September 4, 2014 — Jon McLoone, International Business & Strategic Development
I first came across the knight’s tour problem in the early ’80s when a performer on the BBC’s The Paul Daniels Magic Show demonstrated that he could find a route for a knight to visit every square on the chess board, once and only once, from a random start point chosen by the audience. Of course, the act was mostly showmanship, but it was a few years before I realized that he had simply memorized a closed (or reentrant) tour (one that ended back where he started), so whatever the audience chose, he could continue the same sequence from that point.
In college a few years later, I spent some hours trying, and failing, to find any knight’s tour, using pencil and paper in various systematic and haphazard ways. And for no particular reason, this memory came to me while I was driving to work today, along with the realization that the problem can be reduced to finding a Hamiltonian cycle—a closed path that visits every vertex—of the graph of possible knight moves. Something that is easy to do in Mathematica. Here is how.
February 12, 2014 — Vitaliy Kaurov, Technical Communication & Strategy
An original gift can make people feel much warmer, especially in the icy weather affecting so many places this winter—including our headquarters. Valentine’s Day is a good excuse to get a little creative in the art of gift making. And for me, “getting creative” long ago became synonymous with programing in the Wolfram Language. It is that medium that compels me to treat programming as art, where one can improvise, easily pulling magical rabbits out of a hat.
So what shall we make? I think the best gift is a DIY one—especially if it says a lot without even making a sound. Below you see a 3D-printed silver earring in the shape of a sound wave recorded while a person is saying “I love you.”
January 20, 2014 — Jon McLoone, International Business & Strategic Development
Rock-paper-scissors* isn’t obviously interesting to look at mathematically. The Nash-equilibrium strategy is very simple: choose equally and randomly from the three choices, and (in the long run) your opponent will not beat you (nor will you beat your opponent). Nevertheless, it’s still possible for a computer strategy to beat a human player over a long run of games.
My nine-year-old daughter showed me one solution with a Scratch program that she wrote that won every time by looking at your choice before making its decision! But I will walk you through a simple solution that wins without cheating.
January 14, 2014 — Christopher Carlson, Senior User Interface Developer, User Interfaces
We have a programming competition every year at the Wolfram Technology Conference, which in past years was the Mathematica One-Liner Competition (2010, 2011). This year we held the Egg-Bot Challenge, a change of pace to give attendees a chance to exercise their graphics skills.
The idea of the competition was to use Mathematica to generate designs that could be plotted on spheres via Egg-Bots, computer-controlled plotters that draw on eggs, Ping-Pong balls, light bulbs, mini-pumpkins, golf balls… nearly anything spherical or ovoid that is less than four inches in diameter.
October 30, 2013 — Allison Taylor, Public Relations
I was lucky enough in college to be able to double-major in physics and film/media. One of the coolest connections that formed from these completely opposite subjects was the use of Mathematica. What started out as just a computational tool for all the work in my physics classes turned into an experimental playground for the digital animation I was creating in my film classes.
Mathematica is an ideal program to model the true science of motion. And as you’ll come to see, it looks complicated, but is actually quite simple!
Let’s start with understanding some basic human anatomy (or zombie anatomy, since this post is technically about zombies):
October 8, 2013 — Jason Martinez, Research Programmer
Recently the author of xkcd, Randall Munroe, was asked the question of how long it would be necessary for someone to fall in order to jump out of an airplane, fill a large balloon with helium while falling, and land safely. Randall unfortunately ran into some difficulties with completing his calculation, including getting his IP address banned by Wolfram|Alpha. (No worries: we received his request and have already fixed that.)
August 15, 2013 — Michael Trott, Chief Scientist
This blog post is the continuation of my last two posts (1, 2) about formulas for curves. So far, we have discussed how to make plane curves that are sketches of animals, faces, fictional characters, and more. In this post, we will discuss the constructions of some filled curves (laminae).
July 19, 2013 — Michael Trott, Chief Scientist
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.
May 17, 2013 — Michael Trott, Chief Scientist
Here at Wolfram Research and at Wolfram|Alpha we love mathematics and computations. Our favorite topics are algorithms, followed by formulas and equations. For instance, Mathematica can calculate millions of (more precisely, for all practical purposes, infinitely many) integrals, and Wolfram|Alpha knows hundreds of thousands of mathematical formulas (from Euler’s formula and BBP-type formulas for pi to complicated definite integrals containing sin(x)) and plenty of physics formulas (e.g from Poiseuille’s law to the classical mechanics solutions of a point particle in a rectangle to the inverse-distance potential in 4D in hyperspherical coordinates), as well as lesser-known formulas, such as formulas for the shaking frequency of a wet dog, the maximal height of a sandcastle, or the cooking time of a turkey.
Recently we added formulas for a variety of shapes and forms, and the Wolfram|Alpha Blog showed some examples of shapes that were represented through mathematical equations and inequalities. These included fictional character curves:
April 12, 2013 — Vitaliy Kaurov, Technical Communication & Strategy
What does programming have to do with a passion for the arts and history? Well, if you turn education into a game and add a bit of coding, then you can easily end up in the realm of a modern paradigm called, fancily, “gamification.” Though gamification is a very wide concept based on game use in non-game contexts (design, security, marketing, even protein folding, you name it), at heart it is very simple: play, have fun, and get things done. I may have oversimplified things here for the sake of a rhyme, but if you bear with my lengthy prelude, we may just see a simple case of turning passion into software.
My obsession with diagrams and simple line drawings began almost unnoticeably in the winter of 2003 in New York City after attending an exhibition at The Metropolitan Museum of Art: “the first comprehensive survey of Leonardo da Vinci’s drawings ever presented in America.” You may think it’d be a drag—crowds marching very slowly in a single long line coiling through the exhibition hallways. But perception of time transforms when you stare at 500-year-old craft. I think it was then that it started to dawn on me what special value a first sketch has. A first act when an idea, something very subjective, evasive, living solely inside one’s mind, materializes as a solid reality, now perceivable by another human being. Imagine it happened ages ago. Wouldn’t you be curious what was going on at that moment in time, what got frozen in this piece of craft in front of you?