Tokoh Matematik 292i5n

TOKOH-TOKOH MATEMATIK Rujukan: w.w.w.storyofmathematics.com

1) 570-495 BC Pythagoras (Greek) Expansion of geometry, rigorous approach building from first principles, square and triangular numbers, Pythagoras’ theorem

2) 428-348 BC Plato (Greek)

Platonic solids, statement of the Three Classical Problems, influential teacher and popularizer of mathematics, insistence on rigorous proof and logical methods

Plato the mathematician is perhaps best known for his identification of 5 regular symmetrical 3-dimensional shapes, which he maintained were the basis for the whole universe, and which have become known as the Platonic Solids: a) tetrahedron (constructed of 4 regular triangles, and which for Plato represented fire) b) octahedron (composed of 8 triangles, representing air) c) icosahedron (composed of 20 triangles, and representing water) d) cube (composed of 6 squares, and representing earth) e)dodecahedron (made up of 12 pentagons, which Plato obscurely described as “the god used for arranging the constellations on the whole heaven”).

3) 300 BC Euclid Greek Definitive statement of classical (Euclidean) geometry, use of axioms and postulates, many formulas, proofs and theorems including Euclid’s Theorem on infinitude of primes

Euclid is often referred to as the “Father of Geometry”, and he wrote perhaps the most important and successful mathematical textbook of all time, the “Stoicheion” or “Elements”, which represents the culmination of the mathematical revolution which had taken place in Greece up to that time

Euclid’s method for constructing of an equilateral triangle from a given straight line segment AB using only a com and straight edge was Proposition 1 in Book 1 of the "Elements"

4) 287-212 BC ARCHIMEDES (Greek) He also an engineer, inventor and astronomer, Archimedes was best known throughout most of history for his military innovations like his siege engines and mirrors to harness and focus the power of the sun, as well as levers, pulleys and pumps (including the famous screw pump known as Archimedes’ Screw, which is still used today in some parts of the world for irrigation).

Approximation of the area of circle by Archimedes’ method of exhaustionApproximation of the area of circle by Archimedes’ method of exhaustion.

• Archimedes produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using shapes he already understood.

• For example, to estimate the area of a circle, he constructed a larger polygon outside the circle and a smaller one inside it. • He first enclosed the circle in a triangle, then in a square, pentagon, hexagon, etc, etc, each time approximating the area of the circle more closely. By this so-called “method of exhaustion” (or simply “Archimedes’ Method”), he effectively homed in on a value for one of the most important numbers in all of mathematics, π. • His estimate was between 31⁄7 (approximately 3.1429) and 310⁄71 (approximately 3.1408), which compares well with its actual value of approximately 3.1416.

Archimedes is probably best ed for the anecdotal story of his discovery of a method for determining the volume of an object with an irregular shape.

This gave rise to what has become known as Archimedes’ Principle: an object is immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.

5) 780-850 AD Muhammad Al-Khwarizmi

Persian The word “algorithm” is derived from the Latinization of his name, and the word "algebra" is derived from the Latinization of "al-jabr", part of the title of his most famous book, in which he introduced the fundamental algebraic methods and techniques for solving equations

An example of Al-Khwarizmi’s “completing the square” method for solving quadratic equations

6) 1170-1250 Leonardo of Pisa (Fibonacci) Italian The 13th Century Italian Leonardo of Pisa, better known by his nickname Fibonacci, was perhaps the most talented Western mathematician of the Middle Ages. Fibonacci is best known, though, for his introduction into Europe of a particular number sequence, which has since become known as Fibonacci Numbers or the Fibonacci Sequence

~He discovered the sequence - the first recursive number sequence known in Europe - while considering a practical problem in the “Liber Abaci” involving the growth of a hypothetical population of rabbits based on idealized assumptions.

~He noted that, after each monthly generation, the number of pairs of rabbits increased from 1 to 2 to 3 to 5 to 8 to 13, etc, and identified how the sequence progressed by adding the previous two (in mathematical , Fn = Fn-1 + Fn2), a sequence which could in theory extend indefinitely.

Fibonacci introduced lattice multiplication to Europe

7) 1350-1425 Madhava (Indian) • Madhava sometimes called the greatest mathematician-astronomer of medieval India. • He came from the town of Sangamagrama in Kerala, near the southern tip of India, and founded the Kerala School of Astronomy and Mathematics in the late 14th Century. • Use of infinite series of fractions to give an exact formula for π, sine formula and other trigonometric functions, important step towards development of calculus

Madhava’s method for approximating π by an infinite series of fractions

8)Al-Batani Arab mathematician and astronomer Abu Abdallah Muhammad ibn Jabir al-Battani (868-929) made accurate astronomical observations which allowed him to improve on Ptolemy's data for the Sun and the Moon. He also produced a number of trigonometrical relationships:

He also solved the equation sin x = a cos x discovering the formula:

9) Al-Haytham (b. 965), Al-Haytham (b. 965), Al-Haytham (b. 965), also known as Alhazen, in his work on number theory, seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form where is prime.

10) Appolonius (262-190 SM) Konsepnya mengenai parabola, hiperbola, dan elips banyak memberi sumbangan bagi astronomi modern. Ia merupakan seorang matematikawan yang ahli dalam geometri. Teorema Appolonius menghubungkan beberapa unsur dalam segitiga.

Tokoh-Tokoh Matematik DISEDIAKAN OLEH: SHUHAILY BT YAZID PPG SCE-B AMB FEB 2012