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Impossible Triangles


One area connecting mathematics and the brain is visual phenomena. Human visual information is processed by the brain and uses our amazing eyes. Mathematicians have been involved in a wide variety of problems involving vision:

* What is the geometry of our perceptual system?

* How does the brain process visual information?

It is well known that when humans look at (straight) railroad tracks they appear to converge in the distance. A wide range of scholars are trying to understand the mystery of visual perception. The way that the world looks to us was a challenge for artists who had to represent reality on canvas, and for philosophers who are trying to probe the relation between mind, physics, and perception. Mathematicians (some of them also artists) transformed the insights obtained concerning perspective into what today is known as projective geometry. In projective geometry, unlike Euclidean geometry, there are no parallel lines. It has been suggested that the hyperbolic plane or other geometries might describe this system. The challenge of understanding perspective from a mathematical point of view and being able to use computers to serve the needs of artists, photographers, and architects has been a source of much research. Full article here.

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

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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