I’d never looked closely at the Parachute Jump in Coney Island, but recently noticed the octagons at each vertex of the dodecagon 250 feet up in the sky. It really is a beautiful structure, but I’ll leave it up to you to decide whether or not it deserves to be called “the Eiffel Tower of Brooklyn”.
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Happy Geometric Mean Day! The geometric mean of two numbers a and b is
which makes today a Geometric Mean Day!
A consequence of this is that the numbers in today’s date form a geometric progression
and here is one way to visualize that relationship
I like the multiple takes on hexagons here, both in size and orientation. Not bad for random hotel wall art! This was in Cambridge, though, so maybe that explains it.
Varignon’s Theorem is one of my favorite results in elementary geometry: connect the adjacent midpoints of the four sides of any quadrilateral, and a parallelogram is formed! It is a magical result that defies expectations, and it’s so much fun to play around with, explore, and extend.
Steven Strogatz shared his favorite proof of Varignon’s Theorem on Twitter yesterday, and so I felt compelled to share mine. This is a standard proof of Varignon, but it is so clean and elegant: it is an immediate consequence of the Triangle Midsegment Theorem and the transitivity of parallelism.
Strogatz’s vector proof is beautiful and efficient, but the power of transitivity really shines in this elementary geometric proof.
I created a a simple Desmos demonstration to explore Varignon’s Theorem. And like all compelling mathematical results, there are so many fascinating follow-up questions to ask!
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I don’t know exactly why, but fake graphs on Regents exams really offend me. Take a look at this “sine” curve from the June, 2016 Algebra 2 Trig exam.
Looking at this graph makes me uneasy. It’s just so … pointy. Here’s an actual sine graph, courtesy of Desmos.
Now this fake sine curve isn’t nearly as bad as these two half-ellipses put together, but I just don’t understand why we can’t have nice graphs on these exams. It only took me a few minutes to put this together in Desmos. Let’s invest a little time in mathematical fidelity.
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