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Using Formulas… for Everything—From a Complex Analysis Class to Political Cartoons to Music Album Covers

In my last blog post, I discussed how to construct closed-form trigonometric formulas for sketches of people’s faces. Using similar techniques, Wolfram|Alpha has recently added a collection of hundreds of such closed-form curves for faces, shapes, animals, logos and signatures. In today’s post, I want to show some of the entertaining things one can do with these parametrized curves. Although these are just simple curves, a large variety of fun images (and animations) can be constructed from them. These can then be used, for example, in political cartoons, talk shows, posters, music album covers or just to spice up an advanced calculus or first-year theoretical mechanics class. I will first discuss the fun applications, and then the more mathematical ones.
Michael Trott, Chief Scientist, Wolfram|Alpha Scientific Content
Computation & Analysis

Random and Optimal Mathematica Walks on IMDb’s Top Films

Or: How I Learned to Watch the Best Movies in the Best Way I remember when I lived across the street from an art movie theater called Le Club, looking at the movie posters on my way back home was often enough to get me in the ticket line. The director or main actors would ring a bell, or a close friend had recommended the title. Sometimes the poster alone would be appealing enough to lure me in. Even today there are still occasions when I make decisions from limited visual information, like when flipping through movie kiosks, TV guides, or a stack of DVDs written in languages I can't read. So how can Mathematica help? We'll take a look at the top 250 movies rated on IMDb. Based on their posters and genres, how can one create a program that suggests which movies to see? What is the best way to see the most popular movies in sequence?
Matthias Odisio, Software Developer, Algorithms R&D
Best of Blog

Using Mathematica to Simulate and Visualize Fluid Flow in a Box

The motion of fluid flow has captured the interest of philosophers and scientists for a long time. Leonardo da Vinci made several sketches of the motion of fluid and made a number of observations about how water and air behave. He often observed that water had a swirling motion, sometimes big and sometimes small, as shown in the sketch below. We would now call such swirling motions vortices, and we have a systematic way of understanding the behavior of fluids through the Navier–Stokes equations. Let's first start with understanding these equations.
Paritosh Mokhasi, Kernel Developer, Algorithms R&D
Best of Blog

Is There Any Point to the 12 Times Table?

My government (I'm in the UK) recently said that children here should learn up to their 12 times table by the age of 9. Now, I always believed that the reason why I learned my 12 times table was because of the money system that the UK used to have---12 pennies in a shilling. Since that madness ended with decimalization the year after I was born, by the late 1970s when I had to learn my 12 times table, it already seemed to be an anachronistic waste of time.
Jon McLoone, Director, Technical Communication & Strategy
Announcements & Events

Celebrating Mathematica’s First Quarter Century

Today it’s exactly a quarter of a century since we launched Mathematica 1.0 on June 23, 1988. Much has come and gone in the world of computing since that time. But I’m pleased to say that through all of it Mathematica has just kept getting stronger and stronger.

Stephen Wolfram
Products

Energy Resource Dynamics with the New System Dynamics Library for SystemModeler

Explore the contents of this article with a free Wolfram SystemModeler trial. Wolfram SystemModeler ships with model libraries for a large selection of domains such as electronics, mechanics, and biochemistry. Now I am pleased to present a new library in the family, the SystemDynamics library by François E. Cellier and Stefan Fabricius. System dynamics, a methodology developed by Jay Forrester in the '60s and '70s, is well suited for understanding the dynamics of large-scale systems with diverse components. It has been famously applied by the Club of Rome to investigate the limits of human growth; other applications include production management, life sciences, and economics (some showcases of the methodology can be found here).
Mikael Forsgren, Senior Applications Engineer, SystemModeler
Announcements & Events

There Was a Time before Mathematica…

In a few weeks it’ll be 25 years ago: June 23, 1988—the day Mathematica was launched. Late the night before we were still duplicating floppy disks and stuffing product boxes. But at noon on June 23 there I was at a conference center in Santa Clara starting up Mathematica in public for the first time:

Stephen Wolfram
Education & Academic

A “Trivial” Probability Problem

I am a junkie for a good math problem. Over the weekend, I encountered such a good problem on a favorite subject of mine--probability. It's the last problem from the article "A Mathematical Trivium" by V. I. Arnol'd, Russian Mathematical Surveys 46(1), 1991, 271–278. It's short enough to reproduce in its entirety: "Find the mathematical expectation of the area of the projection of a cube with edge of length 1 onto a plane with an isotropically distributed random direction of projection." In other words, what is the average area of a cube's shadow over all possible orientations? This blog post explores the use of Mathematica to understand and ultimately solve the problem. It recreates how I approached the problem.
Oleksandr Pavlyk, Senior Kernel Developer, Algorithms R&D
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