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How Do You Do That in Mathematica?

Have you ever wanted a set of straightforward, step-by-step instructions for solving a problem or accomplishing a specific task with Mathematica? Have you ever thought that a Mathematica "quick-reference guide" would be useful? If so, take a look at the "How To" Topics in Version 7. "How tos" are a new type of documentation in Mathematica 7 that provide just the information you need without a lot of detailed background information. This task-oriented approach makes these "How tos" ideal for those getting started with Mathematica. Some students, educators, researchers, and others that would benefit from using Mathematica feel that it would take too long to learn, or is just too complex to use. While this sentiment might seem reasonable given the computational power and breadth of features available in Mathematica, it couldn't be further from the truth.
Announcements & Events

7 years of NKS—and its first killer app

May 14, 2009 marks the 7th anniversary of the publication of A New Kind of Science, and it has been my tradition on these anniversaries to write a short report on the progress of NKS. It has been fascinating over the past few years to watch the progressive absorption of NKS methods and the NKS […]

Computation & Analysis

Planning a Trip? Ask Mathematica for the Itinerary.

With all the new aspects of Mathematica in Versions 6 and 7, I've enjoyed visiting universities to talk about how to use Mathematica in even more courses and research projects. Universities enjoy this, too! I am not, however, very good at thinking about the locations of universities or schools in terms of geography. Planning a trip was a seemingly endless task of cross-referencing maps and lists and notes and more lists---I'm sure you see a pattern forming here. The solution, as is often the case with me, was to use Mathematica. After finding a list of 7,000+ universities and colleges in the United States, I wrote a Mathematica program to create a list of all such schools near a particular city, complete with rough mileage and a map to use for my work.
Announcements & Events

The Spoons and the Summer School

During my stay in Champaign, Illinois at Wolfram Research headquarters last summer, I attended the 2008 Advanced Mathematica Summer School. The Summer School gives people from all over the world a chance to present their challenging problems in varied math and science fields and work with others to find solutions using Mathematica. These research topics cover a very wide range of application areas. My personal interest is in numerics, and I had the chance to work on several related projects. While at the Summer School, one of the projects I was involved in was to analytically derive a mechanism to compute the stress distribution in a circular plate with concentrated radial loadings.
Computation & Analysis

Twittering with Mathematica

The popularity of Twitter has really exploded in the past few months. The service poses a simple question: "What are you doing?" Users respond in 140 characters or less. The 140-character limit comes from the 160-character limit of SMS messages, minus a few characters for things like the user's screen name. Twitter could probably best be described as "micro-blogging." It's kind of a cross between blogging and instant messaging. People use Twitter for all kinds of reasons, everything from staying in touch with friends to receiving announcements and support from companies with a presence on Twitter. Here are a few examples:
Education & Academic

Is Mathematica for K–12 Education? You Bet!

Mathematica has long been used by university-level faculty and researchers for work in math, physics, engineering, and many other fields. Good at everything from creating class documents and lab assignments to analyzing and visualizing data collected during experiments, Mathematica has become the software of choice for millions of academic researchers, faculty, and students because it is an all-in-one system that combines powerful computing and visualization capabilities with sophisticated documentation and presentation tools. But in my years of working with universities as Wolfram Research's Academic Program Manager, I've come to realize that many students who will become future high school teachers aren't using Mathematica in their math and science education classes. Why is that? Some have told me that they heard somewhere along the line that Mathematica was too difficult to learn and use. Others had assumed that it was too powerful for their needs, or not completely applicable to the subjects they would be teaching. But those that do take a closer look at Mathematica are usually amazed by what they see.
Design & Visualization

Droste Effect with Mathematica

The "Droste effect" is when images recursively include themselves. The name comes from Droste brand cocoa powder, which was sold in 1904 in a box that showed a nurse carrying the same box which, in turn, showed the nurse carrying the box, and so on. The simplest form is to use a scale and transform on an image to place an exact copy within it, and then repeat. Take a look at this Demonstration using the original Droste box artwork. But much more interesting results can be achieved when you get complex analysis involved. M.C. Escher was the first to popularize applying conformal mapping to images, but with computers we can easily apply the same ideas to photographs, to get results like this:
Design & Visualization

Hybrid Logos and a Fortunate Mistake

The idea struck me as I was toweling off after a swim: what would happen if I crossed the Mercedes-Benz and Grignani logos from my February 2009 blog post, Exploring Logo Designs with Mathematica? Hybrid vigor is a well-known phenomenon responsible for increased yields in corn, and metaphorically, for the economic and cultural flourishing of civilizations that engage in foreign trade. Would the progeny of Benz and Grignani show similar effects?
Education & Academic

Mapping GPS Data

I'm a GPS addict. I have a handheld GPS, a computer GPS, a GPS phone, two GPS watches, two GPS cameras, and maybe some others. Wherever I go, chances are pretty good I have at least one GPS with me. Anytime I run/bike/hike/walk/ski I keep a record of where I went using GPS. Now that I have all this data I want to make use of it in a meaningful way. Mathematica is a fantastic tool to analyze all my geographic data. Here's an example from a recent trail run I did at a nearby park. The data is stored in a GPX (GPS exchange format) file, which is a specific type of XML. We can bring the data into Mathematica using Import.