Growing up, we didn’t have a radio in our house.  Consequently, I wasn’t on the Beatles fan wagon as a child.  Later, at university, there were other things playing on the progressive rock stations so I pretty much missed their musical genius until they showed up on the oldie stations!

The closest thing that I came to meeting a fan who had gone overboard was a computer science student in Grade 11 who was deep into it.  When it came his time to control the music, there was always something Beatle to be played.

One of the things about the Beatles that still strikes me is that their history had a big list of “places”, whether it was a memorable event like the “Ed Sullivan Theatre” or something that they sang about like “Penny Lane”.


Now, thanks to Google’s story telling features of Voyager and Google Earth, you can see these places where they appear today.

Enjoy Beatlemania.


OTR Links 05/31/2017

Posted from Diigo. The rest of my favorite links are here.

It’s all in the communication


Recently, I enjoyed this article “This Math Problem Will Make You Lose Your Mind“.  It all revolves around the solution of this problem.

Screenshot 2017-05-29 at 09.21.42

It generated quite a bit of discussion from friends of mine, along with different answers.  In fact, even the internet doesn’t quite have its act together.  Turning to YouTube, you’ll find a couple of different answers fully documented in video.

How can the internet be wrong?

Our discussion eventually got around to the use of ÷ and / to denote division.  (I threw in \ which in programming means integer division just to make things muddier.)  Peter Been jumped in with his thoughts and a couple of terms that I had long since forgotten – obelus and solidus.

All in all, I found the discussion really interesting.  It also reminded me of a comment from a university professor about mathematics.  “It’s not just a science; it’s an art; it’s a communication vehicle.”

It’s the communication vehicle that we should really give credence to.  If we believe that there should only be one answer to a problem, then the problem needs to be communicated in a way that leads to the solution.  Not the trick problems that we loved/hated on test.

Which led me to this resource, Welcome To Mathematical Communication.

Screenshot 2017-05-29 at 09.47.25

If it’s important enough to do, it’s important enough to communicate it accurately and effectively.  This resource is just packed with advice and suggestions to become more effective mathematics communicators.

OTR Links 05/30/2017

Posted from Diigo. The rest of my favorite links are here.

Because of this, we can do that

If you’re like me, you use Google Maps.  And, probably for a lot of things other than just drawing a map.  You might explore new places, get driving directions, look for traffic problems on highways, get a visual of construction sites to ignore, and much more.

Over the weekend, I read and highly encourage you to read this story.

How Google Builds Its Maps—and What It Means for the Future of Everything

I really enjoyed the part about someone reporting a new round-about; we have one here in the Windsor are for leaving the 401.  It’s possible to see it for free on Google Maps


yet, in my car, I would need to shell out for a maps upgrade to see it.  In the meantime, when I get on it, my in-car maps shows me traversing over a farmer’s field.  It’s not a huge deal; it’s a double lane roundabout and you’re well advised to keep your eyes on the traffic.

But, time and technology move on.  Google Maps (and Streetview) have you covered.


p.s. it’s never this wide open whenever I go there.  The fact that we get these images from Maps, Earth, and Streetview still blow me away.

And when they marry, amazing things can happen.  I’d like to refer you to a post on this blog from a couple of years ago that uses a “Secret Door” to randomly drop you into a Streetview location.

I still think it’s a magnificent starting point for discussions, analysis, or a starting place for great writing.


How many times have your students written a blog post about their dog or their cat? Looking for something new and completely different?

Then, you need to check out “The Secret Door“.