Math/Chaos Theory
Posted by
Isaac M. McPhee
Isaac M. McPhee
There have been several men and women throughout history who have shown, in one way or another, strong mathematical abilities, though they were famous for other reasons.
Yesterday I was working on an article on the life of James Garfield, 20th President of the United States, and was absolutely blown away by the stories of the man's intelligence.
It was said that he was so capable in classical languages that he could write simultaneously in Greek with one hand in Latin with the other.
I was even more surprised that, while he was a Congressman from the state of Ohio, Garfield found the time to develop a very intuitive proof of the Pythagorean theorem (a decent explanation of this can be found on this page, which explains several different proofs).
There have actually been several American politicians who have been drawn to the mathematical arts (as well as many other historical figures who, while not known primarily for their skills in this area, dabbled frequently in mathematical inquiry).
Thomas Jefferson is another well-known math-loving President. Some great examples of Jeffersonian mathematics can be found on this page.
There are many such examples of this, and I find it encouraging that many great men and women throughout history never lost their fascination with mathematics - a topic of learning that is absolutely limitless in its potential application.
The conclusion: Perhaps it doesn't take a mathematician to have some valid insight into mathematics. Perhaps it just takes a person who is willing to look at the subject from a slightly different perspective. If you take a look at the work of Albert Einstein, for instance, you will see that this is one of the secrets to his success in relativity - he was able to see the physical laws in a way that was fundamentally different from others.
I hope this is encouraging to all of those who (like me) love math, but can not be considered mathematicians.
It was said that he was so capable in classical languages that he could write simultaneously in Greek with one hand in Latin with the other.
I was even more surprised that, while he was a Congressman from the state of Ohio, Garfield found the time to develop a very intuitive proof of the Pythagorean theorem (a decent explanation of this can be found on this page, which explains several different proofs).
There have actually been several American politicians who have been drawn to the mathematical arts (as well as many other historical figures who, while not known primarily for their skills in this area, dabbled frequently in mathematical inquiry).
Thomas Jefferson is another well-known math-loving President. Some great examples of Jeffersonian mathematics can be found on this page.
There are many such examples of this, and I find it encouraging that many great men and women throughout history never lost their fascination with mathematics - a topic of learning that is absolutely limitless in its potential application.
The conclusion: Perhaps it doesn't take a mathematician to have some valid insight into mathematics. Perhaps it just takes a person who is willing to look at the subject from a slightly different perspective. If you take a look at the work of Albert Einstein, for instance, you will see that this is one of the secrets to his success in relativity - he was able to see the physical laws in a way that was fundamentally different from others.
I hope this is encouraging to all of those who (like me) love math, but can not be considered mathematicians.
Posted by
Isaac M. McPhee
Isaac M. McPhee
There is a fantastic wesite out there that offers an answer to the question I'm sure you've asked yourself at one point or another: What's special about that number?
Think of a numer between one and... oh, I don't know... let's say ten thousand. Think hard. It can be any number at all.
Got it?
Okay, good. Now go and pay a visit to one of the most remarkable number-based websites I have ever had the pleasure of witnessing: What's Special About This Number?
Was your number 11? This site will pleasantly inform you that 11 is specia because it is the largest known multiplicative persisance. What is a multiplicative persistance? Just click on the handy link and you will find out, via the "Wikipedia of math," Wolfram's Mathworld.
Upon stumbling upon this site, I felt that I had to share it's existence with the world, as I was absoluely humbled by the fact that anyone would have a combination of both the necessary time and the necessary knowledge to come up with something remotely interesting to say about every single number under (but not including) ten thousand.
So, if you haven't done so already, pick a number and go visit this site. If you're anything like me, it will provide you with great enjoyment.
Got it?
Okay, good. Now go and pay a visit to one of the most remarkable number-based websites I have ever had the pleasure of witnessing: What's Special About This Number?
Was your number 11? This site will pleasantly inform you that 11 is specia because it is the largest known multiplicative persisance. What is a multiplicative persistance? Just click on the handy link and you will find out, via the "Wikipedia of math," Wolfram's Mathworld.
Upon stumbling upon this site, I felt that I had to share it's existence with the world, as I was absoluely humbled by the fact that anyone would have a combination of both the necessary time and the necessary knowledge to come up with something remotely interesting to say about every single number under (but not including) ten thousand.
So, if you haven't done so already, pick a number and go visit this site. If you're anything like me, it will provide you with great enjoyment.
Posted by
Isaac M. McPhee
Isaac M. McPhee
A highly entertaining (if slightly dated) video online demonstrates one of the very interesting challenge that geometers have developed for themselves.
I was browsing the Scientific American website this evening when I came across a link to a video on youtube - a computer generated piece from 1994 - which claimed to do the impossible: To turn a sphere inside out without tearing or creasing it.
The video can be found here.
Be warned, unlike many other videos online, this one is somewhat lengthy (just over 20 minutes), but it remains interesting throughout. Apart from simply showing the transformation and leaving it at that, it takes great pains to explain just how it is that such a conclusion can come to, beginning with an explanation of turning a simple rubber band inside out, and following by showing each section individually as it solves the problem one step at a time.
Is it just me or does this problem feel eerily similar to one of those "coffee table" brain teasers with the rings that you have to pull apart or the pile of large nails that have to be balanced on just a single nail? It's a good thing that this problem cannot truly be performed in any "real" sense (apart from on a computer or on paper as mathematics), because I can imagine that it would drive me absolutely crazy if I actually attempted it.
In truth, this is one of those problems that may or may not have any direct relevence as far as applied math goes (though I could very well be wrong in this - having not done any research as of yet, it very well might have found some pragmatic value somewhere), but at the very least lends itself to helping one to appreciate some of the subtle nuances of mathematics.
The video can be found here.
Be warned, unlike many other videos online, this one is somewhat lengthy (just over 20 minutes), but it remains interesting throughout. Apart from simply showing the transformation and leaving it at that, it takes great pains to explain just how it is that such a conclusion can come to, beginning with an explanation of turning a simple rubber band inside out, and following by showing each section individually as it solves the problem one step at a time.
Is it just me or does this problem feel eerily similar to one of those "coffee table" brain teasers with the rings that you have to pull apart or the pile of large nails that have to be balanced on just a single nail? It's a good thing that this problem cannot truly be performed in any "real" sense (apart from on a computer or on paper as mathematics), because I can imagine that it would drive me absolutely crazy if I actually attempted it.
In truth, this is one of those problems that may or may not have any direct relevence as far as applied math goes (though I could very well be wrong in this - having not done any research as of yet, it very well might have found some pragmatic value somewhere), but at the very least lends itself to helping one to appreciate some of the subtle nuances of mathematics.