The Role of Muslims in the Formation and Development of Sciences (Part 26)
A New Method of Subtraction and Advances in Multiplication and Division
The initial method of subtraction used by Muslim scientists did not last long. They developed a new method in which the subtracted number was placed under the original number, and then the remainder was written down. This is the same method that is still used in mathematical calculations today.
Innovation of Muslim Scientists in Multiplication and Division
Arab and Muslim scientists invented various methods for multiplication, including the “grid” method, noted for its simplicity and strong logic. Some experts in modern mathematics education recommend that this method be incorporated in elementary schools.
They also proposed various methods for division until they finally reached a method similar to the present-day method of division. Leonardo Fibonacci, the famous mathematician from Pisa (one of the most prominent arithmeticians of the 7th century AH), admitted that he first learned the method of division from his Muslim teachers in Sicily. He acknowledged the mathematical superiority of Muslim scholars in this field and considered it indicative of their high expertise in arithmetic.
Division of Numbers and the Works of Abu Al-Fawaz Al-Buzjani
Muslim scholars classified numbers into two main groups:
– Even numbers: Numbers that are divisible by 2 and can be represented as 2n (where n is a whole number).
– Odd numbers: Numbers that are not divisible by 2.
Abu al-Fawaz al-Buzjani (328-388 AH/940-998 AD) wrote numerous works on arithmetic, including:
– «المدخل الحفظی إلى صناعة الأرثماطيقي» Translation: “An Educational Introduction to the Science of Arithmetic.”
– «فيما ينبغي أن يحفظ قبل الأرثماطيقي» Translation: “Things That Should Be Known Before Arithmetic.”
In these books, he focused on precise concepts of arithmetic and aimed to teach the basics of mathematics more accurately.
The Precise Definition of Numbers and Their Examination by Muslim Scholars
Abu al-Wufah al-Buzjani discussed absolute, abundant, and defective numbers in a precise and mathematical manner. However, Ibn al-Banna al-Marrakshi (654-731 AH/1256-1321 AD) formalized these definitions as follows:
– The number 6 is an absolute number because the sum of its divisors (1, 2, and 3) equals the number 6 itself.
– The number 12 is an abundant number because the sum of its divisors (1, 2, 3, 4, and 6) is 16, which is greater than the number itself.
– The number 8 is a defective number because the sum of its divisors (1, 2, and 4) is 7, which is less than the number itself.
The Discovery of Amicable Numbers by Thabit ibn Qara
Thabit ibn Qara al-Harrani al-Saba’i (221-288 AH/826-901 AD) defined amicable numbers. Two numbers are considered amicable if the sum of the divisors of the first number equals the second number, and the sum of the divisors of the second number equals the first number.
For example:
– 220 and 284 are a pair of amicable numbers because:
– The divisors of the number 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110) add up to give 284.
– The divisors of the number 284 (1, 2, 4, 7, 14, 28, 57, 84, 142) add up to give 220.
Research by Muslim Scientists on Ratios and Sequences
Arab and Muslim scientists also studied the theory of ratios and sequences, dividing them into three main types:
1. Numerical (arithmetic) sequences: In this sequence, the difference between any two consecutive terms is constant.
2. Geometric sequences: In this sequence, each term is multiplied by a constant number relative to the previous term.
3. Consonant sequences: This type of sequence was used to extract and arrange musical patterns and create melodies.
Muslim scientists invented special rules for adding sequences. They also developed mathematical rules for extracting the square root and the cube root of any number, proving the correctness of these methods. These studies yielded important results in arithmetic and algebra.
In short, Arab and Muslim scientists not only developed the mathematical knowledge they inherited from previous civilizations but also made significant new contributions. These efforts arose from their noble desire to spread knowledge among the Islamic nation and to understand the secrets of the world.
Since the science of arithmetic plays a direct role in the daily lives of people, its development was of great importance, as all daily commercial transactions depend on it.
