Welcome to the 185th edition of the Carnival of Mathematics. Step right up to to marvel at many of the monthly mathematical marvels moving through your modem.

First a few fun facts about the number 185.

- There exists a number, let’s call it x, that when you add it to 185 the sum is 185.

But that’s not all. - The product of this number, which we have named x, and 185 is x.

And there’s more. - The set of all the counting numbers that have been mapped to a Carnival of Mathematics has a maximum. That maximum is… 185

That last fact is a bit controversial as there is a conjecture that 185 is not the maximum of the set of all counting numbers that have been mapped to a Carnival of Mathematics. I have heard that mathematicians are close to proving this conjecture and may have it proved as early as next month.

We shall see.

Oh, 185 is also odd, composite, square free, less than perfect, odious but not evil, not happy nor hungry and greater than 184. It is also, to the best of my recollection, not the number of any taxi in which I have ridden.

## Onward to the mathematical marvels.

Annie Perkins invited you to share “your favorite, most beautiful or beloved part of mathematics” What will you share?

This was the 98th entry into her math art series that she started back in March. She wrapped up after 100 different math art challenges. You can find them summarized here.

In other math and art news the international Bridges math and art conference went virtual this year. This was great news for people like me who have always wanted to participate but never could make it to a physical event. If you like math and its intersection with art (and who doesn’t) definitely visit the site for the 2020 Virtual Bridges Conference.

Ben Leis posted a great piece that shows the connections between puzzles, trisecting segments, Islamic art and some rather famous triangles.

Of course the connections between mathematics and art are not limited to the visual arts. Here is a wonderful interactive way of analyzing the lyrics in the musical *Hamilton*.

Continuing with the interactive art theme, take a moment to explore cellular automata but with cross hatching rather than cells from Kjetil Golid.

Of course mathematics does not just have connections to art. There are some who appreciate that mathematics can be pragmatic, practical and help us understand the physical world.

Siobhan Roberts pointed out at the start of the month in the New York Times how not only should we not be afraid of Bayesain analysis but how it is particularly relevant in the present.

Ethan Rosenthal has created an important tool to help us all complete important tasks most efficiently in our kitchens. It a tool you never knew you needed but will wonder how you have made it this far without it.

The two final things to wrap up this Carnival are great examples of how mathematics can blend art, creativity and the practical in wonderful puzzles.

Matt Macauley started a weekly Friday visual group theory puzzles on Twitter. He was inspired by his enjoyment of the geometry puzzles of Catriona Agg.

And lastly, Roderick Kimball has added a page to his puzzle site to help those interested in creating puzzles. It is a toolkit for puzzle makers that coincides with an event he is leading in September for the National Museum of Mathematics in New York.

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