Giorgia Fortuna

2 Pi or Not 2 Pi?

June 28, 2015 — Giorgia Fortuna, Consultant, Advanced Research Group

Three months ago the world (or at least the geek world) celebrated Pi Day of the Century (3/14/15…). Today (6/28) is another math day: 2π-day, or Tau Day (2π = 6.28319…).

Some say that Tau Day is really the day to celebrate, and that τ(=2π) should be the most prominent constant, not π. It all started in 2001 with the famous opening line of a watershed essay by Bob Palais, a mathematician at the University of Utah:

“I know it will be called blasphemy by some, but I believe that π is wrong.”

Which has given rise in some circles to the celebration of Tau Day—or, as many people say, the one day on which you are allowed to eat two pies.

But is it true that τ is the better constant? In today’s world, it’s quite easy to test, and the Wolfram Language makes this task much simpler. (Indeed, Michael Trott’s recent blog post on dates in pi—itself inspired by Stephen Wolfram’s Pi Day of the Century post—made much use of the Wolfram Language.) I started by looking at 320,000 preprints from arXiv.org to see in practice how many formulas involve 2π rather than π alone, or other multiples of π.

Here is a WordCloud of some formulas containing 2π:

WordCloud

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Posted in: Mathematics

Richard Asher

EWTC 2015: Celebrating Wolfram in Europe

June 26, 2015 — Richard Asher, Public Relations

Thirty talks, one Wolfram Language code tutorial, one image processing workshop, and 130 delegates—plus a rogue appearance from a strategically placed pineapple—all added up to another successful and entertaining European Wolfram Technology Conference in Germany earlier this month.

European Technology Conference with Image Identify

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Posted in: Wolfram News

Michael Trott

Dates Everywhere in Pi(e)! Some Statistical and Numerological Musings about the Occurrences of Dates in the Digits of Pi

June 23, 2015 — Michael Trott, Chief Scientist

In a recent blog post, Stephen Wolfram discussed the unique position of this year’s Pi Day of the Century and gave various examples of the occurrences of dates in the (decimal) digits of pi. In this post, I’ll look at the statistics of the distribution of all possible dates/birthdays from the last 100 years within the (first ten million decimal) digits of pi. We will find that 99.998% of all digits occur in a date, and that one finds millions of dates within the first ten million digits of pi.

Here I will concentrate on dates than can be described with a maximum of six digits. This means I’ll be able to uniquely encode all dates between Saturday, March 14, 2015, and Sunday, March 15, 1915—a time range of 36,525 days.

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Posted in: Mathematics

Bernat Espigulé-Pons

Embrace the Maker Movement with the Raspberry Pi 2

June 18, 2015 — Bernat Espigulé-Pons

“All of us are makers. We’re born makers. We have this ability to make things, to grasp things with our hands. We use words like ‘grasp’ metaphorically to also think about understanding things. We don’t just live, but we make. We create things.”
—Dale Dougherty

I joined the maker movement last year, first by making simple things like a home alarm system, then by becoming a mentor in local hackathons and founding a Wolfram Meetup group in Barcelona. There is likely an open community of makers that you can join close to where you live; if not, the virtual community is open to everyone. So what are you waiting for? With the Raspberry Pi 2 combined with the Wolfram Language, you really have an amazing tool set you can use to make, tinker, and explore.

Raspberry Pi 2 and Wolfram Technologies

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Posted in: Raspberry Pi

Anneli Mossberg

Presenting the SmartCooling Library for SystemModeler

June 9, 2015 — Anneli Mossberg

The SystemModeler Library Store, launched with the release of Wolfram SystemModeler 4, is continually growing with free and purchasable libraries developed by both Wolfram and third parties. One of our commercial newcomers is SmartCooling, a Modelica library developed by the Austrian Institute of Technology (AIT) that is used for modeling and simulating cooling circuits. When I was asked to present this library on our blog, my first thought was, “Who better to demonstrate the ideas of SmartCooling than the people who actually developed it?” So I asked Thomas Bäuml, one of the creators of SmartCooling, to help answer some of my questions regarding the principles behind the library and its applications.

SystemModeler and SmartCooling array

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Posted in: SystemModeler

Jenna Giuffrida

Throwing the Hackathon Gauntlet with Some Friendly Team Coding

June 2, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group

It’s no secret that Wolfram loves hackathons, or that our technology is ideally suited to the fast-paced, high-pressure environment of these events. We’ve supported and/or participated in HackIllinois, MHacks, LAHacks, and many other hackathons. Given how much fun those have been (and just because we can), we decided to host a hackathon for Wolfram staff, pitting our talented and driven developers against one another to see what kind of out-of-the-box projects they could create with our technologies. In truth, the spirit of camaraderie and collaboration that is central to Wolfram could not be set aside, and the final projects were the result of shared ideas and teamwork.

hackathons-logo

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Posted in: Education

Wolfram Blog Team

John F. Nash, Jr. , In Memoriam

May 29, 2015 — Wolfram Blog Team

This past week, on May 23, 2015, the much loved and respected John F. Nash Jr., along with his wife, Alicia Nash, passed away in a tragic car accident while returning home from his receipt of the 2015 Abel Prize for his work in partial differential equations. The Nobel winner and his wife were the subject of the 2001 Academy Award winning film A Beautiful Mind. Nash’s most famous contribution to mathematics and economics was in the field of game theory, which has enabled others to build on that work and was the focus of the film.

Nash’s long career as a mathematician was marked by both brilliant achievements and terrible struggles with mental illness. Despite his battle with schizophrenia, Nash inspired generations of mathematicians and garnered a stunning array of awards, including the 1994 Nobel Prize in economic sciences, the American Mathematical Society’s 1999 Leroy P. Steele Prize for Seminal Contribution to Research, and the 1978 John von Neumann Theory Prize. We were personally honored in 2003 when Nash presented his work with Mathematica at the International Mathematica Symposium in London.

Nash presenting on Mathematica

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Posted in: Mathematics

José Martín-García

New in the Wolfram Language: AnglePath

May 21, 2015 — José Martín-García, Research Staff Member

A brilliant aspect of the Wolfram Language is that not only you can do virtually anything with it, you can also do whatever you want in many different ways. You can choose the method you prefer, or even better, try several methods to understand your problem from different perspectives.

For example, when drawing a graphic, we usually specify the coordinates of its points or elements. But sometimes it’s simpler to express the graphic as a collection of relative displacements: move a distance r in a direction forming an angle θ with respect to the direction of the segment constructed in the previous step. This is known as turtle graphics in computer graphics, and is basically what the new function AnglePath does. If all steps have the same length, use AnglePath[{θ1,θ2,...}] to specify the angles. If each step has a different length, use AnglePath[{{r1,θ1},{r2,θ2}, ...}] to give the pairs {length, angle}. That’s it. Let’s see some results.

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Ed Pegg Jr

Biggest Little Polyhedron—New Solutions in Combinatorial Geometry

May 20, 2015 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project

In many areas of mathematics, 1 is the answer. Squaring a number above or below 1 results in a new number that is larger or smaller. Sometimes, determining whether something is “big” is based on whether a largest dimension is greater than 1. For instance, with sides of length 13,800 km, Saturn’s hexagon would be considered big. A “little polygon” is defined as a polygon where 1 is the maximum distance between vertices. In 1975, Ron Graham found the biggest little hexagon, which has more area than the regular hexagon, as shown below. The red diagonals have length 1. All other diagonals (not drawn) are smaller than 1.

Regular hexagon, biggest little hexagon, biggest little octagon showing lengths of 1

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Posted in: Mathematics

Jenna Giuffrida

Registration for the 2015 Wolfram Technology Conference Now Open!

May 18, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group

The 2015 Wolfram Technology Conference is officially on the horizon, and we are getting excited to show you what we’ve been doing with the Wolfram Language and our growing technology stack. While assembling your calendar for the rest of the year, be sure to save the date for our conference from October 20–22, 2015. Registration is now open, so be sure to secure your spot and submit any talk proposals you may have.

If you’re looking for inspiration or just want a taste of what’s to come, videos from last year’s conference are available on our website. We saw an impressive array of presentations from both guests and our very own developers; below is a sampling of some of the most engaging innovations and projects that were shown.

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Posted in: Wolfram News