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# Date Archive: 2016 March

## New in the Wolfram Language: GreenFunction and Applications in Electricity, ODEs, and PDEs

Picture of Green's Windmill by Kev747 at the English language Wikipedia. In 1828, an English corn miller named George Green published a paper in which he developed mathematical methods for solving problems in electricity and magnetism. Green had received very little formal education, yet his paper introduced several profound concepts that are now taught in courses on advanced calculus, physics, and engineering. My aim in writing this post is to give a brief biography of this great genius and provide an introduction to GreenFunction, which implements one of his pioneering ideas in Version 10.4 of the Wolfram Language.
Announcements & Events

## Ready? Review. Register: The 2016 Wolfram Technology Conference Is on the Way!

Computation & Analysis

## Wolfram Community Highlights: LEGO, SCOTUS, Minecraft, and More!

Wolfram Community members continue to amaze us. Take a look at a few of the fun and clever ideas shared by our members in the first part of 2016. How to LEGO-fy Your Plots and 3D Models, by Sander Huisman This marvel by Sander Huisman, a postdoc from École Normale Supérieure de Lyon, attracted more than 6,000 views in one day and was trending on Reddit, Hacker News, and other social media channels. Huisman's code iteratively covers layers with bricks of increasingly smaller sizes, alternating in the horizontal x and y directions. Read the full post to see how to turn your own plots, 3D scans, and models into brick-shaped masterpieces.
Announcements & Events

## Pi Day Discounts on Mathematica and Wolfram|Alpha

Pi Day is celebrated on March 14 (3.14) every year to properly recognize the constant pi (π=~3.14159)---the ratio of the circumference of a circle to its diameter. At Wolfram, π plays an important part in every one of our products, allowing users to do everything from getting the basic area of a circle to rendering a π symbol filled with the digits of π. On Pi Day last year (aka the Pi Day of the Century), the folks at SXSW got a very special treat from us in the name of π. This year, we decided to bring the celebration to you by offering exclusive discounts on Mathematica. Get 15% off Mathematica Home Edition and 25% or more off Mathematica Student Edition in select territories, including North and South America, Australia, and parts of Asia and Africa. Regardless of where you are, you can still celebrate with us by finding your Pi Day.
Products

## Balancing Rotating Machinery with Wolfram SystemModeler

Explore the contents of this article with a free Wolfram SystemModeler trial. One of the most common causes for vibrations in mechanical systems is imbalance in the rotating parts of a machine. Much effort has therefore gone into developing methods and devices for balancing rotating machines. Balance is a requirement for many types of rotating machinery, such as electric motors, pumps, fans, turbines, generators, centrifugal compressors, and propellers. Many people know about the balance of their car wheels. If these systems are not properly balanced, the vibration will cause not only reduced efficiency and component fatigue but also disturbances for the environment, such as vibration and noise. The most common methods for balancing rotating machinery are the influence coefficient method and the modal balancing method. The car wheel balancing is, for instance, a subpart of the influence coefficient method. Wolfram SystemModeler is used for modeling the rotor, and the Wolfram Language for the evaluation of the results. The workflow shows how powerful it is to combine these two softwares. A disc with mass m is mounted on a shaft with stiffness k. The rotor rotates with the angular velocity W. The disc has an imbalance u. The unit for the imbalance is kg*m.
Computation & Analysis

## Profiling the Eyes: ϕaithful or ROTen? Or Both?

##### An investigation of the golden ratio's appearance in the position of human faces in paintings and photographs.
There is a vast amount of literature on the appearance of the golden ratio in nature, in physiology and psychology, and in human artifacts (see this page on the golden ratio; these articles on the golden ratio in art, in nature, and in the human body; and this paper on the structure of the creative process in science and art). In the past thirty years, there has been increasing skepticism about the prevalence of the golden ratio in these domains. Earlier studies have been revisited or redone. See, for example, Foutakis, Markowsky on Greek temples, Foster et al., Holland, Benjafield, and Svobodova et al. for human physiology. In my last blog, I analyzed the aspect ratios of more than one million old and new paintings. Based on psychological experiments from the second half of the nineteenth century, especially by Fechner in the 1870s, one would expect many paintings to have a height-to-width ratio equal to the golden ratio or its inverse. But the large sets of paintings analyzed did not confirm such a conjecture. While we did not find the expected prevalence of the golden ratio in external measurements of paintings, maybe looking "inside" will show signs of the golden ratio (or its inverse)? In today's blog, we will analyze collections of paintings, photographs, and magazine covers that feature human faces. We will also analyze where human faces appear in a few selected movies.