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Elementary matematical ideas, theorems from the Ancient Greece In this time the greatest mathematicians were Thales of Miletos, Pythagoras of Samos, Aristoteles of Strageria and Euclides of Alexandria in chronological sequence. They also were philosophers except for Euclides. Thales is the first well-known greek matematician lived from BC 624 to BC 546. He founded the school of Miletos and taught there. He has reached famous results in geometry. He said that the sum of angles in the triangle equals 180 degrees, declared the Thales’s theorem for triangles with right angle and the theorem of paralell lines in the circle. Foreign people (italians, frenches, spanishes, russians) call the first one the large Thales’s theorem and the second one the little Thales’s theorem. Pythagoras, who lived from BC 582 to BC 496 was a presocratist philosopher. He travelled to to Egypt in order to learn that culture. After wards he moved to Kroton, Italy, where he founded the phytagorian school. In math, he declared the Phytagoras’s theorem for triangles with right angle, saying that the square of the longest sideline equals the sum of square of the second sideline and square of the third sideline. Aristoteles has lived from BC 384 until BC 322. He was born in Strageria and he was a student of Platon. Finally he was the master of Alexander the Great. Aristoteles was a wellknown philosopher, however he cared for logic too. Also he showed the irrationality of squareroot of two. Aristoteles and squareroot of two a 2 b 2 a 2 2 b 2 a 2b 2 a 2k 2b 2 4k 2 It’s impossible, contradiction.□ Euclides lived in the third century BC. He studied at Platon’s Academy, later he founded a school in Alexandria. He was a simple matematician, and published his mathematical ideas in his book, the Elements, moreover founded the classic geometry. Furthermore he has analysed and solved some problems in number theory. For example he verificated the infinitude of prime numbers firstly and found out the Euclides’s algorithm. The Euclides’s algorithm helps us to find the gcd, greatest common divisor of two numbers. Euclides and the prime numbers pn-s are prime numbers, so N = p1p2p3…pn, but N + 1 is a prime again.□ Euclides’s algorithm A Bq1 r1 B r1 q 2 r2 r1 r2 q3 r3 r2 r3 q 4 r4 rn 2 rn 1 q n rn rn 1 rn q n 1 0 rn is the gcd of A and B.□