In the past I would have incorrectly identified this as a parabolic arch. But now I know better.
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Math Photo: Pentagonal Descent
This hotel’s oddly-shaped floors made for an interesting downward view.
Appreciation Art Photography
Math Photo: Lego-Linear Approximations
This replica of The Thinker at Legoland got me thinking about linear approximations.
One of the fundamental ideas in Calculus is that certain kinds of curves can be very closely approximated by straight lines. In fact, when examined closely enough, these differentiable curves are essentially indistinguishable from straight lines. This is important because lines are easy to understand and analyze, whereas curves can be very complicated.
We see this phenomenon at play in Lego sculpture. Here, The Thinker’s curves are being approximated by rectangular Legos, and beautifully so. And scale plays an important role: a larger Thinker looks better in Lego than a smaller one, because the finer the approximation, the better the fit. This is something that any child who has ever tried to make a Thinker out of handful of Legos knows this firsthand.
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Appreciation
Pizza Pi Paddle
Well, Pi Day has already passed, but better late than never.
I spotted this on the wall of a college town’s pizza shop. I’ll give you 3.14 guesses which college.
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Appreciation Numbers
02/18/2018 — Happy Permutation Day!
Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.
We can also consider today a Transposition Day, as we need only a single transposition (an exchange of two numbers) to turn the year into the day and date.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!