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v ... 570 - . Babylon1 - Anaximander2, Pherekydes3 v . " " Polykrates4 - v vv .. 532/531 㺺 5 - "- v" .

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vv Apolls6 - v 㺺 .. 500 .


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vv . , a2 + b2 = c2

1:

(, b) v (c) vv v (c2) .

( + b) v (a + b)2 - c2 vv.

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vv v.

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(.. - .)

a2 + b2 = c2

v a, b, c . . .

a, b, c pa, pb, pc vv . Vv p vvv. Vv , vvv vvv . ( v p vvv vvv ).

a, b, c , 㺺 vvv. . a2 + b2, , . 2 vvv a, b, c . a, b .

v: , . v . V,

2x + 1, 2y + 1

v

4x2 + 4x + 1 + 4y2 + 4y + 1 = 4(x2 + x + y2 + y) + 2

- vv, , 4- 2- vv v . v 4- vv . v. vv, 3 vvv.

vv a, b , 㺺 , a2 + b2 , c .

, b v.

a2 = c2 - b2 = (c + b)(c - b)

. c + b, c - b vvvvv . V, vvv

(c + b) + (c - b) = 2c

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(c + b) - (c - b) = 2b

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(c + b) (c - b) = a2

v, , 2c, 2b, a2 vvv . vvv 2- . vvv , b, c . v . vv vv c + b, c - b .

v vvv v , ..:

v . Vv m, n . Vv m, n a, b, c . :

m=3, n=1 32 + 42 = 52
m=5, n=1 52 + 122 = 132
m=5, n=3 152 + 82 = 172
m=7, n=3 212 + 202 = 292
m=7, n=5 352 + 122 = 372 ..

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