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Putting another ring around concentric…

February28

circlesLook carefully at the picture above. Circles spiralling inwards? No – these are concentric circles that all share the same centre (aka center). Pretty cool optical illusion. Of course, these circles have different radii. You can make your own concentric circles by dropping a stone into the center (aka centre) of a pond. There are even concentric circles on the moon!
moon craters“In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere). More generally, every two great circles on a sphere are concentric with each other and with the sphere.

By Euler’s theorem in geometry on the distance between the circumcentre and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral.” (source: Wikipedia)

KeplerHere is Kepler‘s cosmological model formed by concentric spheres and regular polyhedra. Read more about Kepler, the amazing German mathematician here.

 

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Largest number between o and 1 million which does not contain the ‘n’ is 88

 

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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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