Curves of Constant Width and Odd-Sided Reuleaux Polygons

A curve of constant width is a convex, two-dimensional shape that, when rotated inside a square, always makes contact with all four sides.

A circle is the most obvious (but somewhat trivial) example. Some non-trivial examples are the odd-sided Reuleaux polygons — the first four of which are shown above.

Since they don’t have fixed axes of rotation, curves of constant width (except the circle) have few practical applications. One notable use of the Reuleaux triangle, though, is in drilling holes in the shape of a slightly rounded square (watch one of the triangle’s vertices and notice the shape it traces out as it spins).

On a less technical note, all curves of constant width are solutions to the brainteaser, “Other than a circle, what shape can you make a manhole cover such that it can’t fall through the hole it covers?”

Mathematica code posted here.

Additional source not linked above.

MIT Offering Free MOOCs on Game Design and Educational Technology

The Massachusetts Institute of Technology (MIT) has announced a new initiative to teach video game design and online education free of charge. Russell Westerholm of University Herald writes that MIT is kicking off the first series of massive open online courses (MOOCs) this week, focusing on educational technology. Next will come game design starting on Oct. 22, and, in the near future, there will be courses on educational gaming and technology.

image via flickr:CC | Nietnagel

Project Ed Launches New Video-Making Resources for Students and Teachers


Project Ed’s mission to build the world’s largest library of high-quality educational videos continues with new resources for using videos in teaching and learning.  This week, Project Ed launched two new categories of resources designed specifically to help students and teachers engage with great educational videos and run video projects in their classrooms.

Sign up for Project Ed to get your hands on all these free resources and get updates on all our contests.

Resources for Educators

In the last year, we’ve heard from educators across the US and Canada about how they use videos and Project Ed in their classrooms. We wanted to make it even easier to use Project Ed’s videos and our contests alongside the common core framework that many teachers are already using.  To do so we’ve put together a new set of standards-aligned, student-driven projects and lesson plans for you to use with your students. Resources include videos, student activities, and step-by-step project plans for creating videos in your classroom in a few two class periods!

Resources for Creators 

Creating great videos take practice, but we’ve got you covered. We looked back over all the amazing videos we’ve received and compiled a list of tips and tricks you’ll need to create winning videos. We’ve got video guides covering  pre-production, shooting, and editing.  We’ve even put together a list of all the secrets you’ll need to know to win one of our contests. And if thats not enough, check out our tip sheets on how to harness the power of light and how to shoot a great video using only your phone.

Current Contests

There are always great opportunities for students and teachers to create and win on Project Ed. Check our current contests below. The best videos win $1000 and become part of Project Ed’s open library of educational videos.


Sign up for here to get your hands on all these free resources and get updates on all our contests.


Happy Mole Day everyone!

Mole Day is an unofficial holiday celebrated among chemists, chemistry students and chemistry enthusiasts on October 23, between 6:02 AM and 6:02 PM, making the date 6:02 10/23 in the American style of writing dates. The time and date are derived from Avogadro’s number, which is approximately 6.02×1023, defining the number of particles (atoms or molecules) in one mole of substance, one of the seven base SI units.

The general consumer base is working more hours for less wage. Technology has “come to the rescue” by providing consumers with tools that improve their ability to jump into a moment of leisure or get educated in something that they care about.

So, is the same finally happening in traditional classroom settings? Does technology no longer get in the way of teach, but instead give teachers tools that transcend normal coursework?

Memoirs of the Oregon Trail


Want to write a guest post on Classcraft or another topic in education? Pitch to stephanie@classcraft.com.

Guest post contributed by Joshua DuCharme, M. Ed

Computer labs today are stock-full of computers that have amazing processors, LCD/LED monitors, Bluetooth capabilities, etc … you get the idea. Although I must admit I get frustrated when my Internet page does not load fast enough that I can’t help but reminisce on my humble beginnings.

When I think back to 4th and 5th grade, I remember a myriad of fun things we did and how amazing my teachers were. But the most exciting part of my younger elementary days was when we had computer lab — a small, 45-minute window to step into another reality. Fill the flux capacitor because we’re about to go back to the future.

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edshelf Weekly - Time-Saving Tools

Time is a precious resource. Think of how much time is wasted everyday on mundane yet important tasks. Fortunately, technology can help you recapture some of that time. Or at least speed up those tasks. Here are some notable time-savers.

  • Permission Click - Send your first digital permission slip home to parents in as little as 15 minutes! Promo code EDSHELF gets you 2 bonus months! KICKSTARTER CAMPAIGN SUPPORTER!
  • Class Charts - Instantly create seating charts based on student behaviors, performance, and other factors.
  • GradeCam - Quickly grade multiple choice assessments using a document camera or webcam, like Scantron but easier.
  • Common Core Checklists - If you use Common Core, here are printable checklists to help you track your instruction.
  • FaceTime - This video conferencing app comes with all Apple devices by default and often has better connection quality than Skype.

Want more? Check out these collections of tools created by educators on edshelf.

Enjoy these great tools for educators!

Want a fresh copy of the edshelf Weekly newsletter in your inbox too? Sign up with edshelf today!

- Mike Lee, Co-founder of edshelf