Here is an interesting opinion paper on why Pi (3.1415…..) is wrong. The author claims that what we all know as Pi, should really be 2 x Pi, or 6.28. Although this would clean up a lot of complex equations, the mathematics behind these equations would remain the same, so it is just a matter of semantics really. Just like in programming, when you are deciding what to name a function that swaps the values of two variables. You would usually call it Swap(var A, var B), but it doesn’t really matter what you call it. You could call it ChickenHead(var A, var B), and it would not change the underlying function, although it does complicate the readability of the code. The author’s argument is much the same that the conventional value of Pi unnecessarily complicates many mathematical equations, which would be simplified with a re-factoring of the value. This was the most amusing part of the paper:
Now that is a fantastic sentiment! Overall though, since the earliest estimates of Pi have been around since 1900 BC, I think it is probably better to leave it just the way it is. Plus there are plenty of equations that only use Pi, and not 2 x Pi, so it would be a waste of time to adjust these equations just to make some others more aesthetically pleasing. As with many things, making improvements in one area, can have negative effects on another. To continue the programming analogy, the word REGRESSION comes to mind. After you get through the complaints on using iPaper to post the article, there are some good comments on the content of the paper here.
Imagine you have a roll of scotch tape. When you go to tear off a piece of tape, ever notice that sometimes, it tears off in the shape of a triangle? Packaging tape is the worst! For anyone that has been part of a move recently, taping up all those cardboard boxes, will leave you very frustrated, when you go to tear off a piece of that tape, and the nice thick piece you start to rip off turns into a slender triangle. Then to have to start a new piece by picking away at the tiny point that is left on the roll … annoying!!! In a report published out of MIT at the end of March, mathematical researchers have explain the physics behind what they have called the "Wallpaper Problem".
The team found that those ubiquitous triangular tears arise from interactions between three inherent properties of adhesive materials: elasticity (stiffness), adhesive energy (how strongly the adhesive sticks to a surface) and fracture energy (how tough it is to rip).
The researchers developed a formulation that predicts the angle of the triangle formed, based on those three properties.
They also figured out just how those triangular tears arise. As the strip is pulled, energy builds up in the fold that forms where the tape is peeling from the surface. The tape can release that energy in two ways: by unpeeling from its surface and by becoming narrower, both of which it does.
Pretty neat stuff! Happenings that you take for granted every day, like pulling off a triangle shaped piece of tape, have very explicit mathematical properties. Given two of these properties, using these new formulas, the third property can be established, which proves to be one of many applied applications of these findings.
Not one of the seven millennium problems, but just as exciting none the less, the Schwarz-Christoffel formula has very real implications in applied mathematics.
A formula, now known as the Schwarz-Christoffel formula, was developed by two mathematicians in the mid-19th century to enable them to carry out this kind of mapping. However, for 140 years there has been a deficiency in this formula: it only worked for shapes that did not contain any holes or irregularities.
“This formula is an essential piece of mathematical kit which is used the world over. Now, with my additions to it, it can be used in far more complex scenarios than before. In industry, for example, this mapping tool was previously inadequate if a piece of metal or other material was not uniform all over – for instance, if it contained parts of a different material, or had holes.”
Here’s a link to the full article. If I wasn’t down with the flu, I’d write more … but this is all I can manage for now … lame, I know!!!!!
I came across this paper, entitled Faster Integer Multiplication, which describes a faster, or the currently fastest, method to compute the multiplication of large integers. The prior fastest method reined from 1971 to 2007, so this breakthrough was one of the big ones for 2007. Much of the computation in the paper is way over my head, but the general theories behind this problem are intriguing and easy to understand. Finding new and better ways to compute large numbers is not only a fun theoretical topic to think about (for some), but it is also crucial to very real world scenarios … in computer security for instance.
Here is a very simple mathematic convolution that depicts a different way of carrying out integer multiplication:
Multiplying the numbers 123 and 456, we set it up in the normal way, but do not perform any carrying operations:
Now take the sequence of numbers 4 13 28 27 18, and perform the carrying operation, by keeping the right most 8, and adding the 1 to the next column of 27, and continue on so that you end up with 56088. This final number is the product of the original two numbers …. 123 x 456 … go ahead and check it with calc!
To indulge your number fetish, see the clock strike, 02:03:04 am on 05/06/07 … this Sunday! There are so many of these silly little numerical time/dates, and some are more clever than others. PI Day for instance happens once every year. This one is pretty good, because it only happens once every century! The next time the clock will strike this time will be in 2107. To continue to feed your number hunger, click here.
Math enthusiasts everywhere are being challenged to answer a sample question from a Chinese University’s entrance exam. Now remember, this type of question is given to prospective students, not mathematics majors. It is designed to access the mathematical skill strength of its incoming students. The UK’s Royal Society of Chemistry is offering 500 euros to one person who can answer this question:
In contrast, here is a sample question from a test for First Years at an English University:
I think that speaks volumes about the Chinese mathematics curriculum in comparison to not only England, but the rest of the world. I have to admit, I gave the 2nd problem a quick glance and knew the answers, but the 1st problem I haven’t even tried to tackle. It looks like a fun one, but I think I would need a lot of scrap paper on hand!
Link to full article
Surfing with Wavelets that is, as I had planned, part of the Clay Mathematics Institutes’s public lecture series. Instead, I was stuck in my own personal hell which included a Linux box and trying to successfully get through an unnamed installation.
Why do tiny things on a Linux machine, like editing a file in VI feel like major victories for *us* windows programmers?! Edit a file in windows, even using notepad via the command line, and it is not even a third as much satisfying as putty’ing into a remote Linux machine, VI’ing a file, navigating to the part you want to edit, and then clumsily toggling between the ESC, x, and i, keys!!! Not to mention when you’re done with your edits and you could just close your notepad in windows, versus the ESC, :wq!, sequence in Linux!!! And loading a CD on a windows machine …. c’mon … that’s way too easy!!! Why don’t we remotely mount it to the machine by guessing which hda and device are the right parameters, and then specify what kind of permissions we want it to load up with?! So much more FUN!! I’m sorry, but it does beg the question … do UNIX machines play to the uber-geeks’s ego?? Make everything much more difficult, and in turn feel oh so much more satisfied when you have successfully completed minuscule tasks.
I’m pretty sure my IT guy is going to LOVE this post!!!! 
If anyone did go surfing last week … I would love an update/review …
Uncaught in 4 design reviews, the mathematical miscalculation made by Fermilab had to do with the longitudinal force generated when loading the magnet. A recent press release by Fermilab states:
Review of engineering design documentation reveals that the longitudinal force generated by asymmetric loading was not included in the engineering design or identified as an issue in the four design reviews that were carried out.
The goal at CERN and Fermilab is now to redesign and repair the inner triplet magnets and, if necessary, the DFBX without affecting the LHC start-up schedule. Teams at CERN and Fermilab have identified potential repairs that could be carried out expeditiously without removing undamaged triplet magnets from the tunnel.
It would be great if they could still make their schedule, as a lot of competitors, specifically Fermilab, stands to gain from this "mishap" and could take the lead in the race of particle accelerators. You can find my original write up with some comments here.
A college mathematics professor, Tim Pennings, observed that his dog, Elvis, can instinctively perform difficult calculus based calculations …
When Pennings throws a stick from land into Lake Michigan, Elvis doesn’t make a beeline. The 7-year-old Welsh Corgi runs in angles, instinctively calculating how far to travel on land before hitting the water.
They are the same angles Pennings would plot if figuring out the optimal route mathematically.
"The dog has an instinct for calculus," Pennings said. "The ultimate in esoteric mathematics hits everyday life."
If a Welsh Corgi can do it, just imagine was a giant yellow lab could do?! Actually, now that I give it some thought, I’m pretty sure Kobe’s calculations would end up with: "the shortest distance between two points is a straight line", which is also calculus, but maybe not as advanced as Elivs’.
Link: http://www.mlive.com/news/grpress/index.ssf?/base/news-35/117570407552390.xml&coll=6
Interesting article (thanks, Art!) about how some mis-calculations caused a huge explosion at CERN, the world’s largest particle physics laboratory. Inconsequentially, CERN was also the back drop for Dan Brown’s book, Angels and Demons, which I recommend.
“There was a hell of a bang, the tunnel housing the machine filled with helium and dust and we had to call in the fire brigade to evacuate the place,” he said. “The people working on the test were frightened to death but they were all in a safe place so no-one was hurt.” An investigation by Cern researchers found “fundamental” flaws that caused the explosion, close to the CMS detector, one of the LHC’s most important experiments.
The one piece of information that this article left out, and that I haven’t been able to find anywhere, is what exactly was the mathematical error that caused this mess? "Fundamental flaws" could mean anything. Rumors are swarming of sabotage, and other rival projects are definitely gaining from this major mishap. It would be interesting to find out what the miscalculation was, and it may shed some light on whether or not it was a true mistake. If I were a conspiracy theorist, I would say maybe that’s why the exact mistake hasn’t been posted. Good thing I’m not!
