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Computation & Analysis

Friends, Earthlings, ETs—Lend Me Your Sensory Organs!

Yesterday, I put together a Demonstration about the Clarke Belt---the ring of satellites 22,300 miles above the equator. Sir Arthur C. Clarke wrote in 1945 about the future usefulness of geosynchronous orbits, and I wanted to see a picture of them. Coverage of the Pacific seemed spotty. A few hours later, I saw the first news reports about his passing.
Ed Pegg Jr, Scientific Information Editor, Scientific Information Group
Education & Academic

Pi Day

Pi (π, the ratio of the circumference of a circle to its diameter), its older brother the golden ratio phi (φ) and the much younger e and i are the most famous numbers in mathematics. Pi is everywhere: not only in circles and spheres, but also in the results of all kinds of integrals, sums and products, as well as in number theory and physics. The personality of π is largely unknown: irrational, transcendental, possibly and probably normal. Because of π’s importance, its digits (3.14159265...) have an almost cult following. The first few digits, 3.14, correspond to notation for March 14, which was first celebrated as Pi Day in 1988, in the San Francisco Exploratorium. Wolfram Research has the most π presence on the web, with material at the Wolfram Functions Site (pi page, pi visualizations), MathWorld (pi, circle, sphere) and the Wolfram Demonstrations Project (pi, circle, sphere, disk, wheel), not to mention several built-in Mathematica symbols (Pi, EllipticPi, PrimePi). For NUMB3RS episode 314 (“Takeout”), we helped to fold many hidden π references into the script review and math notes. The writers, director, cast and crew added many more. The opening Black Box, for example: a 3-course meal, 1 restaurant, 4 robberies, 1592 death squad murders. Charlie mentions a circle-circle tangency joke not working, right before a James Bond reference (007---circle, circle, tangent). Below are a few of our π-related Demonstrations. Click any of them to reach an interactive math demonstration. Enjoy!
Ed Pegg Jr, Scientific Information Editor, Scientific Information Group
Announcements & Events

Get Coordinates: New in 6.0.2

Many new features in Mathematica are manifested in new functions with definite names, but some are not so prominent. You might miss one of the new features that I implemented for Mathematica 6.0.2---but it’s really useful, and so I thought I’d write about it here. Let’s say you have a plot, or some other kind of graphic. You see something in the graphic---some special point---and you want to know where that is, what its (x, y) coordinates are. In earlier versions of Mathematica, there were primitive ways to find this out. Now in Mathematica 6.0.2 there’s a nice, clean, general way to do it. Open the Drawing Tools palette (from the Graphics menu, or by typing CTRL-d or CTRL-t). Choose the “Get Coordinates” tool at the upper right.
Christopher Carlson, Senior User Interface Developer, User Interfaces
Products

Adventures in the Wolfram Demonstrations Project

As the project coordinator of the Wolfram Demonstrations Project, I have an inbox that is overflowing with fantastic ideas from Mathematica users and coworkers for how to make the Demonstrations site even more user-friendly and easy to navigate. One of the most exciting new features we’ve implemented recently is the new topics page. In a few easy clicks, users can fine-tune their searches to browse topics ranging from Middle School Mathematics to the Solar System to Natural Forms and everything in between.
Jessica Paris, Demonstrations Project Administration, Research & Development
Announcements & Events

Mathematica 6.0.2 Arrives

In my ten years at Wolfram Research, I’ve never seen so much software development activity. In the middle of last year, we had our biggest launch in a decade: Mathematica 6. Now there’s a huge pipeline of new development underway. Some people are working on Mathematica 7; some people on Mathematica 8. We’re developing major new frameworks and we’re adding boatloads of new functions. But we’re also continuing to polish and strengthen everything that’s already in Mathematica. We brought out Mathematica 6.0.1 last summer to add a variety of improvements that didn’t make it into 6.0.0. And we’ve now accumulated enough improvements that we’ve decided to release 6.0.2---which is being sent to Premier Service customers as of today.
Peter Overmann, Director of Software Technology
Announcements & Events

Two Weeks of Intense Mathematica

For years, I’ve been hearing about the NKS Summer School, and about how productive people find the three weeks of “immersion” there. For quite a while, people around Wolfram Research have been asking, “Why can’t we do something similar for Mathematica?” Well, now we are. This year, we’re offering a two-week Advanced Mathematica Summer School. Partly, it’s going to provide an opportunity for people to learn about all those parts of today’s Mathematica technology that they haven’t had a chance to work with yet. But the most important objective of the Summer School is to help people take their projects and implement them in incredible ways with Mathematica. It’s going to be an intense experience. We’re expecting that during the two weeks of the Summer School, every attendee will be able to use the latest Mathematica technologies to create a final product of some kind---that they and their colleagues, students or customers will be able to use for a long time to come. We’re planning a mix of attendees, with varying profiles---senior technologists, researchers, programmers, educators, students and perhaps others we don’t expect.
Onkar Singh, Project Director, Consulting
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
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