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2 ;" ": 2 ;" ";: 2 **clean lines** 2 1 logo 1 file 1 Recording 1 PYTHAG1 1 ;"of the": 1 ;"Yes, again there are 8 tiles." 1 ;"Yes, 8 tiles make up the square." 1 ;"Would you like to see the proof again? (press Y or N)" 1 ;"When you are ready to go on to": 1 ;"What is the total number of tiles in the two smaller squares?": 1 ;"UPPER CASE"; 1 ;"Type in file name in "; 1 ;"Turn to chapter five in the" 1 ;"These tiles were laid in the" 1 ;"Then he noticed that a square" 1 ;"The Greek found this was true" 1 ;"That completes the proof.": 1 ;"That completes Lesson One, in" 1 ;"THEOREM": 1 ;"THE THEOREM" 1 ;"THE AREA" 1 ;"Stop and rewind tape" 1 ;"SAVE""file"" LINE 2" 1 ;"Rectangle" 1 ;"PYTHAGORAS" 1 ;"PYTHAG2"; 1 ;"PRESS S" 1 ;"PRESS R": 1 ;"PLEASE WAIT"; 1 ;"Now the Greek wondered if this" 1 ;"No,there are 8 tiles,4 in each square.": 1 ;"No, there are 8 tiles.": 1 ;"No, count them!" 1 ;"No, count them carefully.": 1 ;"NEW followed by": 1 ;"Measure the sides of the" 1 ;"Load main program" 1 ;"Leave tape running" 1 ;"LESSON ONE": 1 ;"LESSON ONE" 1 ;"It is a RIGHT ANGLED" 1 ;"Is the area of the" 1 ;"In each case answer the ques-" 1 ;"If you would like to go over": 1 ;"How many tiles make up the square? ": 1 ;"He then noticed that two" 1 ;"Bye for now!": 1 ;" has the same area" 1 ;" We name the theorem after theGreek thinker named Pythagoras,though it is doubtful whether itwas he who actually discoveredits truth." 1 ;" We can see then, that "; 1 ;" We paint the smaller rect-" 1 ;" Turn to chapter five in theworkbook where you will find anoutline of a right angledtriangle, squares and construct-ion lines. Find the areas of thetwo rectangles and the squaresand so confirm the proof in thatparticular case." 1 ;" This square is the same as the" 1 ;" This red rectangle has the" 1 ;" This parallelogram has the" 1 ;" Then we draw a square on the" 1 ;" The parallelogram has the same" 1 ;" The long side of a right angledtriangle is usually called theHYPOTENUSE of the triangle, sowe can restate the theorem ofPythagoras:" 1 ;" The Greek noticed that if he " 1 ;" So, we can divide the big" 1 ;" Rectangle "; 1 ;" Now we draw squares on the" 1 ;" Now look at the other rect-" 1 ;" Next we draw in a construction" 1 ;" In this case this rectangle" 1 ;" In this section you will beshown a demonstration or PROOFof the theorem for any rightangled triangle." 1 ;" IN A RIGHT-ANGLED TRIANGLE, THESQUARE ON THE HYPOTENUSE ISEQUAL TO THE SUM OF THE SQUARESON THE OTHER TWO SIDES." 1 ;" First, we draw a right angled" 1 ;" But this square has the same" 1 ;" A PROOF": 1 ;" has the same area as the " 1 ;" Many of the major discoveriesin mathematics have come fromidle observation and the suddennoticing of a pattern. Althoughwe do not know for certain, itis possible that the theorem ofPythagoras was first suggestedto a Greek some 2500 years agowhile he was gazing at thepatterns in a floor made upfrom triangular tiles like this-" 1 ;" LOADING PROGRAM 1 ;" ISOSCELES triangle." 1 ;" ": 1 ;" ": 1 ;" " 1 ;" " 1 **two tile triangle** 1 **triangle** 1 **the proof** 1 **shear 2b** 1 **shear 2a** 1 **shear 1b** 1 **shear 1a** 1 **s-square** 1 **input a string** 1 **h-square** 1 **fill rect2** 1 **fill rect1** 1 **fill in side square** 1 **fill in s-square** 1 **fill in hyp square** 1 **fill in base square** 1 **fill in b-square** 1 **ending routine** 1 **draw tile pattern** 1 **draw tile net** 1 **draw single tile** 1 **c-line** 1 **b-square** 1 ***CORE*** 1 "clear (y/n) ?";q$ 1 "address ? ";x 1 "Type in y(es) or n(o) ";A$: 1 "Filename",a$ 1 " yellow square...": 1 " would work in the case of" 1 " up a THEOREM.": 1 " triangles with squares drawn" 1 " triangle...": 1 " triangle.": 1 " tion: "; 1 " three different right angled" 1 " the other two sides.": 1 " the next lesson we shall see" 1 " squares?": 1 " squares could be made up on" 1 " squares and calculate their" 1 " square into two rectangles...": 1 " square into two rectangles "; 1 " side of the triangle.": 1 " same area as the square...": 1 " same area as the red parallel- ogram, for it has the same length and height." 1 " pattern shown above.": 1 " otherwise:-": 1 " other two sides...": 1 " other right angled triangles.": 1 " on their sides.": 1 " of the triangle.": 1 " of the areas of the other two" 1 " make up a larger right angled " 1 " long side of the triangle...": 1 " llelogram...": 1 " line which divides the large" 1 " how the theorem can be put to" 1 " has the same area as the para-" 1 " for all the right angled tri-" 1 " could be made up on the longer" 1 " combined two tiles, he could " 1 " booklet where you will find" 1 " blue square...": 1 " big square the same as the sum" 1 " as the yellow square...": 1 " areas.": 1 " area as the square...": 1 " area as the square on the side" 1 " angles he studied, so he made" 1 " angle. First we colour it red.": 1 " angle red...": 1 " TRIANGLE IS EQUAL TO THE SUM " 1 " THE OTHER TWO SIDES. ": 1 " THE AREA OF THE SQUARE ON THE " 1 " SAME AS THE SUM OF THE AREAS" 1 " OF THE OTHER TWO SQUARES.": 1 " OF THE AREAS OF THE SQUARES ON " 1 " OF THE LARGE SQUARE IS THE 1 " Lesson One again, ": 1 " LONG SIDE OF A RIGHT ANGLED " 1 " LESSON TWO type:-": 1 Q 1 " 1 1