I can’t recall ever seeing this tiling before. It reminds me of the Old Woman / Young Woman optical illusion: Sometimes I see overlapping octagons and sometimes I see disjoint hexagons and squares. The photo also seems impossible to straighten: No matter how I rotate it, it always appears crooked in some way.
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I had a limited understanding of what I could do with math when I was in school, which was as much my fault for being narrow-minded as anyone else’s fault for not showing me the incredible breadth of mathematical applications. This ultimately contributed to an unsatisfying experience in graduate school and a departure from math, which I talked about in this story.
So as a teacher I make sure students know that math will always create options for them. I tell them that whatever they decide to study — science, humanities, the arts — they should keep taking math classes as long as they enjoy them. There are quantitative aspects to every discipline, and knowing math will always set them apart and give them an edge in their field.
Recently a student asked me about how mathematics could be applied to the study of history. She is passionate about studying both, but sees them as disconnected and unrelated. I had a few answers for her, but I was looking to provide her with more. So I put out a request on Twitter.
I have a student who is interested in how mathematics can be applied to the study of history. I’d love to offer her a few entry points. Any suggestions? #math #mathchat
— Patrick Honner (@MrHonner) November 3, 2018
The response was remarkable. I learned a lot, and so did my student! Here is a brief summary of the great resources, links, and ideas that were offered.
There were many more responses, and I recommend looking through the Twitter thread. Thanks to everyone for contributing, and for helping to keep one more student studying math.
My latest column for Quanta Magazine connects the complex numbers from high school math classrooms to the quaternions and octonions, numbers systems currently being used in cutting-edge math and science research.
Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What could be less practical than a number described as imaginary?
But imaginary numbers, and the complex numbers they help define, turn out to be incredibly useful. They have a far-reaching impact in physics, engineering, number theory and geometry. And they are the first step into a world of strange number systems, some of which are being proposed as models of the mysterious relationships underlying our physical world.
Some physicists currently believe that the octonions, an eight-dimensional number system with non-commutative, non-associative multiplication and seven square roots of -1, may be the key to understanding the fundamental interactions between particles and forces. Learn more about their connections to “imaginary” numbers in the full article, which is freely available here.
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!
Here’s a peaceful scene from the West Coast, with a touch of mathematical appreciation.
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