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The Mathematics of Christmas

December29

It does seem strange to be sweltering here in summer heat and wanting to have a swim at the beach, while our Northern Hemisphere friends are fighting off cold, winter blasts, and snow. I really enjoyed this blog entry on the Wondrous Mathematics of Winter:

“There’s the snowman: the human form given in three spheres. It is a sort of absurdist abstraction: the top sphere makes sense, and we can stretch to consider the middle one to have captured the salient properties of those of us with more orbic midsections. But I don’t know what to make of the bottom sphere. There may be some work to do here, which Euclid or Archimedes might have gotten to if it had snowed more often in Greece. The ratios of the spheres matter. A stack of three equally sized white spheres might read as tennis balls in a sleeve or cocktail onions on a toothpick. After considerable investigation, I have discovered that if the proportions of the diameters are 5:4:2.5 (from bottom to top) then the form unambiguously reads as a snowman, with or without carrot, coal, sticks, scarf, or hat. We have then a stack of three white spheres that signify archetypal “winter” quite clearly. I challenge you to signify any other time of year with such simple geometry.” Read more here

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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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