Novel knot news now! You might already be aware that there are 85 ways to tie a tie. Well, cast that preconception aside because there are actually loads.
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Carnival of Mathematics 107
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of January, and compiled by Frederick Koh, is now online at White Group Mathematics.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
Intersections by Anila Quayyum Agha
Intersections by Anila Quayyum Agha.
via Colossal.
Why do $0!$ and $a^0$ equal $1$?
The last two weeks my first year mathematicians and I have covered Taylor series.This means that several times I’ve had the conversation that goes “What’s $0!$?” “It’s $1$.” “Oh, erm, right. Why again?” “Because it works.” This may not be a completely satisfactory answer!
One of my students, Callum Mulligan, tweeted this question.
Why does 0! = 1 better yet, why does a^0 = 1 I must see a proof! #Mission #Unanswered #MathRage
— Callum Mulligan (@Calified) February 1, 2014
Saying “by definition” or “because it makes a bunch of stuff work” won’t cut it. So how to answer this question? To give a somewhat intuitive understanding of why this should be the case to a first year undergraduate. It may be obvious, but it wasn’t immediately obvious to me how to explain this, so I share some thoughts here.
Puzzlebomb – February 2014
Puzzlebomb – Issue 26 – February 2014
The solutions to Issue 26 can be found here:
Puzzlebomb – Issue 26 – February 2014 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.
Open Problems in Mathematics, a new open access journal
Here’s a nice idea: a journal for people to write about open problems, with the aim of inspiring someone to have a go at solving them. Open Problems in Mathematics is a new open-access journal set up by Krzysztof Burdzy and a few others, and it’s online now.
Proof News: Designs exist!
The year in proofs has started with a big result in combinatorics: the existence conjecture for designs. As usual, weightier minds than ours have comprehensively explained the result, so I’ll just give a brief summary of the problem and then some links.