"Is there anyone here who understands the ecclesiastics of geometry? No one? Are you sure? If so, then I shall explain it with confidence. To begin with we have to have a circle. Has anyone a circle in his pocket? No? Such being the case, I will make a circle by tying the two ends of this cord together."
Tie ends of cord together. Illustration shows easiest way to do this. This method will prove very useful later on in the course also.
After ends are tied, show loop to audience. To them it looks as though you had made a loop from an ordinary piece of cord.
"Here's our circle."
Hold up cord with fingers and try to make it circular in shape.
"Not such a good circle, but that is because of the hole we built it around. Of course, you understand that a circle is merely a straight line built around a round hole, and then the ears are chopped off."
Point to ends of cord to show ears.
"Anyway that's my story and I'm going to stick to it."
Pick up scissors.
"I cut a hole in the circle."
Hold up cord and cut through the place WHERE ENDS WERE WAXED TOGETHER. One end, of course, falls downward.
"And behold, the circle has gone."
Bring both ends together, but hold one about half an inch higher than the other. "Just look, how uneven I cut those ends!"
Trim off upper end a little, then lower end a little, and then cut both ends even.
To the audience this looks like by-play, but to you it means destroying evidence. You are cutting the waxed telltale ends away.
Hold ends about a foot apart.
"There, they look a lot evener now."
Pull cord out straight.
"We have a straight line again—that is, it would be straight if it wasn't for those ears."
Nod your head to knot in center of cord.
"Now, we'll tie the ends together again."
Tie ends together.
"And there we have a circle again."
Show loop with knot on each side.
"That is, it would be a circle if it were! round and if it weren't for the ears. We now have two pairs of them."
Hold the loop as shown in illustration (next page). It gives a rabbit-like effect.
"Ah—there's a rabbit—body, head, and ears. I shall now show you the vanishing rabbit." Let cord fall back into original large loop again.
"I think I'll cut the ears off."
Pick up scissors. Hold End B of cord, as shown, in left hand. This is the end with the short piece of cord tied around it. Cut the knot off. This does away with the short piece of cord. You may, if you desire, cut the ends two or three times before cutting the knot off. Start with the ends and work toward the knot.
Hold cord together in left fingers so that it looks as though you are holding two ends. The audience thinks that cord is cut and that two ends are covered by your finger tips.
"That's a good idea, only when you cut the ears off you still have two ends left, and we are just where we were before with our straight line. If I tie the ends together, we have ears again. But ah-ha—I have an idea."
Point at knot hanging downward.
"The knot is made up of two ends—this makes the other two ends in the middle. Well—well, why didn't I think of that before? That changes everything all around. With the two ends in the middle, I have but to say, 'Papa loves mama, mama loves papa,' and unite them as one."
Open up loop and show that cord is united.
"And they lived happy or unhappy ever after."
"Which, of course, brings us back to the problem of the circle. But why worry about a circle? We unknot the knot here. This gives us two ends, so we pull the string out into a straight line, and there I have proved that a straight line is the nearest distance between two ends."
Hold cord out by its ends so that it is pulled taut. Show palms empty while holding cord. Then give cord to a spectator.
"There sir (or madam, or miss), take this cord home and work on your lesson for tomorrow."
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