REMARKABLE FOR WHAT IT DOES NOT SAY by Dr.Khin Maung Win (Maths)

MATHEMATICS 12

REMARKABLE FOR WHAT IT DOES NOT SAY

figure of six lines meeting a line

In this figure, the reader will see six straight lines which meet another straight line. The lines are numbered one to six.The reader can easily see which of the lines make right angles with the line they meet.The lines three and five make right angles while others do not.

Now comes the difficult part which is to  explain the meaning of a right angle , more precisely to tell what makes a right angle, to be able to give the criteria for a right angle .

When Euclid was asked what is meant by a right angle , he answered ” A right angle is formed when two lines meet in such a fashion that two adjacent angles, that is, angles which lie side by side , are equal to each other.”

figure of two right angles A and B

Today’s mathematicians remarked that Euclid’s definition is more remarkable for what it does not say than anything else.He did not say that a right angle is equal to ninety degrees.He managed to define a right angle without even without using the term ‘degree’.