<><><> start of synopsis ><><><><><>
Muslims did not invent the digit zero or the decimal point.
Arabic numerals were copied from the Hindus.
Hindu and Jain mathematicians wrote about step by step processes (algorithms) for solving quadratic equations.
Muslim Persian mathematician al-Khwārizmī copied from Shridhara to produce ”Book on Calculation by Completion and Balancing”.
The only symbols used in Hindu mathematics were abbreviations of the names of colors as the 4 operation signs. In the 3rd century, Diophantus of Alexandria wrote the book “Arithmetica” which used letters of the alphabet to represent unknowns and used a symbol to represent the equal sign. Muslims added the symbols of Diophantus to Hindu mathematics, plus added symbols for squared and square root.
‘Abd al-Hamīd ibn Turk (in around the year 830) wrote an algebra book nearly identical to a book written by al-Khwarizmi but adding additional categories of quadratic equations.
<><><> end of synopsis ><><><><><>
Muslims did not invent the number zero
Muslims spread the use of the digit zero, but played no role in the invention and development of the concept of zero.
There are 2 different meanings for the number zero. Zero as the number one less than one had been used in accounting texts of the ancient (non-Muslim) Egyptians.
In 130 AD Ptolemy (influenced by Hipparchus and the Babylonians) used a small circle with a horizontal line above it for both meanings of zero.
The Hindu mathematician Brahmagupta had rules in the year 628 for zero, including division. This was at the time when the prophet Mohammed and his small number of followers had never heard of zero.
Discussion of the use of zero by Hindus and Muslims is at https://en.wikipedia.org/wiki/0_(number)
The other meaning of the number zero is the placeholder that distinguishes the number 27 from the number 207.
An o as a placeholder was in use in India in the 6th century, prior to the birth of the prophet Mohammed.
Babylonians in around 1500 BC had used a different symbol as the placeholder. http://www.livescience.com/27853-who-invented-zero.html
TRANSLATION OF HINDU MATHEMATICS INTO ARABIC
“Correctly Established Doctrine of Brahma” was written in India in 628 by Brahmagupta, containing the concept of zero and other discoveries by Hindu and Jain mathematicians.
Muslim scholars learned about these concepts 145 years later in 773 when Al Fazari translated the Hindu book into Arabic.
“Arabic” numerals were invented by Hindus in India. Arabs made some changes to their shape. Some numerals of today are shaped more like the Arab shapes and some are shaped more like the original Hindu shapes. http://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system
Muslims websites falsely claim Muslims invented the concept of the decimal point (called a decimal mark or decimal separator in some countries). Mathematicians in India were the first to use a symbol, choosing a horizontal stroke. Arab mathematicians changed the horizontal stroke to a short vertical stroke.
After Gutenberg used the Chinese-invented invented movable type printing press in 1555, there was no short vertical stroke in their typeset characters, so a comma or period was substituted as the decimal separator mark.
Hindu and Jain mathematicians wrote about step by step processes (algorithms) for solving quadratic equations. This was copied by Hindu mathematician Shridhara,
Muslim Persian mathematician al-Khwārizmī (780 – 850), also known as Algorismi, whose parents may have been Zoroastrians, copied from Shridhara to produce”Book on Calculation by Completion and Balancing”.
The Arabic word for restoration, “al-jabri”, is the root of the word “algebra.”
The use of algebraic symbols had not yet been invented, so all of these mathematicians expressed the concepts by giving examples with actual numbers.
In solving 3 quadratic equations with 3 unknowns, Muslim mathematicians added additional examples using actual numbers.
‘Abd al-Hamīd ibn Turk (in around the year 830) wrote an algebra book nearly identical to a book written by al-Khwarizmi but adding a category of quadratic equations that had no solutions.
SYMBOLS ADDED TO ALGEBRA
The only symbols used in Hindu mathematics were abbreviations of the names of colors as the 4 operation signs. In the 3rd century, Diophantus of Alexandria wrote the book “Arithmetica” which used letters of the alphabet to represent unknowns and used a symbol to represent the equal sign.
Abū al-Wafā’ al-Būzjānī (940 – 998) translated Diophantus of Alexandria from Greek into Arabic. This resulted afterwards in combining Arabic versions of the Greek symbols with Hindu algebra to create an algebra that used letters for unknowns and the equal sign instead of giving examples using actual numbers.
Abū al-Hasan ibn Alī al-Qalasādī (1412–1486) used symbols for squared, cubed and square root.
In the 10th century Abū Sahl al-Qūhī (Kuhi) discovered the 4th degree equation of inscribing a regular pentagon inside a square.
GEOMETRY AND POLYNOMIAL EQUATIONS
The Persian philosopher, poet and mathematician Umar al-Khayyām (Omar Khayyám) (1048 – 1131) borrowed from a Sabian star worshiper named Thabit ibn Qurra (826 – 901) the concept of solving cubic equations by drawing geometry diagrams of intersections of conic sections.
FREEING ALGEBRA FROM GEOMETRY
The Persian mathematician, living in Baghdad, Al-Karaji (953 – 1029) copied algebra from the 3rd century mathematician Diophantus of Alexandria, but followed the Hindu practice of not using unnecessary geometry diagrams in algebra.
Hindus used the coefficients of the binomial theorem in probability statistics, and by the 6th century were expressing the probabilities as positive rational numbers (ratios). Pascal’s triangle is a way to display these coefficients.
INTERSECTION OF CONIC SECTIONS
The poet Omar Khayyám (1038 – ????) in Persia obtained the solutions of these equations by finding the intersection points of two conic sections. This method had been used by the Greeks, but they did not generalize the method to cover all equations with positive roots.
To solve the third-degree equation x3 + a2x = b Omar Khayyám constructed the parabola x2 = ay, a circle with diameter b/a2, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the x-axis.
CATEGORIES OF POLYNOMIAL EQUATIONS
The 13th century Persian scholar. (Tusi) Nasir al-Din al-Tusi (1201 – 1274) added to what previous scholars had written about types of 3rd degree equations and which had solutions and which did not have solutions.
BRINGING HINDU MATHEMATICS TO EUROPE
On the 12th century, Gerard of Cremona (an Italian Catholic who came to Toledo Spain after Toledo’s reconquest by Christians) and others in Toledo began translating from Arabic to Latin mathematics texts The translation into Latin of (Persian Muslim) Al-Khwarizmi’s mathematics books brought Indian concepts of positional decimal numbers and use of the decimal point, and of Baudhayana’s 8th century BC algorithms for solving 2nd degree quadratic equations from India to western Europe. http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB
COMPUTING SQUARE ROOTS
Until around the year 900, Muslims were using the Greek successive approximations method of Hero of Alexandria to compute square roots. After 900, Muslims switched to using an algorithm invented by Hindus to calculate square roots and cube roots. Both
methods are explained at http://www.homeschoolmath.net/teaching/square-root-algorithm.php
The Persian philosopher, poet and mathematician Umar al-Khayyām (Omar Khayyám) (1048 – 1131) made the obvious extension of the Hindu algorithm to calculate 4th roots and 5th roots.
Ptolemy had computed the value of pi to 3 decimal places. A Hindu mathematician then computed pi to 11 decimal places.
Ibn Maḍāʾ (1116 – 1196) computed pi to 16 decimal places, a mathematical exercise of no practical use.
ADDITION IS EASIER TO DO BY HAND THAN MULTIPLICATION
At the end of the 10th century, the Cairo astronomer and mathematician ibn Yunus (950 – 1009) invented an algorithm equivalent to the formula cos(a)cos(b) = cos(a+b) + cos(a-b) as an alternate way of computing cos “a” multiplied by cos “b” but which made astronomy calculations easier to do by hand by replacing the multiplication step with an addition step.
Image by jonathan357, via openclipart.org
CC0 public domain
Attribution is not required.
image credit https://openclipart.org/search/?query=zero&page=2ZERO