Lecture provides knowledge the mean value theorem and relative extrema. The main contents of this chapter include all of the following: The mean value theorem, critical numbers, increasing/decreasing functions, the first derivative test for relative extrema. | General Mathematics ADE 101 Unit 3 LECTURE No. 27 PYTHAGORAS THEOREM 1 Today’s Objectives Knowledge Test Pythagoras was a Greek philosopher and religious leader. He was responsible for many important developments in maths, astronomy, and music. Pythagoras (~560-480 .) His students formed a secret society called the Pythagoreans. As well as studying maths, they were a political and religious organisation. Members could be identified by a five pointed star they wore on their clothes. They had to follow some unusual rules. They were not allowed to wear wool, drink wine or pick up anything they had dropped! Eating beans was also strictly forbidden! A right angled triangle A Pythagorean Puzzle Draw a square on each side. A Pythagorean Puzzle c b a Measure the length of each side A Pythagorean Puzzle Work out the area of each square. A Pythagorean Puzzle a b C² b² a² c A Pythagorean Puzzle c² b² a² A Pythagorean Puzzle 1 A Pythagorean Puzzle 1 2 A Pythagorean Puzzle 14 1 2 A Pythagorean Puzzle 1 2 3 A Pythagorean Puzzle 1 2 3 A Pythagorean Puzzle 1 2 3 4 A Pythagorean Puzzle 18 1 2 3 4 A Pythagorean Puzzle 19 1 2 3 4 5 A Pythagorean Puzzle 1 2 3 4 5 What does this tell you about the areas of the three squares? The red square and the yellow square together cover the green square exactly. The square on the longest side is equal in area to the sum of the squares on the other two sides. A Pythagorean Puzzle 1 2 3 4 5 Put the pieces back where they came from. A Pythagorean Puzzle 1 2 3 4 5 A Pythagorean Puzzle Put the pieces back where they came from. 1 2 3 4 5 Put the pieces back where they came from. A Pythagorean Puzzle 1 2 3 4 5 Put the pieces back where they came from. A Pythagorean Puzzle 1 2 3 4 5 Put the pieces back where they came from. 1 2 3 4 5 Put the pieces back where they came from. A Pythagorean Puzzle This is called Pythagoras’ Theorem. c² b² a² c²=a²+b² A Pythagorean Puzzle It only works with right-angled triangles. hypotenuse The longest side, | General Mathematics ADE 101 Unit 3 LECTURE No. 27 PYTHAGORAS THEOREM 1 Today’s Objectives Knowledge Test Pythagoras was a Greek philosopher and religious leader. He was responsible for many important developments in maths, astronomy, and music. Pythagoras (~560-480 .) His students formed a secret society called the Pythagoreans. As well as studying maths, they were a political and religious organisation. Members could be identified by a five pointed star they wore on their clothes. They had to follow some unusual rules. They were not allowed to wear wool, drink wine or pick up anything they had dropped! Eating beans was also strictly forbidden! A right angled triangle A Pythagorean Puzzle Draw a square on each side. A Pythagorean Puzzle c b a Measure the length of each side A Pythagorean Puzzle Work out the area of each square. A Pythagorean Puzzle a b C² b² a² c A Pythagorean Puzzle c² b² a² A Pythagorean Puzzle 1 A Pythagorean Puzzle 1 2 A Pythagorean Puzzle 14 1 2 A .
