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Tessellations – Pt II – Cool interactive site

March7

The Escher blog leads to your own discovery about symmetry in Mathematics. We most often use symmetry in our study of Polygons (from the Greek language where “poly” = many and “gon” = angle or ‘knee’). Actually, I must confess that I find it easier to think of a polygon as “many-sides” for a more practical definition. Either way, we get the same result (the sides are formed by the angles!). In the diagram below we have a Tessellation. The word “tessella” means “small square” and we define a Tessellation as a pattern of interlocking shapes to form a small square. This pattern below is of 6-sided shapes (hexagons). Here is a cool website that has an interactive tool for you to make your own tessellations. Another really good Tessellation site is 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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