In the beginning of Islam, around of 700, the Islam people focus their attention to individual activity. In the next step, the Islamic Scholar has donate their taught and work, especially in Mathematics. They create many theory and solves amount of problem, so we can use their step and theory to solve the similar problem. Here is the Islam’s contribution for mathematics.
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Algebra is from Arabic (al-jabr), means reunion, or collecting a broken parts. Algebra is one of the broad parts of mathematics. In the most general forms, algebra also the study of mathematical symbols and the rules for manipulating the symbols. The study of algebra begun at Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a scholar in the House of Wisdom in Baghdad, is known as the father of algebra.
Based on the book The Compendious Book on Calculation by Completion and Balancing, Al-Khwarizmi deals with ways to solve for the positive roots of first and second degree (linear and quadratic) polynomial equations. He also introduces the method of reduction, and gives general solutions for the equations he deals with.
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Trigonometry is a branch of mathematics that deals with triangular and trigonometric angles such as sinus, cosine, and tangent. Trigonometry has a relationship with geometry, although there is disagreement about what the relationship is; for some people, trigonometry is part of geometry.
In Islam, we have Abu al-Raihan Muhammad bin Ahmad al-Khawarizmi al-Biruni, or just Al-Biruni, as an expert in trigonometry. He put a basis of trigonometry in mathematics (such as sinus, cosinus, tangent as we mention in beginning), which is applied by West scientist for the next century. With trigomonetry, he mathematically allowed the direction of qibla to be determined from everywhere in the world.
Geometry is one of the branch of mathematics, which is the oldest among the others. Geometry came from Greek language; geo means earth, and metron is measure. It concerned with questions of shape, size, relative position of figures, and the properties of space. In the era of Islamic Caliphate, Muslim scientists also helped develop geometry. In fact, in the Middle Ages, geometry was dominated by Muslim mathematicians. No wonder the Islamic civilization also contributed significantly to the development of the branch of modern mathematics.
In the field of geometry, an Islamic scientist name Ibn al-Haitham developed an analytical geometry that links geometry with algebra. In addition, he also introduced the concept of movement and transformation in geometry.
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Arithmetic is one of the branch of mathematics which is emphasize on number as a subject matter and the operations between them such as addition, subtraction, multiplication, and division. In Surah al-Kahfi verse 22 implied about arithmetic. Here is the verse :
“They will say there were three, the fourth of them being their dog; they will say there were five, the sixth of them being their dog – guessing at the unseen; and they will say there were seven, and the eighth of them was their dog. Say, (O Muhammad), ‘My lord is most knowing of their number. None knows them except a few. So do not argue about them except with an obvious argument and do not inquire about them among (the speculators) from anyone'”.
From this verse, we can take a point that there are some rules and formula, which is coherent with arithmetic.
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5. Theory of Number
Number theory, or theory of number, is one of the branch of pure mathematics that studies the properties of integers and contain many open problem that can be easily understood, especially for non-mathematician. It start when Egyptian who settled along the Nile in the Babylonians of Africa along the Tigris and Euphrat rivers, and other civilizations who settled along in the other rivers.
At that time, they need calculations to measure the parcels of land ownes, so it takes a numbers. At Islamic Caliphate, the Babylonian Mathematics mixed with Greek and Egypt Mathematics and Mesopotamia, especially Baghdad, became an important studies center of Islamic Mathematics.
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6. Law of Sines
Law of Sines is a part of trigonometry; an equation which is related with length of the sides of a triangle in any shape to the sines of its angles. This is used to determined a praying time in around the world which has many various of time difference.
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7. Cubic Equation
Cubic equation, or cubic function (in other name, the three-degree function) is the function of which the highest rank of the variable is a power of three. Each cubic function has at least one inflection point, i.e the transition point of the curve shape from concave to convex or vice versa. In addition to the turning point, a cubic function may also have one or two extreme point (maximum or minimum).
The presence or absence of an extreme point in a cubic function depends on the magnitude of the values b, c, and d in the equation. Thus there are several possibilities regarding the shape of the curve of a cubic function. Cubic functions have only turning points, with no extreme points.
In Islam, we have Omar Khayyam, as a scientist, who wrote the Treatise on Demonstration of Problems of Algebra. It containing the systematic solution of cubic or third-order equations, going beyond the Algebra of al-Khwarizmi. He obtained the solutions of these equations by finding the intersection points of two conic sections; which is used by Greeks, but it is not generalized the method to cover all positive roots.
8. Irrational Number
Irrational number is the real number which is not rational number, or it is a real number that can not be shared (the result for him never stops). In this case, irrational numbers can not be expressed as a / b, with a and b being integers and b not equal to zero. Therefore, irrational numbers are not rational numbers. The most popular examples of irrational numbers are the numbers π, √2, and è. Irrational number was found by a Greek scientist.
At that time, they are not happy with them and only able to cope by drawing a distinction between magnitude and number. Abū Kāmil Shujāʿ ibn Aslam and Ibn Tahir al-Baghdadi slowly removed the distinction between magnitude and number. And then, they allowing irrational quantities to appear as coefficients in equations and solutions of algebraic equations.
Induction (or well-known as mathematical induction), is a method of proof that is often used to determine the truth of a given statement in the form of natural numbers.
10. Spherical Trigonometry
Spherical trigonometry is a part of trigonometry and correlated with law of sines. It discovered in 10th century: it has been attributed variously to Abu-Mahmoud Khojandi, Nasir al-Din al-Tusi and Abu Nasr Mansur, with Abu al-Wafa’ Buzjani as a contributor. Nasir al-Din al-Tusi stated the law of sines for plane and spherical triangles, and provided proofs for this law.
In this part, it shows how mathematics giving a contribution to astronomy. If we saw the chronology of astronomy, it takes a long way since the Sumerian and Babylonian live in Mesopotamia at 3000-3500 BC. During its process, astronomy has evolved along with the development of human mindset, with various discoveries and theories. At the golden age of Islam, Astronomy is growing rapidly and some of Islamic scientist such as Al-Khwarizmi using mathematics to determine the time of the new moon, sunrise, moon, planet, and for the prediction of the eclipse in tabular form.
Axiom, or postulate, is one of terms in mathematics, which is defined as a statement that is taken to be true. This word come from Greek language, αξιοειν (axioein), which means to be considered valuable, which then comes from αξιος (axios), which means valuable. In Islam, we found many axiom in Al-Qur’an. One of those axiom is number 19. This number can be found in many calculation. For example, if we count the basmala recite, we can found that there were 19 letter. And we can found many things that has 19 time mentions, and other things that correlated with number 19.
13. Number Zero (0)
One of the most important in Mathematics development is the discovery of a zero. This is relevant with concept ‘Laa Ilaaha Illallah’, which means ‘There is no God but Allah.’ If reviewed further (and divided), we found that there is no God means zero (0), and Allah means (1). Number zero has found by Al-Khwarizmi, which is brought to Europe by Leonardo Fibonacci, but is rejected by many people, especially in church circle at that time.
14. Odd Number
This title is not refer to strange or bizarre number, but refers a number that is not divisible by the number two or even the other number. This type of number completing the other number such as 2, 4, 6, and etc. In Islam, especially Qur’an, we found many odd number inside of it such as pray witr, which is performed three rak’ahs. And then the number of five-time prayer congregations, amounting to 17 rakats.
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15. Completion of Previous Theories
Among all of this discovery, we can take a point that an Islamic Scientist such as Al-Khwarizmi and Al-Biruni has learned or studied the theories from the scientist such as Euclid, Archimedes, and other scientist. They found a weakness and trying to find a solution, so became a new discovery and applied around the world until now.
That was the contribution of Islam in mathematics, we hope you enjoy and increase your knowledge and faith to Allah swt.
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