THE USEFULNESS OF EUCLIDEAN SOFTWARE

TO CALCULATE

THE ANGLES OF PROPERTIES OF POLYGON

BY:

STEPHEN HOU @ CHAN ENG CHIONG

08M0551

1

Table Of Contents:

1. Table of Contents ………………………………………………………….. [2]

2. Introduction ………………………………………………………………… [3]

3. What is Euclidean Reality? .. …………………………………...………….. [4]

4. How to draw using EuclideanReality?............................................................ [4]

5. Conclusion ………………………………………………………………….. [10]

2

2. Introduction

For any good instruction, teachers must adapt different materials to students’

needs. This implied to software as well. Students, nowadays, have different

abilities, interests and preferences that warrant different teaching consideration

and strategies. Therefore, teachers must decide how to use any software according

to the children’s needs. According to V. Sharp (1996:152) choosing good

software is an eight steps process:

1) know the specific software needs of your population,

2) locate the software,

3) research hardware compatibility,

4) examine the program’s contents

5) look at the instructional design

6) check out how easy the program is to learn

7) evaluate the program in terms of consumer value

8) investigate the technical support and cost.

There are varieties of mathematical software available in the markets. Euclidean

Reality software is one of them.

3

3. What is Euclidian Reality?

Euclidian Reality is a dynamic geometry builder. With Euclidian Reality you can

create exact figures regarding their mathematical properties, distort them freely,

check properties such as angles and lengths, print figures and export them in

several formats, vectorial or bitmap. You can perform any kind of configuration

in Euclidian geometry. It is free software which can be downloaded from the

website http://membres.lycos.fr/animgallerie/euclide .

The topic that I would like to illustrate is the properties of circles. I have drawn

three separate diagrams using this software. This will help the students to measure

the angles more accurately rather than using protractor. Beside that, we will know

the characteristics of the properties better.

4. Drawing diagrams using Euclidean Reality

Using the software, the students can learn how the properties of circle.

For Diagram 1:

1a) Draw a circle by click Circle Menu select circle (circle + radius) or u can

click the icon on the left hand side of the tool bar. (Fig 1)

Fig. 1

4

b) Click any radius that you want as shown on the diagram (Fig. 2) and you

can see the circumference of the circle.

Fig. 2

Mark the arc length and circle by putting the points A and C as shown

below. We will fix the two points from moving by using the icon and

thus the diagram are shown below. (Fig 3)

Fig. 3

5

c) To find the angles automatically both centre and circumference.

Click the Direct angle icon on the left side of the toolbar which

display the centre. Click on centre O, followed by the two points on the

circumference, (A and B). Then the angle subtended by the arc AB will

followed automatically as shown below. (Fig. 4)

Fig. 4

Click on Point C, followed by two point A and B on the arc. This will

displayed the angle at the circumference point C, followed by AB. The

diagram is shown below:

6

Fig. 5

It can be seen that i.e. 84° is twice the i.e. 42°.

7

d) We can even experimenting the moving of the point around the circle and

the result remains the same. There are a few diagrams show the same

properties.

(i) Angle at the centre O is twice the angle at the circumference

Fig. 6

(ii) Fig.7

8

e) There are other properties of a circle are (i) angle in the same segment are equal

(ii) The angle in the semicircle is a right angle (iii) angles in opposite segments

are supplementary (e.g. )

(i) Angles in the same segment are equal

Fig. 8

(ii) The angle in the semi-circle is a right angle

(Fig. 9)

9

(iii) Angles in opposite segments are supplementary (e.g. )

(5) Conclusion

Through this Euclidean Reality software, we can see how useful the software

can be used not only for Geometry but it can be used for other features. This

software can be recommended to teachers in schools when they set questions

for their students.

10