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Imam Ali’s (PBUH) Scientific Knowledge in Conjunction With Islamic Heritage In Mathematics, Physics, and Astronomy—Part 1

*PBUH; Peace Be Upon Him Last summer, the UN celebrated the beginning of the 3rd millennium and discussed the main global goals and objectives of the human race. The goals to be achieved during the new century described and reported by the UN are as follows: G

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Imam Ali’s (PBUH) Scientific Knowledge in Conjunction With Islamic Heritage In Mathematics, Physics, and Astronomy—Part 1
*PBUH; Peace Be Upon Him
Last summer, the UN celebrated the beginning of the 3rd millennium and discussed the main global goals and objectives of the human race. The goals to be achieved during the new century described and reported by the UN are as follows:
  1. Global education and knowledge to be available to everybody
  2. Universal training and retaining for everybody to master useful skills
  3. Global health services and free medication to everybody.
Today, in commemorating the 1400th anniversary of Hazrat Imam Ali's (*PBUH) birth, I think the best thing to do is to highlight the importance of his scientific knowledge and contribution, in order to achieve the goals of the global education and knowledge.  Presently there are several active debates and discussions at several European academic institutions in England, France and Germany about the same issue. Many historians of science are full participants in these discussions. The objectives of these dialogues are to determine the right beginning of the history of Islamic mathematics or is Hazrat Imam Ali Ibn Taleb (601-661AD) is the first scholar? In the last two decades a new manuscript on Imam Ali's knowledge of mathematics, physics and astronomy found preserved in Hyderabad written by Yemeni scholar Amer Bin Ahmad Al-Khuzai Al-Uzdi (1226-1283 AD). There are other additional documents found to support this issue. Although the additional sermons of Nahjul-Balagha (Peak of Eloquence) are in full agreement with such issues, several other sources found to support this point of view, with discourses narrated and com-piled by Shaikh Mohammad Taqi At-Tustari (860-937 AD) in Selected Judgements of Imam Ali, Baha Eddine Al-Ameli (1546-1621 AD) in Compendium of Islam- Al-Kashkul. All these recent discoveries were discussed by Dr. David King in A medieval Arabic Report On Algebra before Al-Khawarizmi (1998) and by Dr.J. Lennart Berggren in Mathematics of Medieval Islam (1986). In this perspective I would like to report some examples of the indications and problems of mathematics, physics and astronomy introduced and solved by Imam Ali (PBUH) during 630-660 AD. Almost 150 years before the earliest official reported Islamic works in these subjects.

Unusual Mathematical Problems

Conditional Division of Specific Numbers by Primary Numbers (1-10)

Problem 1: In April 640 AD, a Roman-Syrian mathematician approached Imam Ali (PBUH), and asked him: what is the number which would be divisible by 2,3,4,5,6,7,8,9 and 10 without remainder of fraction? Solution: Imam Ali (PBUH) replied at once: "Multiplying the seven days of your week by the thirty days of the month by the twelve months of your year." That is 7x30x12=2520 2520 / 2 = 1260 2520 / 3 = 840 2520 / 4 = 630 2520 / 5 = 504 2520 / 6 = 420 2520 / 7 = 360 2520 / 8 = 315 2520 / 9 = 280 2520 / 10 = 252 Problem 2: In September 658 AD a Persian attended Imam Ali's court and asked him for a number which can be divided by 2, 3,4,5,6,7,8,9, and 10, without a fraction. But there will be no 1/8th for its 1/4th, not 1/4th for its 1/8th, not 1/7th for its 1/7th, no 1/8th for its 1/8th, and no 1/9th for its 1/9th. Imam Ali (PBUH) asked him: "Do you believe in Islam if I tell you? The man answered, “Yes." Solution: Imam Ali (PBUH) replied at once: "Multiply the days of your week by the days of your month, by the days of your year." The Persian multiplied 7x30(=210), then multiplied it by 360* , he got (7x30x360)75600. The man then converted to Islam. That is 7×30×360= 7 ×2×3×4×5×23 × 32 × 5 = 24×33×52×7 = 75600 75600 / 2 = 37800 75600 / 3 = 25200 75600 / 4 = 18900 75600 / 5 = 15120 75600 / 6 = 12600 75600 / 7 = 10800 75600 / 8 = 9450 75600 / 9 = 8400 75600 / 10 = 7560 (*According to Chaldean (747 BC) and Zoroastrian (389 BC) Calendars, the year contained 12 months of 30 days each.)
  1. The first condition is satisfied 1/4(1/8) or 1/8(1/4)=1/32=1/25, and there is no factor of 32 or 25.
  2. The second condition is satisfied because 1/7(1/7)= 1/49= 1/72, and there is no factor of 49 or 72
  3. The third condition is satisfied because 1/8(1/8)= 1/64= 1/82= 1/26, and there is no factor of 64 or 26
  4. The fourth condition is satisfied because 1/9(1/9)=1/81=1/92=1/34, and there is no factor of 81 or

Division of Odd Numbers by Specific Fractions

Problem 1: In June 635 AD (14 Hijra), three per-sons had a dispute about the division of 17 camels. The ratios of their shares were to be 1/2 for the first, 1/3 for the second and 1/9 for the third. They could not divide the number 17 proportionately without a fraction. Finding no way out, they approached Imam Ali (PBUH). Solution: On hearing their problem, Imam Ali asked them if it is agreeable to them if he makes the total number of camels 18 by adding one of his own to which all of them agreed. Consequently, Imam distributed their shares by giving (18/2) or 9 camels to the first man (having a share of 1/2), and 18/3 or 6 camels to the second man (having a share of 1/3), and 18/9 or 2 camels to the third man (having a share of 1/9). Thereby taking his own camel with-out any fractions, and the total shares 9+6+2=17 Modern solution: Let X be the number to be divided. A is the first fractional share. B is the second fractional share. C is the third fractional share. The total fractional shares =A+B+C=1/2 +1/3 +1/9 =17/18 The first share is A/(A+B+C)X=AX/(A+B+C)=1/2x17/ (17/18) = (17/2)×(18/17)= 9 The second share is B/(A+B+C).X=BX/(A+B+C) =1/3 x17/(17/18)=17/3×18/17=6 The third share is C/(A+B+C)X=CX/(A+B+C)= 19x17/(17/18)= 17/9×18/17=2 Problem 2: in February 637 AD(16 Hijra), three persons from Taif had a dispute about the division of 19 horses. The ratio of their shares to be 1/2for the first, 1/4 for the second, and 1/5 for the third, and nothing to be left. They could not divide the number 19 proportionately without a fraction. Finding no way out, they approached Imam Ali (PBUH). Solution: Imam asked them if it is agreeable to them if he makes the total number of horses to 20 by adding one of his own to which all of them agreed. Then Imam distributed their shares by giving 20/2 or 10 horses to the first, 20/4 or 5 horses to the second, and 20/5 or 4 horses to the third, the total 10+5+4= 19. Thereby taking his own horses which he added before the distribution. Modern Solution: The same previous formulas are applicable. Let  X be the number to be divided A is the first fractional share B is the second fractional share C is the third fractional share The total fractional share =A+B+C= 1/2+1/4+1/5= 19/20 The first share = AX/(A+B+C)=1/2x19(19/20)= 19/ 2x20/19=10 horses The second share =BX/(A+B+C)=1/4x19(19/20)=19/4 x20/ 19 =5 horses The   third   share   =CX/   (A+B+C)    =1/5x   19(19/5) =19/5x20/19 =4 horses

Legal Division of Numbers With Conditional Interconnected Shares

Problem 1: In March 645 AD(24 Hijra), a lady came to Imam Ali (PBUH) and told him that her brother passed away and left 600 dinars, and she was given only one dinar of her brother's inheritance. She wanted him to protect her right, after she mentioned the details of the circumstances. Solution: Then he told her: your brother left two daughters, they got 2/3rd (400 dinars), he left also a mother, she got 1/6th (100 dinars) he left a wife, she got 1/8th (75 dinars). He left also 12 brothers and you (the only sister), your brothers got 2 dinars each (total 24 dinars). The total so far is 400+100+75+24=599 dinars; therefore the rest (600-599) of one dinar is yours. Problem 2: In June 639 AD (18 Hijra), two persons while traveling on a road sat under the shade of a tree for lunch. One of them took out five loaves of bread from his bag and the other man took three loaves and put them near the five loaves of his companion making the total number of loaves eight. They had not yet started eating when a third person happened to cross by them. They invited him for lunch with them to which he agreed and sat down. While going away, he gave them 8 dirhams against the food he had taken. Meanwhile, a quarrel arose between the two men about the portion of each one of the 8 dirhams. The first man having 5 loaves claimed to have 5 dirhams. The companion who had 3 loaves didn't agree to such a division reasoning that the stranger who had shared their food did not give them the 8 dirhams to share proportionately, and moreover asked him that the share of stranger was equal to each of their own. Finally the man was referred to Imam Ali (PBUH) who decided the case is the following matter. Solution: First Imam advised them for a compromise, and when they did not agree, particularly the one who had 3 loaves, he solved the problem as follows; He asked the one who had three loaves: "if you want the righteous decision in this case, you should have only one dirham that was your due actually." When he requested an explanation Imam Ali enlightened him by saying: "you had only three loaves and your companion 5, the total number of loaves you had is 8. Now 8 divided into 3 pieces (each loaf) comes to 24 pieces. Let's say the stranger started your bread equally, he should have eaten 8 pieces (2 2/3 loaves), and you and you companion each have eaten 8 pieces (2 2/3 loaves) as well. The stranger had eaten only one piece (one third) of your 3x3 or 9 pieces of your bread and 7 pieces (seven thirds) of the (5x3) or 15 pieces from your companion's bread, that is why you have only one dirham for only one piece of the eight pieces (thirds or bits) which the stranger ate. Modern solution: Total number of loaves consumed= 5+3= 8 loaves Equal share of each person = 8/3= 2 2/3 loaves The amount of bread given by the person who had five loaves: 5-2 2/3= 2 1/3 loaves The amount of bread given by the person who had three loaves: 3-2 2/3= 1/3 of a loaf Therefore the amount of 8 dirhams must be divided according to what the first and second person gave to the guest. The share of the first (with 5 loaves)= 8/ 2 2/3 x 2 1/3= 7 Dirhams The share of the second (with 3 loaves)= 8/2 2/3 x 1/3= 1 Dirham (Continued here in Part 2)