The “Moving Up” post recalled an unforgettable moment in my past, when I still rode the Washington Metro somewhat sporadically (my youth was spent riding busses, before the advent of the Metro). It was the first time I confronted the escalator at the DuPont Circle stop. I was going to a math talk with a friend and we were busy discussing math when I stepped onto the escalator. Suddenly, I looked up and saw the stairs disappearing 188 feet into the heavens and froze. I have always been afraid of heights, and the escalator brought out all the customary terror. There was of course no turning back. And then people started bolting up the stairs past me, not always avoiding brushing by.
My hand was clamped to the handrail in a death grip. I had to hold on even tighter as the sweat of fear made my hands slippery. In such situations I often feel a sense of vertigo or loss of balance. It was then that I thought the handrail was moving faster than the steps so that I was being pulled forward. I couldn’t tell if it was the vertigo or an actual movement. In any case, I periodically let go and repositioned my death grip. After an eternity, it was over, and I staggered out into the street. Needless to say, on our return I sought out the elevator. Fortunately, it was working—not always the case in the Washington Metro.
Once my brain was functioning a bit, I pondered the question of the relative speeds of the handrail and steps. How could they be synchronized? But after a while I left it as an interesting curiosity.
(Update 9/13/2025) The Railing Does Move Faster Continue reading
Here is a simple problem from an old 
This typical problem from the prolific H. E. Dudeney may be a bit tricky at first.
Here is yet another collection of beautiful geometric problems from Catriona Agg (née Shearer). For some reason I found these a bit more challenging than the previous ones. Some of them required more time to “see” the breakthrough.
Here is another challenging problem from the first issue of the 1874 The Analyst, which also appears in Benjamin Wardhaugh’s book.
Here is a challenging problem from the 1874 The Analyst.
This is another Brainteaser from the Quantum math magazine .
These two interesting problems were posed on MEI’s MathsMonday site on 
I thought it might be interesting to explore the mathematics of a common problem with a store-bought HO model train set that contains a collection of straight track segments and fixed-radius curved track segments that form a simple oval. Invariably an initial run of the train has it careening off the track when the train first meets the curved segment after running along the straight track segments.
Here is another 
