There is such a thing as 'too precise' when it comes to numbers. So what's appropriate? Erik Olsson, CC BY-NC-SA

By Jonathan Borwein (Jon), University of Newcastle and David H. Bailey, University of California, Davis

Kelly Abbott/Flickr, CC BY-NC

By Tim Trudgian, Australian National University

Consider a standard pizza box containing a standard circular pizza. How much more would you be willing to pay for a square pizza that filled the box?

The golden ratio is known as the divine proportion because it is found so often in nature. It has fascinated mathematicians since Euclid. A golden ratio is when the ratio of two numbers is the same as the ratio of their sum to the larger of the two quantities.

Credit: Wikipedia

Represented by the Greek letter phi (φ), its value is 1.61803399.

In a famous mathematical thought experiment, the goal is to make randomness deterministic by closed-form equation, so mathematicians tried to determine the path of a 'drunken sailor' staggering around a town. 

If there are street lamps, he will run into them, change his direction and keep moving until he gets out of the city. Logically, the time he spends in the area depends on the number of street lamps but the surprising answer is that the number of streetlamps are not the big factor.

Vaccines are medical technology and like all technology some of the production runs are misfires. Some shots fail due to "leakiness," lack of effectiveness on certain individuals in a population, or shorter duration of potency.

In the 1980s, a press release writer for an environmental group pulled a metric for meat and fossil fuel usage out of the air. It made its way into a book written by an activist and ever since then the concept of 'embedded' emissions has been used by anti-meat proponents.

"It takes a gallon of gas to make a pound of beef" is easy to remember. It is elegant. It is also completely wrong. Regardless, the virtual environmental cost of meat became a craze and it was soon followed by virtual water. The virtual water in the grain in just one part of Egypt is more than all of the water in the Nile so the concept falls apart rather quickly when it comes to the real world but scholars are still broadening the concept out to new areas.

Humans are primarily social creatures - Thoreau may have pretended he wanted to sit among nature by himself and write a book but he was in a house built by someone else, paid for by someone else, with clothes made by someone else, and writing a book that would be published by someone else.

People band together in groups to be stronger - about causes or for actual defense. How to prompt people to become social rather than anti-social is one of the central goals of game theory. 

Economics is a dwindling field. Long called the 'dismal science' it is now considered just another philosophical school of thought; people in the money business who want quantification hire physicists rather than economists.

And the lack of female interest in the field shows it is no longer in vogue. A new analysis finds that women make up 57 percent of undergraduate classes at UK universities but only 27 percent of economics students. The women who like math are doing something else with it. 1.2 percent of females apply to study economics while 3.8 percent of boys do.  

Now that Major League Baseball’s regular season has ended with the wild wildcard win by the Kansas City Royals over the Oakland A’s and with the Pittsburgh Pirates being eliminated by the San Francisco Giants, I've once again begun analyzing the probability of each team advancing through each round of baseball’s postseason.

The Los Angeles Dodgers (71%) and the Washington Nationals (68%) have the greatest chance of advancing to the National League Championship Series going into their first Division Series games. The Kansas City Royals (61%) and Baltimore Orioles (64%) after winning the first game of their Division Series have turned themselves from underdogs into favorites.

Mathematicians have introduced a new element of uncertainty into an equation used to describe the behavior of fluids, which might make it possible to better reflect the inherent uncertainties of the natural world.