toy treasures - arvind gupta (60 kb doc)

FIVE SQUARESDividing a square piece into four equalsquares is no problem at all.But dividing a square into five equal squaresis no easy task.It will keep most people scratching theirheads.But it is quite easy.First cut a square and fold a plus sign alongthe dotted lines.This will fix the midpoints of the four sides.Now mark one diagonal each, of the fourrectangles so formed.Cut along the dark lines Fig (1).Now arrange the nine pieces into fivesquares as shown in Fig (2).PUZZLING SQUAREAt first sight it looks so easy to assemble amere four pieces that were originally cutfrom a square.Yet the fact is that most people are not verygood at making up certain shapes from ajumbled collection of other shapes.On one square of paper (ABCD) find point Eat the center of AB and H at the midpoint ofBD.Join up EC, CH and HE, then cut the paperalong the lines you have drawn Fig (3).You will be left with four triangles.Hand them to your victim and enjoy thesight of a perplexed puzzler trying to put thefour pieces back together as a square.