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Building Intuition with Layers of Bricks

Audience:

Brick walls are among the oldest and most trusted forms of construction. They offer strength, durability, and aesthetic appeal. Yet, even the most solid-looking brickwork is not immune to cracks. To the casual observer, cracks might look random and unpredictable. However, both engineering and mathematics tell us that cracks follow patterns and rules. By studying these patterns, we can gain a deeper understanding of how and why walls fail, and even develop mathematical models to describe the relationship between crack length and the depth of penetration into the wall.

https://docs.google.com/document/d/1mStna42psKQ0HIN6V8wK_yWPI2rngahzWJAoFhWXTWQ/edit?usp=sharing

Analytics

2.75 Overall score*

77 Rank

6 Votes

4 Comments

Comments

2.5

I enjoyed the enthusiasm for the subject matter, but overall the work had way too much text and was too philosophical to keep the attention of a middle- or high-school student. Some visualisations would help a lot.

I also didn’t feel the light-bulb moment of something being proven true like a good maths lesson gives. If you were able to prove mathematically that rectangles are the actual optimum shape rather than just stating “If the goal is human construction, rectangles win, hands down.” then it would have been more engaging.

4.8

I am interested in the content. However, the content is at the level of an undergraduate student. To appeal to the audience listed here (middle and high schoolers), it needs a lot more pictures and motivation.

2.4

There was a lot of repeating explanations and ideas that were already covered, such as analyzing the different shapes of bricks repeating at least three times with little to no meaningful variation. In general it could be cut down to probably half or less and contain the same overall ideas in a more focused form. Also wanted to point out that the equation for combinations of paths on a grid is, I believe, incorrect, and should be (x+y)!/(x!)(y!)

1.5

There are inaccurate information here. the number of paths is not 10!6!, but 10!/(6!4!). The argument for cubes is also invalid, since the seams don’t need to be in straight lines, by adding offset into the layers, after all, they are just cuboids, but the length just happens to be the same as the width and height. Additionally, “do they tile space without gaps?”, while the document says it’s “definitely” for hexagons, it’s apparently “awkward” for triangles, even though 6 triangles make up a hexagon. Maybe it’s accounting for human error in the generation of the steps?