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The square root of 2 ain’t rational

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(1)

The square root of 2 ain’t rational

A Casual Talk By

Pete Agoras

(2)

Pete Agoras Some centuries B.C.

A simple assumption

(3)
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Pete Agoras Some centuries B.C.

The problem

3 And but so we said a and b have no common

(5)

Pete Agoras Some centuries B.C.

All fractions are reducible

4 Suppose c

d is a rational number. If c and d

have no common factor, then a = b and b = d. If they have a common factor, divide both by their greatest common divisor. The result is a

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Pete Agoras Some centuries B.C.

An even square has an even root

5 An even number, by definition, is expressible

in the form 2k, where k is any integer. On the other hand, an odd number is

expressible by

2k + 1

Thus the square of an odd number is (2k + 1)2

i.e.

4k2+ 4k + 1 i.e.

2 × 2(k2+ k) + 1

which is of the form 2k + 1 with 2(k2+ k) as

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