Mathematics

The Math-e-Monday Puzzle: Polygons In Rings

The diagram below shows five concentric circles constructed in such a way that the area of each annulus is equal to that of the central circle. Within the first annulus, a square has been constructed such that none of the points on the square lie outside t ...

Article - Richard Mankiewicz - Apr 9 2013 - 9:54am

The Math-e-Monday Puzzle: A Jailer's Revenge

This is a fairly new problem, being traced back to as recently as 2003. However, it also has the kind of counter-intuitive solution that has made it a favourite on mathematical websites and forums. In its various retellings, it sometimes suffers from a lac ...

Article - Richard Mankiewicz - Apr 4 2013 - 12:25pm

The Looming Population Implosion

A model based on global population data spanning the years from 1900 to 2010 has caused a research team to predict the opposite of what Doomsday Prophets of the 1960s and beyond insisted would happen-  the number of people on Earth will stabilize around t ...

Article - News Staff - Apr 4 2013 - 11:20am

Solution to The Jailer's Revenge

The solution to the Jailer’s Revenge question is fairly lengthy, so I think it warrants a separate blog entry. Please refer to the original question as it too is fairly long. Let’s firstly simplify the problem with smaller numbers, then scale it back up to ...

Blog Post - Richard Mankiewicz - Apr 8 2013 - 11:30am

The Math-e-Monday Puzzle: Infinite Packings Within Finite Figures

After the scramble to get out of jail, here are some questions about imprisoned shapes! In my last question, we came across parts of the so-called harmonic series 1/2 + 1/3 + 1/4 + 1/5... 1/n. Now, this series is divergent; it does so very slowly, but as n ...

Blog Post - Richard Mankiewicz - Apr 9 2013 - 12:46am

The Math-e-Monday Puzzle: Squares from a Tetrahedral Die

It isn’t Monday, but I’m puzzled every day of the week. Alice is puzzled too; she’s playing with a new tetrahedral die. Each face has a different positive integer on it, but the numbers are peculiar. Alice quickly notices that if she rolls the die and adds ...

Blog Post - Richard Mankiewicz - May 8 2013 - 6:59am

Modeling A Queue

Two days ago I wrote a quick post to stimulate non-flat-EEG readers to consider an apparently trivial question, which in fact hid many subtleties. The general question I wanted to address was whether an estimate missing an uncertainty was more or less usef ...

Article - Tommaso Dorigo - May 10 2013 - 2:34pm

Hierarchical Social Networks: Can A Math Model Of "Seepage" Clobber Terrorism?

Terror networks are comparable in their structure to hierarchical organization in companies and certain online social networks, say the authors of a paper outlining how a mathematical model to disrupt flow of information in a complex real-world network, l ...

Article - News Staff - May 16 2013 - 5:30pm

Music And Mathematics Of Fractal-Like Sloth Canon Number Sequences

The Danish composer  Per Nørgård  uses an endless self similar (fractal like) strict sloth canon structure in some of his compositions such as his Symphony number 2. He first discovered his sequence in 1959. ...

Article - Robert Walker - Jan 19 2014 - 11:24am

The mathematics of sloth canon number sequences and Per Nørgård's infinity series

This describes the maths behind the sloth canon number sequences described in my Self Similar Sloth Canon Number Sequences article It simplifies the proofs here to use a 0 based notation. So we define an integer sequence f(n) as a map from the non negativ ...

Blog Post - Robert Walker - Jan 19 2014 - 11:24am