Carnival of Mathematics 154

Carnival of Mathematics 154

The Math Citadel is happy to host Carnival of Mathematics edition 154, where we take a look at math blog posts from all around. For all those interested in Carnival of Mathematics future and past, visit The Aperiodical.

Observing Tradition

To get things started, we present a few interesting properties of 154, in keeping with Carnival of Mathematics custom.  Firstly, 154 is a palindrome when written in bases 6, 8, 9, and 13:

154=414_6=282_8=181_9=\text{BB}_{13}.

The nearest primes to 154 are 151 and 157.  Since 154 is equidistant from these, that is,

|154-151|=3=|154-157|,

154 is referred to as an interprime number

Finally, a triangle rotated internally 154 times1

Now on to this month’s post selection.

What to Read

First off, Anthony Bonato discusses the hierarchy of infinities and formative study in axiomatic set theory that brought about The Continuum Hypothesis, in a post by the same name at The Intrepid Mathematician. Included is a brief account of mathematicians Gödel and Cohen and their respective constructions of set theory to uphold or prove false the hypothesis.

Next, Arvind Rao examines the case of defining a circle by three non-colinear points in the plane in 3 Points Make a Circle. The evidence in the affirmative that any such three points do indeed define a circle is presented via straight edge and compass as well as programmatically2.

In abstract algebra, we include a post of our own, All the Same Opposites, which demonstrates some of the many forms taken by \text{GF}(2) and the significance of their structural equivalence. 

At Quanta Magazine, Patrick Honner presents the mathematical reasoning behind vaccines in How Math (and Vaccines) Keep You Safe From the Flu, comparing linear and exponential growth rates as basis for understanding how illnesses spread. And Kevin Hartnett discusses the Navier-Stokes Equations and why these merit a spot on the list of Millennium Problems in mathematics in What Makes the Hardest Equations in Physics So Difficult? 

We close with probability theory. Our own Dr. Rachel Traylor writes about the rare (and historically neglected) “singular continuous distributions” in The Red-Headed Step-Distributions. Lastly, an older post: Will Kurt at Count Bayesie gives a detailed look into Kullback-Leibler divergence and its information theoretic roots in Kullback-Leibler Divergence Explained.

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Footnotes

  1. Counting them all the way inward is going to be a little difficult. Made with tikz, the wonderful LaTeX package that we use for our research diagrams.
  2. I personally encourage the reader to try both at leisure.

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