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Paradox – an absurd truth


By definition, a Paradox is an absurd statement which may prove to be true. The amazingly impossible designs of the artist Escher are excellent examples and his work is shown in the sculpture above. Mathematics is one large system of logic – a kind of universal language that transcends individual civilizations and specific languages. As such, certain paradoxes have arisen that have troubled mathematicians from ancient times to the present. Some are false paradoxes in that they do not present actual contradictions, but are merely slick logic tricks. Others have shaken the very foundations of Mathematics – requiring brilliant, creative mathematical thinking to resolve. Others remain unresolved to this day. Check some of these out in the Math Forum.


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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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