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Education & Academic

Lunar Eclipse

Every so often, more often than you might think, a lunar eclipse happens somewhere in the world. Tonight, there will be a total lunar eclipse visible from the United States and numerous other regions. This can only happen when there is a full moon, but not every full moon results in a lunar eclipse. If the moon is directly along a line drawn from the Sun to the Earth, then the Earth’s shadow falls across the face of the moon, typically giving it a reddish hue. If you aren’t afraid of a little bit of cold weather and weather permits, you might try to see the eclipse yourself. You can study eclipse phenomena, both solar and lunar, in real-time using this Demonstration.
Jeff Bryant, Research Programmer, Wolfram|Alpha Scientific Content
Computation & Analysis

A Valentine’s Day Surprise

Search for “heart” on any image search engine and you’ll turn up a wide variety of forms from squat to tall, geometric to curvaceous, all recognizable as heart shapes. In order to explore those possibilities, I wanted to capture the essence of the heart shape in a Mathematica Demonstration that had the smallest possible number of controls, but would nevertheless let me recreate most any heart I ran across. I found that three circular arcs strung together and reflected about the vertical sufficed to capture the essence of “heartness”. The result is the Demonstration “Sweet Heart”. The Demonstration is underconstrained, giving you the freedom to explore hearts as well as a large number of forms that are not even remotely heart-like. But that freedom is good. If there were interesting surprises lurking in those un-heart-like forms, I didn’t want to exclude them a priori. Indeed, while exploring near the boundaries where hearts dissolve into non-hearts, I stumbled onto two different ways of making hearts within hearts---from three simple arcs. I wouldn’t have thought it possible. That’s a nice Valentine’s Day surprise.
Christopher Carlson, Senior User Interface Developer, User Interfaces
Products

Demonstrating Valentine’s Day

As an editor for the Wolfram Demonstrations Project, I see many new submissions every day. The amount of variety is sometimes staggering. Occasionally, we have events that trigger Demonstrations based on a theme, and Valentine's Day is one such event. What in the world do Demonstrations have to do with Valentine's Day? Take a look at some of the new set of Demonstrations that are available for this February 14. They include a puzzle, a parametric surface, an algebraic surface, two parametric curves and one that’s just plain fun. It’s amazing to see how mathematics can be applied to everyday topics (and matters of the heart), not just to classroom math or science.
Broken Heart Tangram A Rose for Valentines Day
Equations for Valentines Sweet Heart
The Polar Equations of Hearts and Flowers Cupid's Arrow
Stay tuned for a blog post from Chris Carlson with details about how he “lovingly” created his "Sweet Heart" Demonstration. I’m looking forward to seeing what Demonstrations the next holidays might bring.
Jeff Bryant, Research Programmer, Wolfram|Alpha Scientific Content
Education & Academic

A New Look and New Features for MathWorld

While MathWorld continues to be the most popular and most visited mathematics site on the internet, and while its mathematical content continues to steadily grow and expand, MathWorld readers will today notice more immediate visual changes. Design changes and major new pieces of functionality are generally years in the making for large informational websites like MathWorld. The last time the site received a major infrastructure upgrade was in July of 2005 (see “MathWorld Introduces New Interactive Features for Teachers and Students,” MathWorld headline news, July 6, 2005). On February 8, we introduced a major update of the MathWorld site featuring improved navigation, higher-quality typesetting and links to interactive Demonstrations. The new features introduced on MathWorld include: New streamlined “platformed” look and feel New interactive Demonstration collections and links Improved mathematical typesetting Collapsible navigation link trails More-prominent ways to contribute to MathWorld Each of these elements is described in more detail below.
Eric Weisstein, Senior Researcher, Wolfram|Alpha Scientific Content
Education & Academic

Losing a Country’s GDP in the Financial Markets

Yesterday it became known that a 31-year-old trader at Société Générale had been performing fraudulent transactions in the futures markets that ended up costing the French bank more than 7 billion USD. Some news sources have even speculated that the large market losses on Monday were caused by SocGen unwinding the bad trades. These market losses, on their turn, were the main cause behind the US Federal Reserve's decision to cut interest rates by 75 basis points on Tuesday. I was chatting about the topic with a coworker today when he mentioned---as people often do when these things happen---that this value was larger than the economy of many countries. Sure, but how many? As we do all the time, we fired up Mathematica to put things into perspective. And indeed, it's trivial to get Mathematica to answer that question: you just use the built-in function CountryData to generate a list of all countries in the world, and select those whose gross domestic product (at market rates) is smaller than 7 billion. The SocGen rogue trader managed to annihilate an amount of money that surpasses the yearly output of the economy of 112 countries, among them Madagascar, Mozambique and war-torn Afghanistan, all of which have population sizes larger than 15 million. A more visual way to present this fact is to use the "FullPolygon" property in CountryData to generate countries' shapes, and then color those countries with a GDP below 7 billion USD: It took me less than a minute to visualize my office mate's comparison, and indeed this is a type of visualization that a lot of Mathematica users can just pull out of their hats---thanks to the effort that was put into designing Mathematica to make sure that all of its functionality fits together. For more examples of CountryData, visit The Wolfram Demonstrations Project.
Fred Meinberg, Special Projects Group
Education & Academic

Flipping Out over Technology in Education

I’ve been interested in education for a long time, and when someone suggests that the software system I’ve been working on for 20 years is bad for education, I take it personally. So I was upset when a New Scientist magazine article “Physics Tool Makes Students Miss the Point,” reported on a study by Thomas Bing and Edward Redish, “Symbolic Manipulators Affect Mathematical Mindsets,” strongly implying that the study concluded that replacing paper-and-pencil calculations with Mathematica was educationally unsound. And I was greatly relieved to find that the study itself says no such thing. Bing and Redish don’t recommend banishing Mathematica; they welcome it in their classrooms and point out many positive things about it, along with one relatively minor pitfall they suggest ways to work around. What mindset led the reporter to jump to such a reactionary conclusion? Why use such an inflammatory headline in connection with level-headed research that showed, when you get right down to it, virtually the opposite of what the New Scientist headline says? The question of what technology to use in the classroom comes up all the time, and the resulting debate often generates more heat than light. People feel strongly about the subject because at its heart it is a question about what it means to be human.
Theodore Gray, Cofounder, Wolfram Research, Inc.; Founder, Touch Press
Education & Academic

Mathematica and the Fundamental Theorem of Calculus

Most calculus students might think that if one could compute indefinite integrals, it would always be easy to compute definite ones. After all, they might think, the fundamental theorem of calculus says that one just has to subtract the values of the indefinite integral at the end points to get the definite integral.

So how come inside Mathematica there are thousands of pages of code devoted to working out definite integrals---beyond just subtracting indefinite ones? The answer, as is often the case, is that in the real world of mathematical computation, things are more complicated than one learns in basic mathematics courses. And to get the correct answer one needs to be considerably more sophisticated. In a simple case, subtracting indefinite integrals works just fine. Consider computing the area under a sine curve, which equals

Oleksandr Pavlyk, Senior Kernel Developer, Algorithms R&D
Announcements & Events

Ten Thousand Hours of Design Reviews

It’s not easy to make a big software system that really fits together. It’s incredibly important, though. Because it’s what makes the whole system more than just the sum of its parts. It’s what gives the system limitless possibilities—rather than just a bunch of specific features. But it’s hard to achieve. It requires maintaining consistency […]

Stephen Wolfram
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