Download e-book for iPad: Adding a Dimension by Isaac Asimov

By Isaac Asimov

ISBN-10: 0234778741

ISBN-13: 9780234778746

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Additional info for Adding a Dimension

Example text

Here's another method of squaring the circle. What you really need, assuming the radius of your circle to represent 1, is another straight line representing S/TT. A square built on such a line would have just the area of a unit-radius circle. How to get such a line? Well, if you could construct a line equal to TT times the length of the radius, there are known methods, using straightedge and compass alone, to construct a line equal in length to the square root of that line, hence representing the \frr, which we are after.

Voila! By that act, you have;,in effect, squared the circle. But no. I'm afraid you're still out of the club. You have made use of a rolling circle with a mark on it and that comes under the heading of an instrument other than the straightedge and compass. The point is that there are any number of ways of squaring the circle, but the Greeks were unable to find any way of doing it with straightedge and compass alone in a finite number of steps. (They spent I don't know how many man-hours of time searching for a method, and looking back on it, it might all seem an exercise in futility now, but it wasn't.

Voila! By that act, you have;,in effect, squared the circle. But no. I'm afraid you're still out of the club. You have made use of a rolling circle with a mark on it and that comes under the heading of an instrument other than the straightedge and compass. The point is that there are any number of ways of squaring the circle, but the Greeks were unable to find any way of doing it with straightedge and compass alone in a finite number of steps. (They spent I don't know how many man-hours of time searching for a method, and looking back on it, it might all seem an exercise in futility now, but it wasn't.

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Adding a Dimension by Isaac Asimov


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