174.--THE SQUARES OF BROCADE.

[Illustration]

I happened to be paying a call at the house of a lady, when I took up

from a table two lovely squares of brocade. They were beautiful

specimens of Eastern workmanship--both of the same design, a delicate

chequered pattern.

"Are they not exquisite?" said my friend. "They were brought to me by a

cousin who has just returned from India. Now, I want you to give me a

little assistance. You see, I have decided to join them together so as

to make one large square cushion-cover. How should I do this so as to

mutilate the material as little as possible? Of course I propose to make

my cuts only along the lines that divide the little chequers."

[Illustration]

I cut the two squares in the manner desired into four pieces that would

fit together and form another larger square, taking care that the

pattern should match properly, and when I had finished I noticed that

two of the pieces were of exactly the same area; that is, each of the

two contained the same number of chequers. Can you show how the cuts

were made in accordance with these conditions?

Amusements in Mathematics · 第 203 / 970 题