If we arrange lines of pebbles each containing one more than the first, starting with one, we obtain a ‘triangular’ number. Special significance was attached to the tetraktys, consisting of four lines and showing that 1+2+3+4=10
c2=(a-b)2 + 4 x ½ab = a2 + b2
An isosceles right-angled triangle of side 1 has a hypotenuse not expressible as a rational number.
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