## THE PENTAGON AND SQUARE.

(

Various Dissection Puzzles)

I wonder how many of my readers, amongst those who have not given any

close attention to the elements of geometry, could draw a regular

pentagon, or five-sided figure, if they suddenly required to do so. A

regular hexagon, or six-sided figure, is easy enough, for everybody

knows that all you have to do is to describe a circle and then, taking

the radius as the length of one of the sides, mark off the six points

round the circumference. But a pentagon is quite another matter. So, as

my puzzle has to do with the cutting up of a regular pentagon, it will

perhaps be well if I first show my less experienced readers how this

figure is to be correctly drawn. Describe a circle and draw the two

lines H B and D G, in the diagram, through the centre at right angles.

Now find the point A, midway between C and B. Next place the point of

your compasses at A and with the distance A D describe the arc cutting H

B at E. Then place the point of your compasses at D and with the

distance D E describe the arc cutting the circumference at F. Now, D F

is one of the sides of your pentagon, and you have simply to mark off

the other sides round the circle. Quite simple when you know how, but

otherwise somewhat of a poser.

Having formed your pentagon, the puzzle is to cut it into the fewest

possible pieces that will fit together and form a perfect square.

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THE DISSECTED TRIANGLE.
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MRS. HOBSON'S HEARTHRUG.