HOW A SPACE MAY BE APPARENTLY EN- 

 LARGED BY CHANGING ITS SHAPE 



HE following is a curious illustration of the errors 

 to which careless observers may be subject : 



Draw a square, like Fig. 19, and divide the sides 

 into 8 parts each. Join the points of division in 

 opposite sides so as to divide the whole square into 64 

 small squares. Then draw the lines shown in black and cut 

 up the drawing into four pieces. The lines indicating the 

 cuts have been made quite heavy so as to show up clearly, 



Fig. 19. 



Fig. ao. 



but on the actual card they may be made quite light. Now, 

 put the four pieces together, so as to form the rectangle 

 shown in Fig. 20. Unless the scale, to which the drawing 

 is made is quite large and the work very accurate, it will 

 seem that the rectangle contains 5 squares one way and 

 13 the other which, when multiplied together, give 65 for 

 the number of small squares, being an apparent gain of 

 one square by the simple process of cutting. 



126 



