Sharp EL-531RH Teachers Manual page 55

Triples
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
This activity assumes that students have done some previous work on Pythagoras' theorem. After
a short introduction, the students can be set the task of trying to find right-angled triangles where
the sides are all integers. The students can be shown how to use the rectangular-polar coordinate
conversion function of the calculator to find the hypotenuse given the two shorter sides. It is
important that it is explained to students that the calculator is converting a pair of rectangular
Cartesian coordinates to polar coordinates, which comprise a distance and an angle.
Students should be encouraged to identify the different 'families' of right-angles triangles, (e.g. 3, 4,
5 and 6, 8, 10 etc.,) and concepts of similarity should be discussed. It is important that students'
generalizations are collated and discussed.
• • • • • • • • • • • • • • • Points for students to discuss • • • • • • • • • • • • • •
To generate a Pythagorean triple, square any odd number and split the answer into two consecu-
tive integers. The original number and the two consecutive integers will form a Pythagorean triple.
2 = 25 = 12 + 13. Alternatively, square any even number, divide it by two, and then
For example: 5
split it into two 'close' integers. The original number and the two 'close' integers will form a
Pythagorean triple. For example: 6
Further Ideas
• When are the areas and perimeters of right-angled triangles numerically equal? Investigate.
• A consideration of the angles obtained by converting rectangular Cartesian coordinates to
polar coordinates could form the basis of an introduction to trigonometry.
= 36; 36 ÷ 2 = 18 = 8 + 10.
2
54
High school