Read The Nature of Mathematics Online

by Geeky Nigeria

14 THE NATURE OF MATHEMATICS 

cided ; the point thus indicated was marked by a peg R. 
The result was to form a triangle PQR whose angle at P was 
a right angle, and the line PR would give an east and west 
line. A similar method is constantly used at the present time 
by practical engineers, and by gardeners in marking tennis 
courts, for measuring a right angle. This method seems also 
to have been known to the Chinese nearly three thousand 
years ago, but the Chinese made no serious attempt to classify 
or extend the few rules of arithmetic or geometry with which 
they were acquainted, or to explain the causes of the phenomena 
which they observed. 

The geometrical theorem of which a particular case is in- 
volved in the method just described is well known to readers 
of the first book of Euclid's Elements. The Egyptians must 
probably have known that this theorem is true for a right- 
angled triangle when the sides containing the right angle are 
equal, for this is obvious if a floor be paved with tiles of that 
shape. But these facts cannot be said to show that geometry 
was then studied as a science. Our real knowledge of the nature 
of Egyptian geometry depends mainly on the Rhind papyrus. 

The ancient Egyptian papyrus of Rhind, which was written 
by an Egyptian priest named Ahmes considerably more than 
a thousand years before Christ, and which is now in the 
British Museum, contains a fairly complete applied mathe- 
matics, in which the measurement of figures and solids plays 
the principal part ; there are no theorems properly so called ; 
everything is stated in the form of problems, not in general 
terms but in distinct numbers. For example : to measure a 
rectangle the sides of which contain two and ten units of 
length ; to find the surface of a circular area whose diameter is 
six units. We find also in it indications for the measurement 
of solids, particularly of pyramids, whole and truncated. The 
arithmetical problems dealt with in this papyrus which, by 
the way, is headed " Directions for knowing all dark things "- 
contain some very interesting things. In modern language, 
we should say that the first part deals with the reduction of 
fractions whose numerators are 2 to a sum of fractions each 
of whose numerators is 1. Thus ^ is stated to be the sum 
of -Jf, -^g-, yfj-, and -j^-. Probably Ahmes had no rule 
for forming the component fractions, and the answers given 

Was this article helpful?
Yes0No0

You may also like

error: Content is protected !!