Posts in category Roots of Unity
Happy Numbers Have No Density
If you’re feeling a little down today, maybe a happy number will cheer you up. To see if an integer is happy, start by squaring its digits (in base ten, though happiness is defined analogously in other bases as well) and adding them together. So the number 23 would become 13 because 22+32=4+9=13. Now iterate the process. For 13, we get 1+9=10 [...]
Inka History in Knots (Book Review)
This post originally appeared at scientificamerican.com.
Imagine that in a few hundred years, archaeologists stumble on some of your old files. Maybe they find spreadsheets of tax information, medical bills, or bank statements, or maybe text files with old emails or drafts of your novel. These archaeologists cannot read Latin script, and no o [...]
A Curious Sequence of Prime Numbers
This post originally appeared on scientificamerican.com.
Prime numbers are often described as the “atoms” of mathematics, or at least of numbers. A prime has exactly two distinct factors: itself and 1. (Hence 1 is not considered a prime number.) All whole numbers greater than 1 are either primes or products of primes.
One of the first questio [...]
Moon Duchin’s Favorite Theorem
This post originally appeared at scientificamerican.com.
On this episode of our podcast My Favorite Theorem, Kevin Knudson and I were pleased to have the opportunity to talk with Moon Duchin, a mathematician at Tufts University. You can listen to the episode at kpknudson.com, where there is also a transcript.
Dr. Duchin has appointments not o [...]
The Serendipity of Swiss Cheese
This post first appeared on scientificamerican.com.
Approximation is a recurring theme in mathematics. Sometimes it seems like all of mathematics is saying, “Well, I know how to solve the problem in this domain. Is there a way I can approximate other domains with this domain?” A lot of calculus boils down to approximating arbitrary functions [...]
I Can Has Numberz?
This post first appeared at scientificamerican.com.
My favorite genre of tumblr post is “humans are adorable.” We like to decorate ourselves with shiny things! We burn things for fun even though fire is inherently very scary! We bond with nonhumans and even feel empathy for spaceships and robot vacuum cleaners! We are ridiculous creatures, bu [...]
Why Isn’t 1 a Prime Number?
This post originally appeared on scientificamerican.com.
An engineer friend of mine recently surprised me by saying he wasn’t sure whether the number 1 was prime or not. I was surprised because among mathematicians, 1 is universally regarded as non-prime.
The confusion begins with this definition a person might give of “prime”: a prime number [...]
What Are the Odds of a Family with 14...
A few months ago, I read an article about a family with 14 children, all boys. That is a lot of boys! My first thought was what their grocery bills must be. (Whether they’re all boys or not, a family with 14 kids has multiple teenagers for decades. I remember fondly the damage I could do at my favorite all-you-can-eat pizza buffet when I was [...]
Ken Ribet’s Favorite Theorem
This post originally appeared on scientificamerican.com.
In today’s episode of our podcast My Favorite Theorem, Kevin Knudson and I were happy to welcome Ken Ribet on the show. Dr. Ribet is a math professor at the University of California Berkeley and president of the American Mathematical Society. You can listen to the episode at kpknudson. [...]
Emily Riehl’s Favorite Theorem
This post first appeared at scientificamerican.com.
In today’s episode of our podcast My Favorite Theorem, my cohost Kevin Knudson and I were happy to welcome Emily Riehl to the show. She’s a mathematician at Johns Hopkins University, and like our previous guest John Urschel, she’s also a football player. (She plays Australian rules football, [...]
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