Ok, so this is not Math-related but I did discover it in the book Fun With Mathematics. The book, by the way, which is out of print and only available used, is definitely worth a couple of bucks plus the shipping cost.
So, what do the following words have in common?
Yes, they each have 11 letters but there's something else interesting about each of these words. Can you see what that is? Are there other words you can add to this list?
Something new is coming to the blogosphere. It's Monday Math Madness!
Stay tuned for details ...
With summer fast arriving (yeah, I know we have to get through winter and spring first) kid's thoughts turn to summer Math camp. "Yeah, right", you say. Well, for those of us who really enjoyed Math in high school, Math camp was a lot of fun.
This post is not intended to be a list of Math camps. I may create one later but you can Google and find a bunch. The list from the American Mathematical Society (AMS) is a good starting place for your research if you're looking for camps for high school kids.
In the late '70s I attended the Ross Program at the Ohio State University. It was the toughest summer I ever had and the most rewarding one at the same time. I was pretty good at Math in school but this camp really worked me. While I can't say that I was mature enough at the time to fully appreciate what I was learning I will say that the camp opened my eyes to how cool Math is at a much deeper level than ever before. The camp left me with a deeper appreciation for the beauty and rigor of mathematical thinking.
While surfing the web I discovered this very cool 10 page Math cheat sheet!
You can download the PDF file here.
Scoring this gem led me to wonder if there were other Math cheat sheets. In particular, I was looking for concise lists of formulas for various subjects. PDF was my first choice for file type.
The best source I found was Paul's Online Math Notes, which has algebra, trig, and calculus cheat sheets.
A while ago I discovered an interesting web site, Berkeley Science Books, that publishes a set of very comprehensive Ebooks called "Calculus Without Tears." Author Will Flannery has a pretty detailed explanation on the home page of his web-site of why he thinks Calculus can be taught in elementary school. His view is that Calculus in college is bogged down with lots of theory; if you change the focus of Calculus to application first and theory later, and if you teach the fundamentals of Calculus that don't require algebra, trigonometry, or geometry (except for the formula for the area of a rectangle) then you can teach Calculus to 4th graders. Flannery sees the motivation for all of mathematics, beyond basic arithmetic, to be physics, and the building basics - derivatives, integrals, and differential equations, which are fundamental to physics and to Calculus - can be taught to those with no mathematical sophistication.
Flannery questions the wisdom of the Math and science curriculum teaching algebra, geometry, and trigonometry before teaching the physics that drives the need for these other branches of mathematics. To be honest, part of me agrees with Flannery and part of me doesn't. I've always enjoyed pure and recreational Math. I absolutely love Math for the sake of doing Math. I love the logic, the creativity, the problem solving, the beauty, the joy, and the elegance of mathematics. But, I get that I'm not typical. Many people find Math to be too abstract and don't see the value of manipulating abstractions. For those people I can see the value of learning Math in a very concrete fashion. I can see the value in approaching Math from the desire to understand how our physical world works, starting with basic formulas for force and distance, and proceeding from there. I believe that someone with an engineering mindset or teachers who want to approach Math from the very concrete will really appreciate Flannery's books. I'm not an educator so I can't speak to what works best in the classroom. I would suspect that a combination of concrete and abstract might work best but I'm not sure in what combination or sequence.
I recently discovered a great web-site, Griddlers.net. The site has lots of puzzles called Griddlers, which I had never before heard of. Griddlers remind me of Sudoku; they're logic puzzles like Sudoku, but with an interesting twist. Once you've solved the puzzle you end up with a nice picture in a grid, like the one shown here. Griddlers have number clues around an image. You use the clues to determine which squares in the grid to fill in. Some Griddlers are even multi-colored. If you get all of the clues right then you get a pretty picture. What I like so much about Griddlers is the positive and very visual reinforcement that comes from solving a puzzle. With Sudoku, which is a great kind of puzzle, you do get the satisfaction of completing the puzzle but there's something neat about seeing a picture appear before your eyes. Griddlers come in all levels of difficulty so even the younger ones can enjoy it.
Griddlers.net has instructions for solving Griddlers, a helpful tutorial, user accounts that let you track which Griddlers you've solved, and a community forum. There are even Griddlers for the little ones, called Kiddlers. And, you can create your own Griddlers to share with the community and even upload image files and have their software convert them to Griddler puzzles. Wow! As of this writing there are 53,867 Griddlers. Most everything on the site is free. What Griddlers.net sells is downloadable books of Griddler puzzles at pretty reasonable prices.
There are a bunch of Griddler sites. The easiest way to find some to check out is to do a google search for the two words "griddler puzzle", without the quotes. Wikipedia has a nice article about Griddlers. The article tells of the many names that used to refer to these puzzles, including Nonograms, Paint By Numbers, Pic-a-Pix, Picross, Pixel Puzzles, and many others. The article also tells of how Griddlers were invented in Japan in 1987 by two people independent of one another.
I'm delighted to discover Griddlers and I'm surprised that I've never heard of them up to now given that they've been around for years.
Last November I wrote about the Trachtenberg system of speed mathematics and showed one of the techniques - multiplying an arbitrarily large number by 12 with great ease. In this article I want to show you why the technique for multiplying by 12 works, share two more of the Trachtenberg multiplication techniques, and give you some direction as to how you can develop your own multiplication techniques.
In that first article about Trachtenberg multiplication I taught you to multiply by 12 by "doubling the digit and adding its neighbor (on the right)." I gave an example of multiplying 346 by 12:
I received this very heartening testimonial the other day. It was a great reminder for me about my real purpose for blogging here. It's especially nice to receive emails like this one when I feel myself getting caught up in subscriber counts, how many people read a particular post, etc.
Do you go around to the blogs you enjoy and express your gratitude in the form of comments or emails? I do and I'm planning to do ever more of it.
With the author's permission, here is the letter, and thank you, Moshe, for such a heart-felt message.
I am Moshe maor from Israel.
Till this moment I thought that I am the only weird person who loves math.. The big difference between us is that I know math quite little... although I am 60 y.o.
All my life math was something I liked, but the internet opened many doors of knowledge for me, including math.
Do not be misled : Algebra, Logariths and second power equations (ax^2 +bx+c=0) and verbal questions is the stuff I know very well. I know it much better than other regular person on the street, but not higher subject in math.
Derivatives: I have a plan to study in near future. I have a feeling that it is very interesting. But I am still young. 60 y.o ...
Although my knowledge in math is very limited , I have a passion to study. This bring me to many math sites. Some of them are beyond my understanding. Some are very nice. I bookmark many of then, for the time when I get retired.
So, I found today you site very intersing, beaitiful and neat. This impression I have got after 10 minutes viewing your site. I am sure that I will visit your site a lot in the near future.
In my neck of the woods in northern New Mexico, the Fractal Foundation lives the mission of inspiring interest in science, Math, and Art through the beauty of fractals. The Foundation puts on fractal-related programs in schools and takes them on the road. The Foundation also sponsors a very popular First Friday Fractals night, on the first Friday of the month, for locals and tourists at the planetarium of the New Mexico Museum of Natural History and Science in Albuquerque.
At the Foundation's website are some nice fractal-related resources, many of them free.
- The Fractal Software page has a great fractal viewer (runs on Windows and Mac) that lets you pick from 23 different fractal patterns and zoom in. This one is great fun.
- On the same page there is also a program called "Electric Sheep" that seems to be like the SETI At Home project, but for fractals. For those of you who don't know, SETI At Home is a collaborative effort among millions of PCs to find extraterrestrial life by using some of the compute power in each cooperating PC to analyze signals from space looking for patterns. The idea is that when your computer is idle, like at night, it can give some computer time to the SETI project. Well, Electric Sheep does something similar for fractals. I've not downloaded it but the idea of collaborative fractal building sounds fascinating.
- And, there's "Fractal Grower" (same page) that lets you create certain kinds of fractal patterns.
- There are a half dozen fractal videos at the Fractal Video page. I downloaded the first one, named Glomey, which is 3 minutes 20 seconds long and found the video plus accompanying music to be absolutely mesmerizing.
- The Fractal Art page has some beautiful fractals.
Check out the site. There's a fractal store, a page on chaos theory, and more.
Wild About Math! has been growing. The blog has many more RSS readers than it had even a month ago, people are leaving more comments, and I'm getting a few purchases through the Amazon search box and occasional clicks on links of books I've reviewed. While the revenue for this blog is quite tiny - barely enough to pay for its web hosting - I am grateful to those of you who do contribute to this blog through your purchases, readership, and participation. But, most importantly, I am grateful to have the opportunity to share my love of Math with everyone.
As I spend more time in the world of interesting Math I'm finding that I am running into lots more fun Math-related stuff than would make for full blog posts. So, I'm going to be using the mailing list, (the sign-up form is near the top of the right sidebar), as a way of sending little "Math bites" to interested people. These will be little puzzles, games, links to cool web-sites, quotes, and other things I run into. And, I may run highly relevant ads on the list. My intent is to send a "Wild About Math! Math bites" email about once a week, again, containing goodies you won't find on the blog.
So, join the list if you enjoy what you've been reading on this blog.
To keep spam off the list I'm the only one who will send to it, and I'm paying Aweber to manage the mailing service. Aweber is the premier mailing list service. They require you to verify your subscription by sending you an email link to verify you got the email address right and aren't being subscribed against your wishes, Aweber doesn't tolerate spam, and Aweber makes it completely hassle free to unsubscribe at any time.