In this Newsletter:

1. Your math secret
2. TED-ED – Flip your lesson
3. Image conversion project – thank you!
4. Twitter update
5. Math puzzle
6. Friday math movie – The $8 billion iPod
7. Final thought – Apply yourself

1. What’s your math secret?

Do you have a secret about your math experiences? Several interesting ones have gone up already. Share yours too! You don’t have to reveal your real name. What’s your math secret?

2. TED-ED: Flip your Lessons

This one is mostly for teachers, but math students should also find something interesting here.

TED (the place where the world’s great thinkers get us to re-evaluate the way we look at the world) recently released TED-ED.

TED-ED is a collection of "Lessons worth sharing". There are lesson plans built around interesting TED talks, and you can either use those lessons, modify them to your own needs, or create a completely new lesson based on the talk.

“Flipping” your lesson involves getting students to learn some things before the actual in-class lesson. This allows students more time to process the concepts during class time, rather than hearing the concepts for the first time. Flipping gained a lot of momentum with the growth of resources like the Khan Academy.

This tour explains the TED-ED concept.

Here is the Math Category

There’s also a Math in Real Life series of TED talks.

3. Twitter update

There are now over 3000 people following IntMath on Twitter! The 3,000th follower was a design engineer.

There are many good people sharing educational messages and resources there. It’s a great place for getting to know people and for sharing interesting finds.

Why don’t you join us?

IntMath on Twitter

4. Convert images project – thank you!

A big thank you to all those who helped out in the recent IntMath image conversion project. There were a few thousand images converted and now it’s all done.

I’m in the process now of removing the old images and replacing them with the new ASCIIMathML-produced, MathJax output equivalents.

You an see some examples of converted images in the math on these pages:

Matrix Multiplication and Inverse

Related Rates (calculus)

5. Math puzzles

Several people wrote in to answer the last puzzle about numbers. The correct answers were 41 and 50. Great to see reasons given for the answers!

New Puzzle

Line ABCD is a diameter of a circle whose radius is r. Length AB = BC = CD. Semicircles are drawn on AB and BD to create the shaded figure as shown.

What is the perimeter of the shaded figure?

6. Friday math movie: The $8 billion iPod

Rob Reid gets us to think about how silly the music and movie industries have been regarding copyright. He explains Copyright Math. Friday math movie: The $8 billion iPod

7. Final thought – application

Lee Iacocca, colorful chairman of Chrysler Motors for many years, was named one of the top American CEOs of all time. The following quote could apply to what we do with our math knowledge:

Apply yourself. Get all the education you can, but then, by God, do something. Don’t just stand there, make it happen. [Lee Iacocca]

Until next time, enjoy whatever you learn.

Related posts:

1. IntMath Newsletter – Overcoming fear of math tests, free calculus book
2. IntMath Newsletter: Cultural math, visual stats, matrices and persistence
3. IntMath Newsletter: Length of a curve, resources, 1000 posts

The TED speaker is Rob Reid.

Related posts:

1. Friday math movie – string theory
2. Friday math movie: How algorithms shape our world
3. Friday math movie – Bass guitar design

Frank Warren started PostSecret by handing out self-addressed post cards to strangers on the street, and invited them to share whatever secret they liked. He was stunned with the response. More than half a million people have sent in postcards sharing all sorts of secrets about the lives, their loves and their activities.

What’s your Math Secret?

Since mathematics makes many people very emotional, here’s your chance to share your own secrets about your experiences with math (in the comments).

You don’t have to use your real name, of course (or even your real email, if you do, you can get updates and people add their own secrets. Either way, your email is not published.)

You are encouraged to use an image like the original PostSecret examples, but text is fine, too!

If you want to use your own image (450×450 px maximum), upload it to somewhere on the Web and then use this code to show it:

<img src="IMAGE-URL-GOES-HERE" />

More background

Warren spoke at TED SXSW recently about how the PostSecret concept started.

So, enter your own math secret in the comments below!

I’ve started by sharing my own secret.

Related posts:

1. Lorenzo Aureli and farazhasan_59 – are you out there?
2. Friday Math Movie – the Web’s secret stories
3. This cheeses me off…

In this Newsletter:

1. Radius of curvature interactive graph
2. Easy math input and nice output using ASCIIMathML and Mathjax
3. Math poll
4. Math puzzles
5. Final thought: Never stop

1. Radius of Curvature interactive graph

Here’s an interactive graph where you can explore the interesting concept of radius of curvature. This update now works in all browsers. I also added an explanation of where the radius of curvature formula comes from, under “Proof”. Radius of Curvature interactive graph update

2. Easy math input and nice output using ASCIIMathML and Mathjax

Here’s a system that allows for easy input of math (using calculator-like syntax) and good-looking output on any browser. Easy math input and nice output using ASCIIMathML and Mathjax Calling for volunteers: I need people to help with the conversion of images to MathJax. If you have some time, even if you can only do a few pages, it would be great to have your inputs. In the process, you’ll learn this new system of math input, and learn some math notation. You’ll also learn some math from doing it! Please let me know if you can help out, either via a reply to this email, or in the comments.

3. Math polls

A poll during Mar/Apr 2012 asked readers: The math you are studying now – how useful is it for your future job?

It was gratifying to see more than half of those responding felt math is "very useful" for their future job. Many math educators believe we shouldn’t worry about the "usefulness" of math, but I believe everyone – students and teachers alike – should know why we study various topics.

Sometimes the topic is included just because it’s interesting (or gives some mathematical insight) which is fine, but when the topic has many "real-life" uses, everyone should know what they are. There are too many math students who struggle with the genuine question, “Why are we doing this?”.

Very useful
 55%

Not useful
 19%

Somewhat useful
 14%

Don’t know yet
 13%

Total votes: 3400

Latest poll: The current poll asks readers about their use of math software. You can respond on any page in IntMath.com.

4. Math puzzles

There were plenty of responses to last Newsletter’s puzzle on the coefficient of x⁹⁹. Several people wrote correct answers (-5050), but gave no indication where their answer came from. It’s always best to show your working! (Some people can just “see” the answer, but that doesn’t help anyone else to know where it came from.)

Tom provided one of the more interesting correct answers, involving a "shift" to make things easier. This is often a good technique, to change the problem to one that is simpler.

Craig approached it using technology, and found his TI-89 calculator choked, but Mathematica software instantly gave him the answer.

Story: This math puzzle reminded me of the famous story where mathematician Carl Friedrich Gauss astounded his (terrible) teacher by adding the numbers 1 to 100 in just a few seconds. The teacher, a Mr. Buttner, was not a very nice person and would give his students very long calculations to do just so he could rest.

Gauss, aged 10 at the time, proceeded as follows. He paired the first and last numbers, then the inner 2 numbers and so on, like this:

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

He realized there would be 50 such pairs (1/2 of 100), so the total must be 101 × 50 = 5050.

Here are some other methods for finding this particular sum.

Latest puzzle: Find a 2-digit number equal to the square of the ten’s digit plus the square of the sum of its digits

5. Final thought: Never stop

I’ve enjoyed helping others with math for as long as I can remember. And in the process of teaching others, I could see my own math skills improve.

Joseph Joubert, French Essayist and moralist (1754-1824), quite rightly said:

To teach is to learn twice. [Joseph Joubert]

The second and related thought is by an unknown writer:

Never stop striving, never stop learning, never stop teaching.

Your own math skills improve whenever you help others with their math difficulties. Don’t do it for them – but help them to figure it out for themselves.

Until next time, enjoy whatever you learn.

Related posts:

1. Radius of Curvature interactive graph update
2. IntMath Newsletter: radius of curvature, log curve, free math videos
3. Easy math input and nice output using ASCIIMathML and MathJax

The process of entering math into Web pages is slow and tedious. Also, when students need to ask questions involving math in forums or through email, they have difficulty typing math and resort to attaching a PDF or Word document with their question (or worse, a photo of some hand-written math).

Creating math in document editors like MS Word is also a clumsy process.

For developing my own math Web pages, over the years I’ve used images (created via MS Word, or various math software) which need to be uploaded to the server, and take a lot of time to maintain (if errors are found, or other changes are needed), and more recently, I’ve used LaTeX-based images (which are created on-the-fly by the server).

LaTeX-based images are much easier to deal with, but this system has its own issues, not least of which is the relatively complicated syntax for LaTeX, and its fussiness (for example, you can’t have spaces in your math or it fails).

ASCIIMathML

I really liked the concept of ASCIIMathML when it first came out. It allows the user to input math very easily, using just the keyboard, and spaces in the math are no issue.

For example, consider this fraction, surrounded by braces.

In ASCIIMathML, we can type it using only 24 characters, all on the keyboard. It looks a lot like calculator input:

{x^2 / sqrt ( y^3 + sin theta ) }

The downside with ASCIIMathML (up to now) was it only worked nicely in Firefox browser, since ASCIIMathML is based on MathML and Firefox is the only browser with native MathML support. In all other browsers it either looked bad (like in Chrome) or didn’t work at all.

We needed a cross-browser, cross-platform math rendering system which didn’t use images.

Enter MathJax.

MathJax

MathJax promises "beautiful math in any browser without plugins" and essentially that’s what it delivers. It’s not perfect, but it is very, very good.

Once Mathjax has loaded (it’s a javascript file), it processes any math it finds (the math needs to be surrounded by special characters) into attractive and easy to read math.

But the downside, to now, has been that you needed to code your math in LaTeX. As mentioned earlier, LaTeX is certainly not very user-friendly, and it’s not a system you could expect the average math student to learn.

There are WYSIWYG editors for LaTeX entry, but it is a 2-stage process, where you have to copy-paste from the editor. Most of the editors are not very user-friendly and you really need to know the syntax anyway to get things to work. Usually I found it was quicker just to type the math expression.

What does LaTeX look like? Here’s the same fraction I used above.

Here’s the corresponding LaTeX expression for that fraction:

\left\{\frac{x^2}{\sqrt{y^3+\sin\theta}}\right\}

It uses 48 characters, which is exactly 100% longer than the corresponding ASCIIMathML expression in this case. LaTeX is also much more cumbersome and harder to maintain, since it’s harder to read.

While LaTeX is great for math geeks, I don’t think we should make the average math student learn it, just so they can communicate math on the Web.

We needed a solution that brought these 2 approaches together – and now it’s here.

ASCIIMathML input, MathJax output

With the release of version 2.0 of Mathjax, we can now enter math easily using ASCIMIMathML, and get "nice" output processed using MathJax. It’s simple to set up (add one line of javascript in your code) and implement. (There are many possible configurations for MathJax which can complicate things, but the standard settings will get you started.)

This set up works well in all browsers, even on mobile devices. It is a great solution for math forums, developing math in Web pages, and it can be modified for sending emails containing math.

Example pages

To see an example of what I am talking about, go to ASCIIMathML input, MathJax output. (This page is like a sandbox – you can play around entering math expressions to see how it works.)

On that page, you can see example input (using ASCIIMathML) and the resulting output (which renders via Mathjax). It works in all browsers.

You can also enter your own math expressions (between backtick delimeters, ` and `), and see the result. (Note they are not single quotes, like this ' and this '.)

There’s also a page where you can write an email containing math.

Updates to IntMath

I’m now converting all the images in IntMath to use this ASCIIMAthML-Mathjax system. The math looks much nicer now, and the pages load faster. You can see example pages where most of the math has been created this way here:

Division of Algebraic Expressions (fractions)

Split Functions (piecewise-defined functions)

For new development, this system is so much more productive than using images, or using LaTeX input.

I’m a happy camper.

Related posts:

1. MathJax – render math on the Web on all browsers
2. IntMath Newsletter: Radius of curvature, easy math publishing with MathJax
3. Enter math in emails, forums and Web pages using ASCIIMathML

I recently updated the interactive graph on that page.

Screen shot – radius of curvature interactive graph

So go and explore what Radius of Curvature means and how it is applied, here:

Radius of Curvature

(Technical background: I originally created the graph using GeoGebra and imported that .GGB graph into JSXGraph, but this approach does not work in Internet Explorer. Did I ever mention I hate Internet Explorer?

The new version was created from scratch in JSXGraph and it works in all browsers.)

Related posts:

1. IntMath Newsletter: radius of curvature, log curve, free math videos
2. IntMath Newsletter: Radius of curvature, easy math publishing with MathJax
3. Online graph plotter using JSXGraph

In this Newsletter:

1. April is Math Awareness Month
2. Modulus or absolute value of a complex number?
3. Google’s "Solve for <x>"
4. IntMath Privacy Statement
5. Math puzzle
6. Friday math movies
7. Final thought – Tenant farmers

1. April is Math Awareness Month

2. Modulus or absolute value of a complex number?

A reader challenges me to define modulus of a complex number more carefully. Modulus or absolute value of a complex number?

3. Google’s Solve for <x>

This is an interesting initiative from Google. It’s an invitation to suggest "radical technological solutions for today’s big problems".

You can hear some insights by people who’ve already suggested good ideas, in TED-style talks.

This is the kind of thing we should be doing in schools to make learning more meaningful and relevant! Is there space for it in your school?

The link: Solve for <x>

4. Updated IntMath Privacy statement

You probably hear endlessly about privacy updates from Facebook, Google and other sites.

Well, I keep certain information about you too, my faithful readers. The updated IntMath Privacy Statement indicates what that information is, and how it is used.

Brief summary: I never share your private information with anyone, ever.

5. Math Puzzle

There were many "correct" answers for last Newsletter’s math puzzle about birds and beasts. Special mention goes to all those (too many to mention) who showed full working – that’s a very good habit to get into!

But here’s the thing. In the "real" world, nothing is ever as straightforward as it seems (especially when considering typical math text book questions).

Some of the respondents considered there may be more to the question. Take Guido‘s comment "Birds are animals, too", and gfrblxt who amusingly said "Assuming that the zoo had no push-me pull-yous ^_^ ".

Devin included an excellent feature in his answer – he stated the assumptions for his solution (always a good thing to do when solving problems):

"Assuming all animals have 1 head, each beast has 4 feet and birds have 2."

Ricky, Anthonette and Alex also stated their assumptions, making their answers much more "correct".

But Tomas thought about it some more and began with:

Assuming snakes, snails, fish, and all other footless beasts are excluded…

Now, the original question used both of the terms "beast" and "animal" and for most of us, that means "tiger", "elephant" and so on. But strictly, an animal is any living creature belonging to the kingdom "Animalia", which includes 6-legged insects, 8-legged spiders, many-legged millipedes, and even zero-legged fish and sponges.

While we wouldn’t call most of those "beasts", they are certainly not plants!

How about chimpanzees and other apes? They use all four limbs for walking, but we generally don’t say they have 4 feet. Kangaroos are another example of a 4-limbed "beast" with only 2 feet.

As for the number of feet birds have, we won’t even consider here Leviticus 11:20, where a few translations have “All fowls that creep, going upon all four, shall be an abomination unto you.”!

All this makes the question a bit more difficult to answer! Of course, the question writer had the simple case in mind so the answers given are fine.

The bottom line is, when answering any math question that involves the "real" world, it’s a good idea to think about what else could be included and what should be excluded – and then state your assumptions.

For the teachers who have read this far, math questions should probably be either clearly "close-ended" (all assumptions are stated in the question, and students should aim for the one correct answer), or (better), more "open-ended", like "real" problems, where the process of thinking through the possibilities makes it more interesting, more motivating and more useful for developing future problem-solving skills.

New puzzle: (This puzzle is close-ended and has only one correct answer – promise!)

What is the coefficient of x⁹⁹ in the expansion of

(x − 1)(x − 2)(x − 3) … (x − 100)?

You can add your answer here.

6. Friday math movies

(a) The real meaning of MPH Here’s an agonizing video demonstrating how we really should spend more time on fundamental concepts in math class. Friday math movie: The real meaning of MPH

(b) Calculus Rhapsody This is clever – and funny: a calculus parody of the classic Queen song, Bohemian Rhapsody. Friday math movie: Calculus Rhapsody

(c) Inspirations – animation of Escher art Here’s a celebration of Escher, and it includes many crucial math concepts. Friday math movie: Inspirations – animation of Escher art

7. Final thought – Tenant farmers

Inventor and businessman Thomas Edison held over 1,000 patents for inventions ranging from the lightulb to the phonograph. He founded General Electric, an energy, technology and finance conglomerate.

His view on renewable resources is very interesting:

We are like tenant farmers chopping down the fence around our house for fuel when we should be using Nature’s inexhaustible sources of energy – sun, wind and tide… I’d put my money on the sun and solar energy. What a source of power! I hope we don’t have to wait until oil and coal run out before we tackle that. [Thomas Edison (1847-1931)]

Until next time, enjoy whatever you learn.

Related posts:

1. Modulus or absolute value of a complex number?
2. IntMath Newsletter: DUI, math dancing and printing a kidney
3. IntMath Newsletter – Complex numbers, Pi Day, Formula sheets

At the time of writing, 4 million other people had agonized over (or been ghoulishly amused by) this video.

One wonders about the safety aspects of the driver who is operating the camera while also in command of a deadly missile.

This video is along the same lines as: Patricia Heaton Fails at Math.

Related posts:

1. Friday math movie: Symphony of Science
2. Friday math movie – Can you answer this for 50K?
3. Friday math movie: Fractals without a computer

Enjoy.

If you need some background:

Original Queen song: Bohemian Rhapsody

Most of the math is in this chapter: Integration

Related posts:

1. Friday math movie: U + Me = Us (calculus)
2. Friday math movie – Dancing Honeybee Using Vector Calculus to Communicate
3. Friday Math Movie – Math Girl

The story behind the opening chessboard scene can be found here: Math Fairy Story.

Related posts:

1. Friday math movie: OK Go This Too Shall Pass
2. Friday math movie: Pi Day Song
3. Friday math movie: Ken Robinson animated