We at CatSynth are happy to be hosting the 38th Carnival of Mathematics, a bi-weekly round-up of mathematical posts from around the blogosphere. This is our second time hosting, and it falls on an auspicious day, August 8, 2008 or 8-8-8!
Eight is associated with good fortune and prosperity in Chinese culture, and so a trio of eights is especially fortunate. It is no accident that the Olympics in Beijing opened today.
Mathematically, 8 is of course a power of two, the third power of two in fact. 8 * 8 * 8 is 512. 8 raised to the 8th power raised the 8th power is…well…a very big number:
Coincidentally, “888” is the name of a popular former product by my current employer.
So, with so much coincidence and good fortune surrounding the three eights, one would think this would be a great day for us at CatSynth. And they would be wrong, it is in fact rather bad day, capping a not-so-great week. So does that make us uniquely star-crossed? Probably not, but it does call into question the idea of using numerical patterns to divine good fortune.
And that brings us to our first entry, entitled Don’t Listen to Numbers from epsilonica. People have found significance in the patterns of digits of ? and the square root of 2 and countless other numbers for centuries, but as this post suggests, such patterns are inevitable. And very profound, when you think about the fact that this blog post, or any great work of literature or digitized music file can be represented by a unique number in binary, or English text in base 27.
So numerical patterns should be viewed with caution. So should the well-known statistical tool, the histogram, as described the Parable of the Histogram at ecthathy. The parable shows how the partitioning of data in to histograms can lead to very different interpretations, as a slight offset produces very different results for a group of students.
A numerical reality today is the explosion of online math videos, as report by the Teaching College Math Technology Blob. Videos on mathematical topics can be quite interesting and entertaining, especially for people who read blog posts about math. But they can be a source for media-oriented students to get answers to math problems without fully understanding the solution. And since correct solutions should be identical, it is more difficult to track down such sources than it is for essays.
Some of us learned mathematics not just to pass a class in school, but for the enjoyment, and perhaps for the realization that it is valuable to many aspects of our lives. You can read more about why we learn math at the blog It’s the Thought That Counts. This site has a lot of articles about science, religion and politics, and Barack Obama as well, so worth a detour…
Ok, back to mathematics. Sam Shah offers us a mind-boggling maximization problem, it is deceptively simple, but ends up brining in some rather difficult numbers (which I am sure have some strange and mystical patterns hidden inside of them). He also explains the Richter Scale and Logarithms, a topic close to many of us here in California.
Larry Ferlazzo presents a math word game, in which players have to chose the words that correctly describe the displayed numbers. It is geared towards beginning English Language students. I wonder if they can find the solutions to these problems on YouTube…
One of my favorite disciplines within mathematics is number theory, and our friends at Walking Randomly offer a method to generate Fibonacci numbers from matrix determinants. In particular, they can be generated from the determinants of a tridiagonal matrix with the imaginary number i in the “side bands.” It is always fascinating to see interesting mathematical concepts unified, in this case imaginary numbers, linear algebra and the Fibonacci sequence.
More interesting ideas with matrices and sequences can be found in this discussion of Phylogenetics and Algebraic Geometry at Rigorous Trivialities. Again, this crosses over into the complex numbers, and vector spaces.
The order of operations is a fundamental concept in arithmetic and computation. Apparently, it does not apply to the world of reality television, where producers have about as much mathematical literacy as a $1 calculator. Our friends at 360 analyze a recent mathematical puzzle given to contestants on the popular British TV program Big Brother.
Jon Ingram presents the game of Nim at Lessons Taught; Lessons Learnt. He starts with volunteers at conference to introduce this simple but fascinating game, and then plots the losing positions using Autograph. The result is quite surprising.
More observations on innumeracy in Why Can’t Johnny Add? at Staring at Empty Pages. The problems illustrated are not so much basic arithmetic as basic algebra, and how students can lack these basic skills in both 1983 and 2008.
From basic algebra, we move back to probability statistics, and normal errors for binomial and Poisson distributions. Textbooks say the normal distribution is good when “n is large”, but how large is large enough?
Next, The Endeavor presents an article on connecting probability and number theory. Prime numbers, and some properties of integers like the number of distinct prime divisors, can behave like random variables. This is an area of interest for me right now, not only with prime numbers, but also the other problems such as the Collatz Conjecture.
The above link to the Collatz Conjecture and related problems is from our friend Andrée of meeyauw, who this week presents aFriday Fractal: Pink Dragon Spewing Pink Flame.
That concludes the carnival for now. We will continue to post submissions through the weekend (including any we have missed due to 8-8-8 contrary fortunate), so please let us know if we missed you.