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### The Art of Rectangular Pyramids

January15

Ahâ€¦The Louvre – perhaps the world’s most famous museum and an iconic, classical building which is noted for its modernistic entry which uses pyramids to contrast its surroundings. (H3 was taken aback by the beauty of this entry and the way in which it differed so much to the style of the French buildings and monuments in the adjacent Napoleon courtyard). The main Louvre Pyramid is a large glass and metal structure surrounded by three smaller pyramids. EachÂ pyramid is made up of diamond-shaped glass panels and provides a sharp focus for entry to some of the most valuable art works, including the Mona Lisa. Factoid: some 8 million visitors come to The Louvre each year and half of these only come to see the Mona Lisa – no wonder she has that slight smile!.

This futuristic entrance was opened in 1989 and has become symbolic of the Louvre itself and is probably photographed as much as the Mona Lisa herself? The entrance design and manufacture is an excellent example of the synergy between Mathematics and Art!

Given these measurements for the length of a side and the slant height, can you calculate the vertical height of the entrance?

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#### Post Support

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)?]