COPYING AND ADDING TO HINDU MATHEMATICS

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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.
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COPYING AND ADDING TO GREEK MATHEMATICS

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In the 9th century, Al-Mahani and Al-Nayrizi copied the Byzantine tradition of writing commentaries on Greek works by scholars such as Euclid.
Muslim mathematicians invented the concept of the tangent function of trigonometry.
Several Muslim mathematicians discovered methods of “doubling the cube” (using a ruled straightedge and a compass to construct a line segment whose length is the cube root of 2 times the length of a given line segment) that were different than the 5 different methods discovered by 5 different Greeks over a thousand years earlier.
The astronomer Abū Sahl al-Qūhī (940 – 1030) may have been the first to inscribe a pentagon inside a square.
Alhazen (Ibn al-Haytham) was the first person to have integrated a fourth-degree polynomial. He extended the 3rd century BC integral calculus heuristics of Archimedes into an algorithm for integrating polynomials of any positive degree,
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AL-KASHĪ’S SLIDE RULE

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In the early 1400’s, astronomer al-Kashi invented a table-sized linear interpolation device. Unlike modern slide rules, it could not do multiplication. It had markings at equal intervals, not at logarithmic intervals.
It was used for astrology purposes such as calculating when Jupiter would align with Mars.
To align non-adjacent sliding parts, it did not use a fine central hairline in a sliding cursor, but a pivoting part.
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MAGIC SQUARES

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The ancient Chinese constructed the first magic squares in size 3 x 3 and several other sizes, and thought that magic squares had magical powers.
In the numerology of the alchemist Geber (Jabir ibn Hayyan) the numbers in a corner of the 3 x 3 magic square are 3 (=earth), 8 (=air), 1 (=fire) and 5 (=water).

The Sabian star-worshiper Thabit ibn Qurra ( 836–901), living in Baghdad, added several additional sizes of magic squares.

A Muslim in 12th century Persia discovered the general method of how to construct magic squares for all odd numbers of rows and columns [11 x 11, 13 x 13 etc.].

In another type of magic square used by Muslims, not all the rows and columns added up to the same number, but the numbers used had magical properties.

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