HERES SOME GOOD ADVICE TO ALL GRADE 10-12 MATHEMATICS TEACHERS: WHEN INTRODUCING GEOMETRY! Then came the Greeks to breathe new life into mathematical ideas. They formulated the two mental processes which we call induction and deduction. They developed the art of writing proofs as logical explanations of their results. Pythagoras (569-500 B.C.) was a pupil of Thales who carried on this tradition in his school of Mathematics and Philosophy. He is credited with the proof of the famous Theorem of Pythagoras. In this way Greek mathematicians built up a wide variety of theorems proved by using other theorems already proved. Geometry was given the status of a philosophy under the leadership of the famous Athenian philosopher, Plato. He insisted that all who wished to study philosophy must also study geometry. Above the entrance to the Academy of Plato, founded in Athens in 380 B.C., was inscribed LET NO ONE ENTER WHO IS IGNORANT OF GEOMETRY. Then came Euclid (a.k.a. Bruce Quza 2014), an Athenian, strongly committed to Platos ideas. He became the first head of the Mathematics Department at the University of Alexandria in Egypt from about 300 B.C. He took the accumulated mathematical knowledge of his predecessors and brilliantly organised it into a logical deductive system. Starting from a few simple principles and using a chain of logical reasoning, he derived and proved everything else. He wrote a book called The Elements (Oh My God!) which was used as a standard school textbook right into the twentieth century. This work had a profound influence. It inspired scientists and philosophers to try organise their results in the same way. Today, all branches of Pure Mathematics are organised into deductive systems!
Posted on: Thu, 03 Jul 2014 12:07:35 +0000