Water clocks, water wheels, irrigation
• Geometry and algebra in optics• Trigonometry refine earth-center
picture of Ptolemy
![Page 6: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/6.jpg)
Tracing Mathematic progression throughout
the Islamic era and development of concepts
that we still use today
![Page 7: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/7.jpg)
MOHAMMAD BIN MUSA AL-KHAWARIZMI
• Father of algebra• Analytical solutions to linear and
quadratic equations• Zero• Decimals• Algorithms-formal procedure of
calculating• Introduce “Arabic numerals”• Trigonometry tables-sine
![Page 8: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/8.jpg)
MOHAMMAD BIN MUSA AL-KHAWARIZMI
• Geometric representation of conic sections
• Calculus of two errors• Collaborate with Mamun
al-Rashid on degree measurement
![Page 9: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/9.jpg)
YAQUB IBN ISHAQ AL-KINDI
• 4 books on number system• Foundations of modern arithmetic • Spherical geometry-astronomy
![Page 10: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/10.jpg)
JAMSHID AL-KASHI
• Al-Kashi’s greatest contribution was the calculation of Pi
• He calculated that Pi was 3.1459265358979325 the only digit wrong in this approximation was the five at the end.
![Page 11: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/11.jpg)
THABIT IBN QURRA
• Traditional geometry and geometric algebra
• Theories• Non-Euclidean geometry• Spherical trigonometry• Real numbers• Integral calculus
![Page 12: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/12.jpg)
THABIT IBN QURRA
• Apply arithmetical terminology to geometric quantities
• Study conic section-parabola and ellipse
• Determine surfaces and volumes
![Page 13: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/13.jpg)
ABUL WAFA MUHAMMAD AL-BUZJA
• Geometry• Use compass• Square equivalent to other squares• Regular polyhedra• Regular hexagon and equliateral triangle• Parabola by points• Geometric solution to
• x^4=a and x^4+ax^3=b
![Page 14: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/14.jpg)
ABUL WAFA MUHAMMAD AL-BUZJA
• Trigonometry• Relate sine theorem to spherical triangles• New method of sine tables• Sin30 correct to eighth decimal place• 2 sin2 (a/2) = 1 - cos a andsin a = 2 sin
(a/2) cos (a/2) developed• Table of tangents• Secant and cosecant
![Page 15: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/15.jpg)
OMAR AL-KHAYYAM
• Algebra• Classify equations-based on complexity,
degree, number of terms• Offer solutions-cubic equations• Binomial theorem, binomial coefficients• Contribute to theory of parallel lines
![Page 16: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/16.jpg)
NASIR AL-DIN AL-TUSI
• Trigonometry• Compiled as a subject of study• 6 formulas for the solutions of
spherical right angle triangles
![Page 17: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/17.jpg)
Location of Mathematicians
• Born throughout Islamic Empire• Turkey, Nishapur, Aral Sea• All flourished in Baghdad
![Page 18: Mathematics in Islamic Society](https://reader036.fdocuments.us/reader036/viewer/2022082414/56813cf9550346895da69eb4/html5/thumbnails/18.jpg)
Bibliography
• “The Islamic Tradition.” John B. Christopher. Harper and Row Publishers. 1972. p 123-125.
• “Great Moments in Mathematics, Before 1650.” Howard Eves. The Mathematical Association of America. 1983. p 160.
• http://www.ummah.net/history/scholars/