from my daughter’s math text book. no foolin.
Mind-Melter of the Day
It turns out that if you divide 1 by 998,001 you get all three-digit numbers from 000 to 999 in order.
Except for 998.
(via Futility Closet)
Zachary Abel can’t help himself when it comes to making really cool mathematical sculptures out of everyday objects:
I think about math constantly, and I see and look for math in everything around me. Geometry in particular fascinates me, and I delight in discovering hidden patterns even in the most mundane of objects. By transforming often-overlooked household items into elaborate, mathematical sculptures, I hope to share this sense of excitement, curiosity, and beauty that a mathematical outlook has instilled in me. Maybe I’ll even be able to learn and teach some math along the way.
You can see more examples of his creative compulsion here
![matthen:
Chaos Theory is a very important area of mathematics which can explain a lot of what we see in the real world. A pendulum with one mass is relatively easy to explain mathematically, and it behaves nicely. However if you put another mass in there, it behaves chaotically. Technically, this means that if you change the starting positions only slightly, the state of the system a short time later can change drastically. The weather is chaotic- a small error in measuring it today could be the difference between rain and no rain in a weeks days time. Watch these two pendulum systems quickly diverge, though they both start off with nearly the same settings. [more] [code]](http://25.media.tumblr.com/tumblr_loshhy8REd1qfg7o3o1_400.gif)
Chaos Theory is a very important area of mathematics which can explain a lot of what we see in the real world. A pendulum with one mass is relatively easy to explain mathematically, and it behaves nicely. However if you put another mass in there, it behaves chaotically. Technically, this means that if you change the starting positions only slightly, the state of the system a short time later can change drastically. The weather is chaotic- a small error in measuring it today could be the difference between rain and no rain in a weeks days time. Watch these two pendulum systems quickly diverge, though they both start off with nearly the same settings. [more] [code]
Weierstrass functions are famous for being continuous everywhere, but differentiable “nowhere”. Here is an example of one:
The graph zooms in quite a ways, and you can see that the graph does not become smooth, or linear, as a differentiable function does. However, at the last frame, the graph looks rather smooth due to computational limits of the software used, but theoretically one could zoom in forever and it would never become smooth or linear.
Wikipedia and MathWorld both have informative entries on Weierstrass functions.
Source: Weierstrass functions, Dr. Conroy’s Math Department Page, Department of Mathematics, University of Washington
Okay, I just had to come out of the mathematical closet.
There is a beauty in mathematics that is every bit as wondrous and profound as that of music or art. I wish more people could see it.
