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Notre Dame – Mathematics on Fire?

April17

A very sad moment when we heard yesterday that Notre Dame cathedral was ablaze in Paris. H3 visited this amazing Gothic cathedral just a few years ago and the soaring roof detail seemed inexplicable – its heavy brick pattern seeming unsupported. Yes, this fire-proof lining may have saved the cathedral from absolute ruin. Notre Dame was build over a period of more than 200 years – amazing architecture which placed its achievement in the hands of mathematically-skilled craftsmen.

“The subtle grace of the Gothic cathedral touches us powerfully on so many levels. But that grace is vested in engineering design. Those barrel vaults, flying buttresses, Gothic arches, and spiral stone staircases had to be born of mathematics.

Mathematics means handling numerical quantities symbolically, not a subject medieval masons studied. In fact, some couldn’t even read. As we comb the rich medieval record, we find not only no mathematical basis for these glorious buildings, we don’t find architectural drawings. We find only the crudest sketches. Yet the medieval cathedral is geometry and proportion — from labyrinths in mosaic floor tiles to the criss-crossing ribs that hold the ceiling. It just doesn’t make sense. Then we realize:

The building is the geometry text. The master mason, with his fingers touching stone, used stone to express geometry. If mathematics is the symbolic expression of magnitude, that’s what the cathedral itself is. The balance of mass and space goes by square roots of 2 and 3, and the so-called Golden Section.

Medieval iconography regularly shows one mathematical instrument in the hands of the mason — a pair of dividers. When medieval artists show us God, He often appears as the Master Craftsman, holding a great pair of dividers. With dividers and a carpenter’s square alone, you can prove the Pythagorean theorem, and you can create any of those seemingly sacred proportions.

The cathedrals were not so much designed by mathematics as they are mathematics. They are mathematics that flowed straight from the mind’s eye to the fingers of masons who built them.”

From: John Lienhard, at the University of Houston

More on Gothic Design here

Update: Using lasers to peer inside ancient workmanship

(all photos taken by H3)

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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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