In this video, Hans Rosling and his son discuss some of the misconceptions regarding income distribution, and population and health trends.

The post Hans and Ola Rosling: How not to be ignorant about the world appeared first on squareCircleZ.

]]>In this latest installment, he triggers the audience to think more deeply about how the world has changed over the years. He has a particular interest in population, health, poverty and income, and how such things have intertwined.

After getting his audience to participate via clickers, he proceeds to try to clarify their understanding of wealth distribution and poverty.

His son Ola joins in to outline where he believes the misconceptions come from. It’s probably not a good idea to tell people all the time they are ignorant (as Ola seems to do), but it’s actually very important that people have better skills at scanning and interpreting data in its many forms.

It’s always interesting to see what people say about such videos on YouTube. One guy ranted about this chart:

He wrote as part of a very critical comment:

Should $10-per-day be the MID point of the chart? Why is there the same distance between $1-$10 as $10-$100?

Clearly this person was not listening during the logarithm lesson in his school days, where he would have learned about Semi-log and Log-log Graphs.

It’s sad that an essential data presentation concept like this is poorly understood by many.

The chart is highly simplified for the sake of Rosling’s argument. Perhaps that is a mistake – what does the real data actually look like when plotted? It may have been more convincing.

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]]>The post IntMath Newsletter: Ellipse, IQ, mobile mystery appeared first on squareCircleZ.

]]>In this Newsletter:

1. New ellipse animation

2. IQ and how we see the world

3. Mystery – mobile and desktop visitors

4. How to code JSXGraph axes, ticks and grids

5. Friday math movie – Music and math: The genius of Beethoven

6. Math puzzles

7. Final thought – inequality

The above animation is simple and doesn’t do much. You may find the following more interactive and useful for learning about ellipses:

In a 2013 study by the University of Rochester, researchers found interesting differences between the way high IQ people perceive different sized objects. In the summary, People with high IQs process sensory information differently, we read:

"It is not that people with high IQ are simply better at visual perception," says Duje Tadin of the University of Rochester. "Instead, their visual perception is more discriminating. They excel at seeing small, moving objects but struggle in perceiving large, background-like motions."

As I read more about this, I thought about how it affects success in mathematics study, especially in word problems.

The ability to focus on the important small details, and ignore the larger, distracting unimportant details bodes well for students, researchers, and all of us who are daily swamped with information overload.

Here is the original Rochester University journal article:

A strong interactive link between sensory discriminations and intelligence

In my school system, our IQ was tested, but we were never told what it was. The teachers didn’t want us to either feel despondent and unmotivated if we had a low IQ score, or to be lazy because we knew we had a high score.

Do you know your own IQ? Has it affected your approach to learning? Do you feel it really matters?

Leave your responses here.

As you may know, IntMath presents a mobile version of the site to users with mobile phones.

For a while now, I’ve noticed differences in traffic betwen mobile and desktop visitors to IntMath.

All things being equal, you would expect users to be interested in the same math topics, no matter what device they are using for access. But this is not the case.

I have color-coded the following table (yellow for algebra topics, green for graphs, pink for probability and orange for calculus).

Rank 6 is the only case where traffic rank is represented by the same page.

This is taken from the most recent 500,000 page views.

Rank | (Desktop/tablet) Pages | # views | (Mobile) Pages | # views |
---|---|---|---|---|

1 | Problem Solver | 25749 | Domain and Range | 9413 |

2 | Domain and Range | 20854 | Home page | 6571 |

3 | How to find the Equation of a Quadratic Function from its Graph | 15490 | Derivative of sin, cos and tan | 5887 |

4 | Derivative of sin, cos and tan | 14536 | Basic Algebra Introduction | 4250 |

5 | Home page | 12655 | Derivative of csc sec and cot | 3318 |

6 | Derivative of Logarithms | 10392 | Derivative of Logarithms | 3288 |

7 | Poisson Distribution | 9603 | Matrices and Determinants Introduction | 2605 |

8 | Solving Differential Equations | 9067 | Perpendicular distance point to a line | 2564 |

9 | Normal Probability Distribution | 8741 | Exponents and Radicals | 2462 |

10 | Graphs Sine & Cosine – Amplitude | 7627 | Factoring and Fractions | 2456 |

(Most tablet users go to the desktop version of the site, so they are included in desktop figures.)

The Problem Solver does not have a mobile version, so that explains why it doesn’t appear in the mobile column.

But overall, it’s a mystery to me. Why are desktop users interested in finding out about quadratic graph functions, where mobile users are not as much? Why are mobile users more interested in algebra topics than desktop users? Is this an age issue, perhaps?

Do you have your own hypothesis? Leave your ideas here.

This is a technical article and is for those who want to create their own graphs on Web pages.

Trying to code JSXGraph so the axes and grid lines work can be a battle. This article points to a summary with examples of how to do it. |

Did Beethoven use math to create music when he was going deaf? This video is part of a TEDEd lesson. |

The puzzle in the last IntMath Newsletter asked which is the next image in a given series. The correct answer with explanation was given by Felix and Nicos. (Chris and Sachin had "almost" correct answers.)

Pattern recognition questions often seem to have more than one correct answer, depending on how good the reasoning is. But in this case, answer (b) is the only one that stands up to scrutiny.

**New math puzzle**: A beaker contains 250 mL of gasoline. A small cup is used to scoop gasoline out of the beaker and that gasoline is replaced by a cup of oil. The process is repeated, and it is found the final gasoline to oil mix is in the ratio 16:9. What is the capacity of the small cup?

Leave your responses here.

Today is Blog Action Day, where bloggers all over the world join together to provide insight into a particular theme. This year, the topic is **inequality**, and articles I’ve seen so far concentrate on income, gender and racial inequality.

But since "inequality" is also a mathematical concept (see the chapter on Inequalities), I thought I would add some thoughts in this Newsletter.

I grew up in a country where there was relatively equal opportunity. Education was cheap and there were many choices after leaving school. It was only when I moved to Asia to live that I was confronted with serious inequalities – of opportunity, of hope, of educational and technological opportunities, and of wealth.

I also realized how different countries go about defending themselves. Most spend huge amounts on their militaries (at the cost of educational and health opportunities for their people), which they use to defend themselves from others, and from internal threats. Some countries even go looking for enemies.

Other (wiser) countries use their military to provide humanitarian aid after natural disasters (thereby making friends), as well as for defense. Such countries (which are very few), also see great value in educating their population (without prejudice to certain races, ethnic or religious groups, or gender) and provide resources to get it done, and provide a range of job opportunities.

So that’s a summary of what I think is necessary to reduce the dangerous inequalities that exist in the world today – educational opportunities without prejudice against any one group of people, and job opportunities based on merit.

For some mathematical background on this issue, see Gini Coefficient of Wealth Distribution, which explains a concept we often hear about when discussing inequality.

Until next time, enjoy whatever you learn.

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]]>Trying to code JSXGraph so the axes and grid lines work can be a battle. This article points to a summary with examples of how to do it.

The post How to code JSXGraph axes, ticks and grids appeared first on squareCircleZ.

]]>

No *y*-axis scale indication – JSXGraph plot

Similarly, I found the business of creating grids (or are they ticks?) was quite troublesome.

So I set about trying to get it clear in my own mind. I wrote a summary of my discoveries here:

It’s presented in several steps which increase in complexity. By the end, you’ll see a graph that allows you to:

- See grid lines and labels all the time, no matter what zoom level is used
- See axes all the time (by "docking" them to the side if the graph is dragged – or zoomed – so the axes would go beyond view)
- Zoom in and out in one direction only (along the
*x*- or*y*-direction)

Improved grids on a JSXGraph graph

I hope those of you new to JSXGraph will find it useful.

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]]>Did Beethoven use math to create music when he was going deaf?

The post Music and math: The genius of Beethoven appeared first on squareCircleZ.

]]>How is it possible for a composer to write music, without being able to hear it? This video attempts to answer that question.

The video is actually the opening motivation for a TEDEd lesson, Music and math: The genius of Beethoven, by Natalya St. Clair. The introduction on that says:

How is it that Beethoven, who is celebrated as one of the most significant composers of all time, wrote many of his most beloved songs while going deaf? The answer lies in the math behind his music. Natalya St. Clair employs the “Moonlight Sonata” to illustrate the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.

Well, maybe.

I fear this is a case of “mathematizing” something which is not very mathematical in the first place. Don’t get me wrong – I agree there are a lot of mathematical concepts behind writing music. (See Music and Transformation Geometry where I outline some of these ideas.) And it’s certainly true that once Beethoven settled the main themes of his music, the rest of it would follow as a consequence of the agreed structure of that type of music. For example, symphonies were usually made up of 4 movements, where each movement had a certain speed, and key changes occurred in predictable, and relatively set patterns, which were fairly geometrical in nature.

But the key thing that’s missing in this video is that “real” composers hear it all in their mind, before anything appears on paper. Not much mathematics involved in that.

But with that in mind, on with the show.

What do you think? Feel free to add your comments below.

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]]>1. 20 Gifs That Teach You Science Concepts

2. Make!Sense

3. MOOC: Audio Signal Processing for Music Applications

4. Inspiring teachers (8 TED talks)

5. KaTeX - a new way to display math on the Web

6. Math puzzles

7. Final thought - Why I'll Never Tell My Son He's Smart

The post IntMath Newsletter: Resources, inspiring teachers, KaTeX appeared first on squareCircleZ.

]]>In this Newsletter:

1. 20 Gifs That Teach You Science Concepts

2. Make!Sense

3. MOOC: Audio Signal Processing for Music Applications

4. Inspiring teachers (8 TED talks)

5. KaTeX – a new way to display math on the Web

6. Math puzzles

7. Final thought – Why I’ll never tell my son he’s smart

If a picture is worth a thousand words, a good animation is probably worth a million. Here’s a collection of animations that I hope you find interesting: 20 Gifs That Teach You Science Concepts Better Than Your Teacher Probably Can |

A lot of math (and science) is text-book driven, whereas it’s often better to learn concepts as a result of observing and interacting with actual objects.

Make!Sense is a new product that helps to achieve this goal. Here’s the developer’s description:

I’ve found that students respond well to playing with such data loggers. It’s hands-on and usually a lot more meaningful than worksheets.

Here’s their KickStarter page:

[KickStarter is a crowd funding platform.

Disclaimer: I have no connection with this product.]

Stanford University is offering a free MOOC starting this week (1st Oct 2014) A MOOC is a "massive online open course". This one promises to be a very interesting application of math to music. |

For some background on what this course is about, and to get an idea of the concepts involved, see:

Fast Fourier Transform (on IntMath)

See more Stanford University MOOC offerings.

Here’s some good ideas from great teachers for the start of the school year.

The role of the teacher is crucial in every class, but especially in math. Here’s a collection of TED talks by inspiring teachers. All of them are relevant for improving math education. |

I think it’s important to be able to communicate math concepts easily in online forums and other digital media. KaTeX is similar to MathJax in that it can display math without using images.

KaTeX is a new method for publishing LaTeX-based math on the Web. It’s faster than MathJax, but not as robust (yet). |

There’s also KaTeX with ASCIIMathML input and MathJax fallback

The puzzle in the last IntMath Newsletter asked about a rectangle whose perimeter equals its area. The correct answer with explanation was approached in 3 different ways by the following respondents:

**Algebraic:** Francis, Joe, Tomas, Smitha, Francisco, and bahaa;

**Tabular:** Janet;

**Graphical:** Nicos and Abby S.

In their answers, Nicos and Abby are talking about the graph of

(where *x* and *y* are the side lengths). Here’s what it looks like (it’s a hyperbola):

We don’t use the lower-left arm of the hyperbola (which would give us negative lengths).

The point A on the graph is (4, 4), the solution which gives us a square. (But the question said it cannot be a square.)

The answer has to be near this point on the curve (the further you are away from this point, the bigger the rectangle becomes.)

If we try *x* = 5, it gives *y* = 10/3, which isn’t an integer.

But *x* = 6 gives *y* = 3. Both are integers, their product (the area) is 18 and this equals the perimeter 2(3 + 6) = 18. Hence point B represents the answer. (It’s equivalent to (3, 6).)

**New math puzzle**: Consider the following sequence of images.

Which one of the following represents the next in the series?

Leave your responses here.** **

Salman Khan, well-known creator of the Khan Academy, has some great things to say in his article, "The Learning Myth: Why I’ll Never Tell My Son He’s Smart".

He talks about 2 ways of approaching learning, with either a **fixed** or **growth** mindset. Here’s a quote:

Fixed mindsets mistakenly believe that people are either smart or not, that intelligence is fixed by genes.

People with growth mindsets [however], correctly believe that capability and intelligence can be grown through effort, struggle and failure. [They] embrace challenges, and understand that tenacity and effort can change their learning outcomes.

The take-home message is that we should praise effort, diligence and tenacity, not inherent skills.

See the complete article: |

Until next time, enjoy whatever you learn.

The post IntMath Newsletter: Resources, inspiring teachers, KaTeX appeared first on squareCircleZ.

]]>KaTeX can handle ASCIIMathML input, and fall back to MathJax when KaTeX gives up with this approach.

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]]>While KaTeX is a lot faster than MathJax, for me there are 2 downsides with KaTeX:

- KaTeX only accepts LaTeX input. However, I have used ASCIIMathML for all the equations and formulas on IntMath, because it is signiicantly simpler and easier to use than LaTeX. If I wanted to use KaTeX for my site, I’m stuck.
- KaTeX doesn’t recognize many math expressions yet, for example matrices, determinants, various symbols, "aligned" environments (where you can align everything on the equal sign), various accents, case definitions and so on.

So I set about writing a page that handles both of these issues.

I needed a system that recognised ASCIIMathML input, converted it to LaTeX, and then was processed by KaTeX so it looked like "real" math. In the cases where KaTeX cannot handle the math, it needs to fall back to MathJax so all the math is rendered properly.

Here is a demo of my solution:

You’ll see some equations appear quickly (those done by KaTeX), then the MathJax-rendered ones will appear. They have a green mark next to them so you can see what MathJax can do that KaTeX cannot.

This is deliberately a “heavy” page (with many equations) to push its performance.

Fortunately, ASCIIMathML comes with a script, ASCIIMathTeXImg.js, which converts the simple ASCIIMathML input to LaTeX, and then outputs each math expression as an image (using MimeTex or MathTex).

I modified the function AMTparseMath() in ASCIIMathTeXImg.js, so it no longer converts math to images, but outputs LaTeX.

My tweaks were:

- Create a span in the place of each piece of ASCIIMathML
- Give the span a unique id
- Try first to render it with KaTeX
- If that fails, put back the original ASCIIMathML and render it with MathJax

Here’s the relevant parts of the changed script.

var node = document.createElement("span"); thisId = "mathId"+counter; node.id = thisId; try { katex.render(texstring,node); } catch(err) { node.className = "mj"; node.innerHTML = "`"+str+"`"; MathJax.Hub.Queue(["Typeset",MathJax.Hub,thisId]); } counter++;

Of course, the main aim is speed, and if the user needs to download both KaTeX and MathJax, as well as ASCIIMathTeXImg.js, there is going to be a significant delay before any rendering occurs, especially on a mobile device.

On my phone, the first KaTeX equations on the demo page appeared in about 6 seconds, and the MathJax matrix came in around the 13 second mark.

But it is a feasible solution for mobile devices, especially if your more complicated equations are low down the page (so they will process in the background and be done before the user gets to them).

Another downside is that the user will need to download 2 sets of fonts – one for MathJax and one for KaTeX. One way out of that would be to specify one or the other.

You may also be interested in this demo, where you can see how much faster KaTeX does its thing compared to MathJax:

This page gives background on KaTeX:

This page is a sandbox where you can play with ASCIIMathML input:

This page uses the script mentioned above, ASCIIMathTeXImg.js, to send math in emails:

And finally, this page gives examples of how to enter math using ASCIIMathML:

Peter Jipsen and David Lippman for ASCIIMathML.

The MathJax team (especially Davide and Peter) for MathJax.

The Khan Academy team for KaTeX.

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]]>KaTeX is a new method for publishing LaTeX-based math on the Web. It's faster than MathJax, but not as robust (yet).

The post KaTeX – a new way to display math on the Web appeared first on squareCircleZ.

]]>It’s a direct competitor to MathJax, which I’ve been using on IntMath for some time now.

You can see immediately that KaTeX produces math much faster than MathJax. This is because KaTex "renders its math synchronously and doesn’t need to reflow the page", according to their short blurb on Github.

There is obviously much less time required for processing. KaTeX doesn’t suffer from the page reflow jumps that MathJax has after each equation is created. (To be fair, there are ways around those instabilities in MathJax.)

I wrote a page so you can see the same input as processed by both methods. See

There’s a rough "time to process page" at the top. It’s not a fair comparison in the sense that KaTeX doesn’t handle several of the equations (yet), and MathJax handles them all.

The difference is stark on a mobile phone – around 1 second for KaTeX and around 30 seconds for MathJax.

It claims to "supports all major browsers, including Chrome, Safari, Firefox, Opera, and IE 8 – IE 11". So does MathJax, and it also copes with the vagaries of earlier IE versions.

So far the only differences I’ve noted are some font weight issues. In Chrome, the rendering seems "thin" to me. Sometimes it’s too much so, and the "equal" signs almost look like minuses, and some minus signs almost disappear.

But that is not such an issue in Firefox or IE. Here are some screen shot comparisons.

Using KaTeX in Chrome, where "=" and “−” are thin :

Using MathJax in Chrome is bolder, and easier to read:

Here’s how KaTeX looks in Firefox (somewhere between the first 2, and most pleasing to me):

KaTeX in Internet Explorer looks almost identical to the above FF rendering, but has some alignment issues. (Note where the *u* and *v* are in relation to the fraciton line.

It’s no surprise that IE falls over here and there. It almost always does. Here are 2 instances that I’ve spotted so far:

The right hand side should have been: (*a*^{2} + *b*^{2} + *c*^{2})^{3}

This surd also has obvious problems in IE:

As mentioned earlier, KaTeX doesn’t do everything yet (it chokes on anything starting with \begin, \align or \choose, and many symbols don’t work yet.

You can see what currently works on the Demo page.

This list on the GitHub KaTeX wiki shows what functions are currently available.

The setup for KaTeX is similar to what you have to do with MathJax, but there is no CDN version of KaTeX yet.

First, download the KaTeX zip.

Extract the zip amd upload it all to your server. (This is much smaller than MathJax, as there is no image fallback with KaTeX, so there aren’t thousands of images to upload.)

Next, in the head of your page, point towards the KaTeX javascript and css, something like this:

<link rel="stylesheet" type="text/css" href="/path/to/katex/katex.min.css">

<script type="text/javascript" src="/path/to/katex/katex.min.js"></script>

If you have only a few equations on your page, you can proceed as follows:

<p><span id="mykatex1">...</span></p>

<script> katex.render("f(a,b,c) = (a^2+b^2+c^2)^3", mykatex1); </script>

This will place the equation into your Web page, as properly rendered math.

A second equation would need a new id on the span, and in the script, like this:

<p><span id="mykatex2">...</span></p>

<script> katex.render("f(a,b,c) = (a^2+b^2+c^2)^3", mykatex2); </script>

If you want to present a lot of LaTeX on your page, it would be better to proceed as follows.

You would use the same class name for the DIVs (or spans) containing math. Your HTML would look something like:

<div class="math"> f(x) = \sqrt{1+x} \quad (x \ge -1) </div>

<p>Some other text here. </p>

<div class="math"> f(x) = \sqrt{1+x}, \quad x \ge -1 </div>

Next, we use javascript to iterate over all the DIVs with class "math" (they can be <p>, <span> or <td> too, as long as the class is "math" and it contains LaTeX only.

I’m using jQuery to do this, but there are pure javascript methods as well.

The following code just means:

- Iterate over all the objects with class name "math"
- Get the text from the object (this is the LaTeX that we want to convert)
- Get the type of element. If it’s a DIV, then add "\displaystyle" so it will be presented as math centered on the page.
- Try to convert it to math using katex.render.
- If it fails, output an error message.

(function(){ $(".math").each(function() { var texTxt = $(this).text(); el = $(this).get(0); if(el.tagName == "DIV"){ addDisp = "\\displaystyle"; } else { addDisp = ""; } try { katex.render(addDisp+texTxt, el); } catch(err) { $(this).html("<span class='err'>"+err); } }); })();

There’s also an option to generate HTML on the server, so "you can pre-render expressions using Node.js and send them as plain HTML."

To do this you use "katex.renderToString".

This is where the math will appear:

<p><span class="katex">...</span></p>

This is the script you use:

var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}");

Apparently Khan Academy will be using both KaTeX (for speed) and MathJax (for more complicated equations) in the near term. Hopefully they will continue to develop KaTeX, but there’s a long way to go to catch up with MathJax’s flexibility.

MathJax has promised :significant speed improvements” in their next version.

Interesting times.

The developers answer some issues here, including “Why is it so fast?” (because it uses CSS for positioning and does a lot fewer things than MathJax), and some of their plans for future development (including matrices – yay!)

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]]>1. Carnival of Mathematics #114

2. Updated Graphs of tan, cot, sec and csc

3. Graphing letters

4. Math puzzles

5. Asking questions

The post IntMath Newsletter: Math carnival, new interactives, graphing letters appeared first on squareCircleZ.

]]>In this Newsletter:

1. Carnival of Mathematics #114

2. Updated Graphs of tan, cot, sec and csc

3. Graphing letter distribution

4. Math puzzles

5. Final thought – The skill of asking questions

It was my turn to host the 114th Math blog Carnival. I hope you find something interesting in the 16 articles there!

The Carnival of Mathematics is a collection of recent math blog articles covering visual math, various rants and some math history, by various authors. See: |

The updated applets on the Graphs of tan, cot, sec and csc page now run on mobile devices, albeit rather slowly. This leads to one of the most popular pages on IntMath. |

We live in a great age where it’s possible to see a lot more in data that was ever possible before computers.

Prooffreader (by David Taylor) has some interesting data visualizations, including several displaying trends in baby names. The name "Shirley" sky-rocketed in the mid-1930s, and "Linda" even more so in the the late 1940s. "Brittany" and "Ashley" were hits in the late 1980s. There’s an interesting animation of the rapid rise in boy’s names ending in "n".

He also has some infographics on cancer and mortality rates.

One of the graphics that caught my eye was Graphing the Distribution of English, which demonstrates how letters are used in words in the English language.

For example, the image below for the first 2 letters indicates that "a" occurs mostly in the middle of a word, whereas "b" occurs mostly at the beginning.

Go check out Prooffreader – there are some interesting things there.

The puzzle in the last IntMath Newsletter asked about a strange pyramid of ancient Egypt. The correct answer with explanation was given by Tomas and Nicos. The difference in their approaches was quite interesting.

**New math puzzle**: Find the smallest rectangle (non-square and with integer sides) where the perimeter equals the area (ignoring units).

Leave your responses here.

This quote comes from Annie Murphy Paul. It’s a summary of the Rothstein and Santana book, *Make Just One Change: Teach Students To Ask Their Own Questions**:*

"This book makes two simple arguments: 1) All students should learn how to formulate their own questions. 2) All teachers can easily teach this skill as part of their regular practice. This inspiration for the first argument came from an unusual source. Parents in the low-income community of Lawrence, Massachusetts, with whom we were working twenty years ago told us that they did not participate in their children’s education nor go to their children’s schools because they ‘didn’t even know what to ask.’ It turns out that they were actually pointing to a glaring omission in most formal and informal educational enterprises. The skill of being able to generate a wide range of questions and strategize about how to use them effectively is rarely, if ever, deliberately taught. In fact, it has too often been limited to students who have access to an elite education. Our goal is to democratize this teaching of an essential thinking and learning skill that is also an essential democratic skill."

—Dan Rothstein and Luz Santana,Make Just One Change: Teach Students To Ask Their Own Questions

Until next time, enjoy whatever you learn.

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]]>The Carnival of Mathematics is a collection of recent math blog articles covering visual math, various rants and some math history, by various authors.

The post Carnival of Mathematics 114 appeared first on squareCircleZ.

]]>Helix Bridge and Flyer, Singapore

114 is a **sphenic **number (the product of 3 distinct prime numbers):

114 = 2 × 3 × 19

It’s also a **repdigit**: 114 = 222_{7} (the digits repeat in the base 7 representation)

It’s the 19th number in the **Padovan** sequence, given by the recurrence relation *P*(*n*) = *P*(*n* − 2) + *P*(*n* − 3), and where the first 3 terms are 1.

114 is an **abundant number **(where the sum of its proper divisors is greater than itself):

114 < 1 + 2 + 3 + 6 + 19 + 38 + 57

That’s appropriate, as we have abundant posts for this, the 114th Carnival of Mathematics!

On with the show.

Now here are some animations that could be the basis for some interesting class discussion. See |

Andrea Hawksley gives us a nice roundup of the recent meeting on Origami, Science Math and Educaion. She features some of her own work, as well as other gems that were presented. See: |

6th meeting on Origami, Science, Math, and Education (6OSME)

While you’re there, mouse over Andrea’s name in the header of her blog. It’s cute.

That’s logical, as it’s the name of his blog! See

See:

BBC Sport’s Anti-Smartness Bias

In a similar vein, Gilead of “Tycho’s Nose” rants about inaccuracies (or part-truths) in background equations as seen in the new Doctor Who series. See: |

Here’s a rant of a different nature. Stephen Cavadino of "cavmaths" questions whether stem-and-leaf plots are a necessary part of the math curriculum. See: |

Mark Dominus provides us with a neat exploration of numbers that are permutations of each other. His first example is the decimal expansion of |

See:

When do n and 2n have the same digits?

Richard Elwes introduces us to an interesting knotty problem. It turns out this generally accepted picture is wrong… See how at: |

Jeremy Kun of "Math ∩ Programming" explores optimal greedy algorithms and matroids.

See:

When Greedy Algorithms are Perfect: the Matroid

This post, right here on "squareCircleZ", was inspired by a reader’s question. He makes solar cookers for use in Africa and wanted to know how to construct the spiral length around his cookers. It’s some "real-world" math that involves sustainable, cheap energy.

See:

Arc length of a spiral around a paraboloid

0 |
In a lot to do about nothing, Evelyn Lamb of the Scientific American blog, recounts her journey of discovery with her students, which involved decipering Plimpton, the 4000 year-old Babylonian tablet. |

So how did the Babylonians work in base 60, without 0 as a place holder?

See:

See:

How The Ancient Egyptians (Should Have) Built The Pyramids

α β γ δ ε ζ |
Here’s a summary of the Greek alphabet by SixWingedSeraph of Gyre&Gimble. We should spend more time on this topic in class, so students are more comfortable with this foreign script. See |

This post is a plug for an experimental MOOC (Massive Open Online Course). The blurb says:

"Citizen Maths is an online resource anyone can use — to discover how maths can be a powerful tool for solving those problems that come up at work and in your life."

See:

So, what is mathematics? Shecky Riemann of "Math-Frolic" has a quote from *How Mathematicians Think*, by William Byers, which ponders that math is a series of situations where we are led to observe,

I hope you’ve enjoyed Mathematics Carnival #114, coming to you from Singapore.

The next carnival will be at MathTuition88, slated for October 2014. See where and how to submit.

*Singapore Helix and Flyer* by ensogo, accessed from http://www.ensogo.com.ph/escapes/singapore-flyer-cruise-09092012.html

*BBC Sport logo*, by BBC, accessed from http://www.bbc.com/sport/0/

*Stem & leaf plot* by ck-12.org, accessed from http://www.ck12.org/book/Basic-Probability-and-Statistics-A-Full-Course/r4/section/7.2/

*Reflection*, by Marcia Birken, accessed from http://alumnae.mtholyoke.edu/blog/light-motifs-marcia-birkens-images-meld-math-and-art/

All other images are from the posts to which they link. If you have any objections to their use in this manner, let me know and I’ll remove them.

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]]>IntMath will be hosting the next Carnival of Mathematics, a collection of recent blog posts about math.

The post Carnival of Maths is coming to IntMath appeared first on squareCircleZ.

]]>To submit an article, go to:

As it says on the submission form:

The Carnival of Mathematics accepts any mathematics-related blog posts: explanations of serious mathematics, puzzles, writing about mathematics education, mathematical anecdotes, refutations of bad mathematics, applications, reviews, etc. Sufficiently mathematized portions of other disciplines are also acceptable. We also accept YouTube videos, and non-blog based content, as long as it’s new and has been recently posted online.

The most recent carnival was hosted by Mike at Walking Randomly. It covered the full gamut from limits to Ninjas and 3D printed geometry to mathematically-related underwear. See

All the previous carnivals can be found on Aperiodical. See:

See you back here in mid-September for edition #114!

The post Carnival of Maths is coming to IntMath appeared first on squareCircleZ.

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