mathematics in islamic society becca and hank. the role of math scholars contributions in other...

Mathematics in Islamic Society

Becca and Hank

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

Islamic Mathematics

• Islamic algebra based on Greek and Hindu foundations

• Many believed that through numbers-ascend into higher world

Apply Math to Science

• Astronomical table• Direction of Mecca• Schedule 5 daily prayers• Fix holy days on lunar calendar

• Navigate monsoon swept Indian Ocean

Apply Math to Science

• Water clocks, water wheels, irrigation

• Geometry and algebra in optics• Trigonometry refine earth-center

picture of Ptolemy

Tracing Mathematic progression throughout

the Islamic era and development of concepts

that we still use today

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

MOHAMMAD BIN MUSA AL-KHAWARIZMI

• Geometric representation of conic sections

• Calculus of two errors• Collaborate with Mamun

al-Rashid on degree measurement

YAQUB IBN ISHAQ AL-KINDI

• 4 books on number system• Foundations of modern arithmetic • Spherical geometry-astronomy

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.

THABIT IBN QURRA

• Traditional geometry and geometric algebra

• Theories• Non-Euclidean geometry• Spherical trigonometry• Real numbers• Integral calculus

THABIT IBN QURRA

• Apply arithmetical terminology to geometric quantities

• Study conic section-parabola and ellipse

• Determine surfaces and volumes

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

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

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

NASIR AL-DIN AL-TUSI

• Trigonometry• Compiled as a subject of study• 6 formulas for the solutions of

spherical right angle triangles

Location of Mathematicians

• Born throughout Islamic Empire• Turkey, Nishapur, Aral Sea• All flourished in Baghdad

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/