August 6, 2014 — Devendra Kapadia, Mathematica Algorithm R&D
What is the sum of all the natural numbers? Intuition suggests that the answer is infinity, and, in calculus, the natural numbers provide a simple example of a divergent series. Yet mathematicians and physicists have found it useful to assign fractional, negative, or even zero values to the sums of such series. My aim in writing this post is to clear up some of the mystery that surrounds these seemingly bizarre results for divergent series. More specifically, I will use Sum and other functions in Mathematica to explain the sense in which the following statements are true.
The significance of the labels A, B, C, and D for these examples will soon become clear!
July 30, 2014 — Wolfram Blog Team
Kenzo Nakamura uses Mathematica to create Escher-inspired mathematical art. His trademark piece, Three-Circle Mandala, depicts a large circle covered by three smaller, repeating circles that form a Sierpinksi gasket.
When Nakamura began using Mathematica, he didn’t originally intend to use it for his artistic endeavors. He found the program by chance at a seminar while looking for the right tool to help him write his master’s thesis.
Now, in addition to using Mathematica for technical and operations research, Nakamura uses it to create Mathematica-derived visual illusions. Although his works are static drawings, their infinite properties create the illusion of movement.
Watch Nakamura discuss using Mathematica to create his drawings, and see a few of his creations.
(YouTube in Japanese)
May 22, 2014 — Bernat Espigulé-Pons, Consultant, Technical Communications and Strategy Group
Without doubt, the golden ratio is nowadays considered the most mysterious, magical, and fascinating number that exists:
. As we will see in this post, this number still has many interesting properties that can be investigated, some even dating back to the works of the ancient Greeks Pythagoras and Euclid, the Italian mathematician Leonardo of Pisa, and the Renaissance astronomer Johannes Kepler. Though it might sound strange, I will unveil new geometric objects associated with the golden ratio, which are the objects that illuminated my way when I attempted to map an unknown region of the Mathematical Forest.
The following findings aren’t a mere accident; I’ve been working hard to grasp a glimpse of new knowledge since high school. After seeing Hans Walser‘s drawings of golden fractal trees in 2007, I was convinced that there was still space for exploration and new discoveries. Though I had to wait quite a while, I finally found the right tools: Mathematica, combined with Theo Gray‘s “Tree Bender” Demonstration. After gathering some intuition and a rudimentary knowledge of the Wolfram Language, I encountered my first insights. For example, here is one of the first self-contacting golden trees that I discovered when I created my own version of “Tree Bender” in order to explore ternary trees (trees with three branches per node):
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.”
February 10, 2014 — Crystal Fantry, Manager, Education Content
We are happy to announce the Mathematica Summer Camp 2014! This camp, for advanced high school students entering grades 11 or 12, will be held at Bentley University in Waltham, Massachusetts July 6–18. If you are ready for two weeks of coding fun, apply now on our website. Students who attend the camp have a unique opportunity to work one-on-one with Wolfram mentors in order to build their very own project in Mathematica.
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.
December 30, 2013 — S M Blinder, Wolfram Demonstrations Project
I had intended to write a treatise describing the history of the hydrogen atom over the last 100 years. Unfortunately, my time is running out this year, so I will content myself instead with this much briefer blog post outlining the major events associated with Niels Bohr’s three epochal papers in 1913.
The hydrogen atom has been the most fundamental application at each level in the advancement of quantum theory. It is the only real physical system that can be solved exactly (although some might argue that this is also true for the radiation field, as an assembly of harmonic oscillators).
November 6, 2013 — Wolfram Blog Team
Last month, students in the midterm review session of Harvard’s Math 21a class received a lesson in Mathematica they would not soon forget. Professor Oliver Knill coded a 3D-animated Miley Cyrus swinging on a wrecking ball to the beat of her song (by the same name). Knill used the same principles of mathematics that his class was reviewing for the midterm—and now he just may be the coolest professor ever.
October 24, 2013 — Wolfram Blog Team
By now, most of you students are likely getting into the thick of the academic year, preparing for the first wave of exams and projects and presentations to come your way… But don’t freak out just yet! Here’s a list of Wolfram’s most recent apps and programs that might help make your life a little easier. After all, it never hurts to have a few powerful resources on your side.
September 30, 2013 — Johan Rhodin, Kernel Developer
What is the cost of extending a warranty for a car? I’d be interested to know, since my car broke down just past the 100,000 mile marker on a road trip through America. With Mathematica 9 comes complete functionality for reliability analysis that can help us analyze systems like cars. I thought it might be worthwhile to take Mathematica for a spin and look at how some technical systems can be modeled and analyzed.