In my dealings with the internet this week, I am reminded of a quote by William Arthur Ward, the professional inspirator:

We can throw stones, complain about them, stumble on them, climb over them, or build with them.

In particular, I have been notified by two different math-related things. Firstly, most importantly and more interestingly, my friend Diana Davis created a video entry for the “Dance your PhD” contest. It’s about *Cutting Sequences on the Double Pentagon*, and you can (and should) look at it on vimeo. It may even be the first math dance-your-PhD entry! You might even notice that I’m in the video, and am even waving madly (I had thought it surreptitious at the time) around 3:35.

That’s the positive one, the “Building with the Internet,” a creative use of the now-common-commodity. After the fold is the travesty.

On the other hand, I have also been nominated for a blog award… but not in a good way. I received this email and notification:

Hi there,

An article you wrote in 2011 titled2401: Additional Examples for Test 3has earned your blog a nomination for a Fascination Award: 2012’s Most Fascinating Middle School Teacher blog.The comments posted in response to your post prove that your content not only inspires your audience, but it also creates discussion around your posts, both of which are requirements for the nomination of a Fascination award.As a nominee of this award, you have full permission to display the “Nominated” emblem on your website. To learn more about the contest, the rules, or the prizes, click here:2012 Fascination Awards Rules & Prizes.

To get started:

- Accept your nomination by replying to this email by August 15 (11:59 PM EST).
- Claim your “Nominated” badge to display on your blog: Nominated Badge
Voting begins August 18th at 1:01 AM (EST). The blog with the most votes by August 25th at 11:59 PM (EST) will win the grand prize, a $100 restaurant gift card.Good luck and thank you for your participation!Matthew PelletierDirector of Public RelationsAccelerated Degree Programs

Hello. Apologies for posting this comment here where it is not relevant; I can’t find any other way to contact you directly. I’m struggling enormously with some elementary number theory, and your answer here: http://math.stackexchange.com/questions/180002/legendre-symbol-second-supplementary-law/180022#180022

is proving very illuminating, but that I can’t follow some of the working; I can’t get to “(−1)1+2+…+s=(−1)s(s+1)/2”. Any chance of some intermediate steps for the likes of me? It’s one of the remaining pieces in my two-day struggle to prove what values p can take if p divides 2^((p-1)/2), which I understand is supposed to take me about three minutes :(

Sure, I can do that for you. It won’t take me long, but I’ll have to wait until tonight. Feel free to ask me anything else you would like too.

I lied – I wrote a comment back at the thread. In short, I used the fact that the sum of the first $latex n$ natural numbers is $latex n(n+1)/2$. If you haven’t seen this before, I would recommend proving it. If you search MSE, I’ve even uploaded a proof by picture (that’s well-known). And for future reference, my email can be found in the about page here. It’s david_lowry@brown.edu.

I am terrible at the internet. I didn’t even think of looking in “about”. Your help much appreciated; I have taken it to eMail to stop polluting your blog comments.

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