Wolfram Computation Meets Knowledge

Computation & Analysis

Mathematica and NVIDIA in Action: See Your GPU in a Whole Different Light

Wolfram Research is partnering with NVIDIA to integrate GPU programming into Mathematica. CUDA is NVIDIA's performance computing architecture that harnesses modern GPU's potential. The new partnership means that if you have GPU-equipped hardware, you can transform Mathematica's computing, modeling, simulation, or visualization performance, boosting speed by factors easily exceeding 100. Now that's fast! Afraid of the programming involved? Don't be. Mathematica's new CUDA programming capabilities dramatically reduce the complexity of coding required to take advantage of GPU's parallel power. So you can focus on innovating your algorithms rather than spending time on repetitive tasks, such as GUI design.
Education & Academic

Finding Interesting Dynamics in the Asteroid Belt with Mathematica’s AstronomicalData

Almost everyone has heard of the asteroid belt. This is the place between the orbit of Mars and Jupiter that is home to a very large percentage of the known minor planets in the solar system. Movies love to have space battles in asteroid belts to add to dramatic dogfight scenes. Even the Star Wars universe pays homage to asteroids: in The Empire Strikes Back, C3PO makes a popular statement about the possibility of successfully navigating an asteroid field. Popular fiction, especially in Hollywood, loves to twist reality for cinematic effect. Often it shows an asteroid belt as an intricate maze of chaotically tumbling boulders that are moving at high speeds relative to each other, requiring advanced evasion techniques to avoid hitting one of them. They are also often shown to collide with each other at high speed, resulting in large explosions. In reality, at least for our asteroid belt, things are not quite so dramatic. If you were actually in our asteroid belt, the chances that you would see an asteroid are fairly small. Most of them are quite small relative to the Earth and the space between them is relatively large. NASA has sent numerous probes through the belt, and not one has had an accidental encounter with an asteroid, although there have been a couple of intentional encounters. We know very little about the physical characteristics of asteroids compared to planets. Very few have been visited. However, their orbital dynamics are well studied and show some pretty amazing features. Let's take a look at a view of all of the asteroids used in Mathematica's AstronomicalData out to the orbit of Jupiter.
Design & Visualization

Twisted Pictures

I have a lot to study at the moment, as I learn how to use the technology that's in our development pipeline. One of the first features I played with was so much fun I thought I would share it with you. You will be able to efficiently and easily texture map over any 3D image. Texture mapping has all kinds of practical uses for improving visualization, but the first thing that I thought of was setting fire to a plot...
Education & Academic

Tetrahedra Packing

Back in 325 BC, Aristotle talked about which polyhedra can fill space, and noted that regular tetrahedra could fill space. Around 1470 AD, Regiomontanus showed that Aristotle was wrong. He also found the spot where a statue on a pedestal appears the largest, as shown in the Demonstration “The Statue of Regiomontanus”. In 1896, Minkowski tried to solve the problem of how well tetrahedra could pack. He failed. But he did introduce many valuable tools to math, such as “The Minkowski Sum of Two Triangles”. In 1900, Hilbert tried the problem of tetrahedra packing and included it as a part of problem 18 in his list of unsolved problems. Hilbert is also famous for the Hilbert curve and “The Hilbert Hotel”.
Education & Academic

A Call to STEM Teachers: What’s Your Plan for Back to School?

It's back-to-school time in the U.S., and we're starting our trips to meet with educators ranging from the high school to post-graduate level. Many schools will be hearing about Mathematica for the first time, while others have requested specialized training to expand Mathematica usage in their work and in the classroom. Several schools are taking advantage of a program created in response to a recent domestic focus on science, technology, engineering, and mathematics (STEM) education called the STEM Education Initiative.
Best of Blog

25 Best Hangman Words

A simple question from a six-year-old about hangman turned into another analysis obsession that made me play 15 million games of hangman recently. Back in 2007, I wrote a game of hangman for a human guesser on the train journey from Oxford to London. I spent the time on the London Underground thinking about optimal strategies for playing it, and wrote the version for the computer doing the guessing on the return journey. It successfully guessed my test words and I was satisfied, so I submitted both to the Wolfram Demonstrations Project. Now, three years later, my daughter is old enough to play, but the Demonstration annoys her, as it can always guess her words. She asked the obvious question that never occurred to me at the time: "What are the hardest words I can choose, so that I can beat it?"
Products

Nine Cool Points on the Complex Plane

Pick some points at random. What can be said about them? What curves go through them? What polygons and polynomials can be made from them? Deep mathematics lurks behind these questions, but the answers can be explored just by moving points around within some Wolfram Demonstrations. Simply by moving points you can see deep mathematics in action. For example, "Five Points Determine a Conic Section" (Ed Pegg Jr and Paul Abbott) uses a matrix determinant on five points to produce an equation going through all five points.
Computation & Analysis

Is the Weather Biased?

My mother has a theory: "The nicest weather is when you are at work, and then it rains on the weekend." Hearing this from her once again, I think it is time to expose her theory to the facts and prove her wrong. We'll start by setting up some tools to help retrieve and categorize the data in terms of the type of day. In the United Kingdom, the weekend is Saturday and Sunday.