#MathProblemOfTheDay: Slopes in a Subway Station

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This is part of the subway stop at 59th street and Lexington Ave, in New York City.

Estimate the slope of this escalator, by comparing the diagonal line to the grid of square tiles on the wall.

I found this interesting for two reasons:

(1) it seemed fun to consider different visual approaches here, and

(2) in real life, the staircase and adjacent escalator seemed *really steep.*  Yet if you look at boxes, the slope is less than 1, ie the angle of elevation is less than 45 degrees (a slope of 1 would be 1 full box up for every box over).

I remember in math class, I thought of a slope of 1 as kind of average. Not too flat, not too steep. But in the physical world it is pretty steep! I’m trying to think if I’ve ever seen a road, walkway, or ramp that actually had a slope of 1.

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