The BBC Does Mathematics


I’ve discovered a nice podcast that is produced by the BBC: In Our Time. Melvyn Bragg hosts a different group of guests every week, depending on the topic being discussed, which can be anything related to the history of ideas. I’ve enjoyed hearing how the Book of Common Prayer came to be, the significance of George Orwell’s Animal Farm, and how radio was invented, among many interesting topics. Melvyn keeps things moving along, and the guests are always very knowledgeable and entertaining.

Of course, I most enjoy the math-related conversations, so for my fellow math teachers here is a list of the programs – at least the ones I’ve found so far – that are devoted to that subject (click on the title to go to that program’s download page):

Mathematics (May 6, 1999)

Maths and Storytelling (September 10, 1999)

Mathematics and Platonism (January 11, 2001)

Zero (May 13, 2004)

Renaissance Maths (June 2, 2005)

Mathematics and Music (May 25, 2006)

The Fibonacci Sequence (November 29, 2007)

Pythagoras (December 9, 2009)

Mathematics’ Unintended Consequences (February 10, 2010)

Imaginary Numbers (September 22, 2010)

Logic (October 20, 2010)

Random and Pseudorandom (January 12, 2011)

Fermat’s Last Theorem (October 24, 2012)

e (September 24, 2014)

P vs NP (November 4, 2015)

Euclid’s Elements (April 28, 2016)

Zeno’s Paradoxes (September 21, 2016)

You can subscribe to the In Our Time podcast via iTunes by clicking here.

Happy listening!







Algebra 2 Screencasts!

I’m teaching Algebra 2 for the first time in many years, so I am recording lots of screencasts for it. I’m putting them into a YouTube playlist, and you can access them all here. So far, I’ve covered completing the square, linear inequalities, radical and quadratic form equations, absolute value equations and inequalities, solving quadratic equations, basic tools of graphing, lines, circles, function basics, graphing functions, transformations, and functions operations and composition. (Whew!)

If you’re really bored and want to binge-watch them, here you are:

Math, Desmos, and Artglass Windows

In a earlier post, I explained the steps involved in making an artglass window using lead came. In this one. I’ll show you how to make a window using the copper foil technique. This technique is good for smaller pieces, and designs that have a lot of detail.

I’ve been using Desmos to brainstorm window designs. It’s so easy to plot polar graphs with it, and they usually have a lot of symmetry. For this particular design, I played around with a tangent plot. In Desmos, I entered r = a*tan(b*theta) + c, and created sliders for a, b, and c. Then I adjusted them until I found a promising design; in this case a = 1.8, b = 1.6, and c = 5.3:

desmos tangent window

Next, I printed out the design and traced it onto a large sheet of paper. This will be my working pattern, called a cartoon:

Tangent Window CartoonNow comes the most time-consuming step: cut all the pieces of glass to fit into the cartoon. I decided to go with green in the center, then alternate clear, blue, and yellow pieces as you work out from the center. Here are the pieces of glass as I cut them in stages:

Tangent Window Cuts 1 Tangent Window Cuts 2 Tangent Window Cuts 3

Once all the pieces are cut (make sure there are no pieces overlapping their boundaries), I wrapped them in copper foil tape. It’s exactly like it sounds: copper with a sticky backing.

Tangent Window Taped

Now the window is ready for soldering. I brush all the copper with flux (a chemical that enables the lead/tin solder to adhere to the copper tape), and then use a soldering iron to melt the solder onto the tape. I do this on both sides. On the front side, I add more solder to “raise a bead” and make it look finished. Here’s the result:

Tangent Window Final

The ease with which Desmos plots complicated polar equations makes it an ideal tool to design symmetric artglass windows. I think this is the beginning of a beautiful relationship!

Update: I’ve made three more windows using Desmos.

This one uses the polar plot of r = 1.9tan(0.3θ) – 5.1:

tan window

r = 0.3sec(1.6θ) – 3.65:

sec window

r = sqrt(10sin(3.3θ)) – 6:

sqrt(sin) window


And two more:

r = -2.8³√(csc(0.6θ) + 0.8):


r = tan(0.5θ) + sin(0.8θ):







Summer Reading For Math Teachers

My school had graduation yesterday, so I can look forward to having some extended periods of time to do some reading. Here are three books I’ve enjoyed recently and you might find interesting (clicking on the titles will take you to their Amazon pages):

Love and MathLove and Math: The Heart of Hidden Reality, by Edward Frenkel. This is a terrific book about Frenkel’s struggles to overcome institutional anti-Semitism in his native Russia and become a world-class mathematician. He is currently a professor of mathematics at UC Berkeley. He intersperses autobiographical details with explanations of how his mathematical research helped physicists develop their theories of quantum mechanics, as well as unite seeming unconnected branches of math. Along the way, he shares his love of the Platonic world of mathematics: “Nothing can stop us from delving deeper into this Platonic reality and integrating it into our lives. What’s truly remarkable is mathematics’ inherent democracy: while some parts of the physical and mental worlds may be perceived or interpreted differently by different people or may not even by accessible to some of us, mathematical concepts and equations are perceived in the same way and belong to all of us equally. No one can have a monopoly on mathematical knowledge; no one can claim a mathematical formula or idea as his or her invention; no one can patent a formula!” (pp. 235-236) Frenkel delves into some very deep and advanced mathematics, but he manages to explain it terms most everyone can understand.

Program or Be ProgrammedProgram Or Be Programmed: Ten Commands For A Digital Age, by Douglas Rushkoff. My daughter gave me this book after she read it for a coding class in college. It is in the vein of Neil Postman, asking users of social media to be aware of digital technologies’ inherent biases. It’s relatively short, but very powerful. Rushkoff’s main point is that unless users understand basic coding principles, they will be at the mercy of an élite who create the social media platforms that can manipulate them. The ten commands are:

  1. Time: Do Not Be Always On
  2. Place: Live In Person
  3. Choice: You May Always Choose None of the Above
  4. Complexity: You Are Never Completely Right
  5. Scale: One Size Does Not Fit All
  6. Identity: Be Yourself
  7. Social: Do Not Sell Your Friends
  8. Fact: Tell The Truth
  9. Openness: Share, Don’t Steal
  10. Purpose: Program or Be Programmed

Favorite quote: “In a digital culture that values data points over context, everyone comes to believe they have the real answer and that the other side is crazy or evil.” (p. 65)

Brain on Music

This Is Your Brain On Music: The Science of a Human Obsession, by Daniel Levitin.

This technically isn’t a book about math, but if you’ve ever wondered why humans are the only animals to create and appreciate music, then you will enjoy this. Levitin knows what he’s talking about: he’s been a record producer of very successful rock artists, and he is now a neuroscientist at McGill University, where he runs the Laboratory for Musical Perception, Cognition, and Expertise.

Levitin spends the first few chapters explaining what music is, and what terms like pitch, timbre, rhythm, and tempo mean. He also discusses the mathematical relationships in tones and octaves.

Levitin spends the rest of the book explaining the latest research in how the brain processes music, and what is involved in creating, performing, and enjoying it. No other activity involves as many parts of the brain as performing music does. He laments the separation between performer and audience that has happened in western cultures. In earlier times, everyone played some sort of instrument or sang. The easy availability of recorded music has caused a decline in music performance, however, to the detriment of us all.

So, three books with three very different foci, but I believe teachers of mathematics will find all of them interesting and enjoyable. Have a great summer!