Peter Krautzberger on the web

Carnival of Math No. 146

This month I have the pleasure to host the 146th Carnival of Mathematics, the moveable feast of mathematical blogging shepherded by the best math blogging collective on the planet, The Aperiodical.

As tradition decrees, we shall begin our show by taking a closer look at our number.

146 is an octahedral number (and thus a figurate number).

146 magnetic balls, packed in the form of an octahedron
An octahedral number represents the number of spheres in an octahedron formed from close-packed spheres (146 the image above).

Even more amazingly 146 is an untouchable number which means it cannot be expressed as the sum of all the proper divisors of any positive integer (including itself). Can you guess how many untouchable numbers there are? Of course, infinitely many and, of course, this was first proved by Paul Erdős. But did you know that the only known proof that 5 is the only odd untouchable number depends on a stronger version of the Goldbach conjecture? Amazing!

Now that you’ve warmed up, let us enter the magnificent, magnetic madness of the mathematical blogging carnival.

If you have any affinity to football (the real kind, not the funny American stuff), then start off with Nira Chamberlain who reviews the mathematical simulation model he built for his favorite team - you know, like any normal awesome football fan would do.

Next, follow Sean and Jamidi to the depths of the chalkdust magazine where they spoke with one of the great mathematical storytellers, Marcus du Sautoy.

Beware now, lest you be pulled into the enchanted world of The Mathemactivist who can draw a Hilbert Curve by hand.

See if you can spot the two mistakes!

Come now, and follow us to the trickster’s lair where Tom rocks math takes a closer look at three fun numbers to tell you things you didn’t realize you ever wanted to know. From here, follow us to the depth of the mathvault and let Scott Hartshorn lure you with an introduction to statistical significance after which all your paper-nerd needs will be met by Nick Higham, who looks at the benefits of dot grid paper (including, of course, a LaTeX template).

Before you leave, be sure to witness the spectacle of John Cook taming the Weibull distribution and connecting it with Benford’s law. And as an encore, John will take you far from the equation systems you solved in algebra when you were a kid to the “simple” generalization that can be solved using a Gröbner basis (which, as so many things in mathematics, were not actually discovered by Gröbner).

And if you still can’t get enough, be sure to check out the many fabulous results of Christian Lawson-Perfect’s call for proof-in-a-toot.

That’s it for the beautiful month of May!

Be sure to stop by next month’s Carnival, hosted by Lucy at Cambridge Mathematics. You should submit your favorite blog posts/videos/content from the month of June. If you’d like to host an upcoming show, please get in touch with Katie.