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Binabik
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Legendary Hero
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posted August 03, 2010 12:10 AM |
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As far as magazines here's the one I always liked when I was in my early teens (maybe earlier, can't remember for sure). My dad had several stacks of old Scientific Americans laying around. I never read the articles because I had no idea what they were talking about, but I liked doing the math games in the back. Gardner tended to do a lot of visual type of math puzzles that I really liked.
Clicking those links brings back memories. I used to love some of those. And the Hex game is one I used to play for hours as an adult.
I also forgot all about Humpty Dumpty magazine until I saw it in the Wiki article. It's for much younger children, but I remember it had a lot of cool puzzles too.
Scientific American is still around although the format and target audience has changed. They still have some games too.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted August 03, 2010 03:48 AM |
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Edited by dimis at 04:37, 03 Aug 2010.
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Magazines
I will disappoint you. When they stopped Quantum in Greece, since they relied about 90% on translating the american version, they promoted Scientific American as the alternative. So, they started the translation of Scientific American about the time they stopped publishing Quantum. I subscribed for a year but never renewed my membership there. The problem with Scientific American is that it usually contains high level articles and apart from "good stories" you don't gain any serious skill. Quantum on the other hand held the "whip" right from page 1. If you were willing to learn, you would learn a lot. Just have a look on the sample that I have for Quantum in the previous page. There is no comparison; at all. But of course they have different purpose. Perhaps, Gardner's column was the best thing Scientific American ever had in its 150+ years. But I think that was all about it. By the way, the Mathematical Association of America (MAA) recently published this collection of Martin Gardner's Scientific American columns on one CD.
I am also looking about similar magazines, ever since I made the post, because it brought back many memories to me too. Here is what I've found so far:
- Mathematics Magazine, MAA.
- The College Mathematics Journal, MAA.
- Math Horizons, MAA.
With each release of the above, MAA publishes Focus and The American Mathematical Monthly, both of which I receive in my office, and hence I always forget I have online access to the the first two journals above. Now I created a directory in my Desktop so that I will force myself to check periodically at MAA. The thing is that Focus primarily has news and you can skim it in about 1 minute (it is about 10 pages long and about 90+% is irrelevant to you); the AMM is well written and has good articles, but usually you can hardly follow (be interested in) more than 2-3 articles. Nevertheless, if you are a professional mathematician, this is a good magazine, although, as maths tend to be on high level, it is rather dry (equation after equation, lemma, theorem, proof, and repeat).
Now the American Mathematical Society has other journals. I get the Bulletin and the Notices. I see the Bulletin as something similar to the AMM above, and the Notices as a mathematical-only version of an enhanced Scientific American; "enhanced" because of articles with proofs. As of the rest, closer to my interests seems to be the Mathematics of Computation, but I have never tried it so far; I just saw its existence and in any case I don't believe it can be interesting for high school students anyway.
So, if there is some hope for the target group 13-20 year-old that Kvant addresses, I believe the first two magazines by the MAA above should give the pace (especially the Mathematics Magazine).
Now all these, until yesterday night. I ordered Kvant Selecta: Combinatorics, I after my previous post, and yesterday I was going through an article there for counterfeit coins, and there was a reference to an English journal, called The Mathematical Gazette which has as target group the age 15-20 and in the article about coins it was mentioned that the purpose of Gazette is similar to Kvant. This rings a bell, since the target group and the purpose is precisely what I want.
The thing is, that Kvant and Quantum, were real gems (and none of the other magazines above are close to the quality of these two; I don't know about the Gazette though). They were written in order to address even problems that you can not possibly counter at high-school; yet with high/junior high -school knowledge you could get insight on what is going on on a higher level and actually solve special cases or small problems. And sometimes, when I want to have some insight to a new field, I always go back there and check if they have something. This helps a lot in understanding, and it has happened a few times. But the most important thing, which actually made both Kvant and Quantum more appealing, is that in one magazine you could find articles about Mathematics (about 40%), about Physics (another 40% roughly), and depending on their mood they had an additional 10% on Algorithms and Computer Science, or a little bit of Chemistry, or a little bit of Astronomy, or the biography and the work of some guy. Finally, about 10 % was devoted to various articles; sometimes even literature or art! So Kvant and Quantum played the role of a "passe-partout" for a high school student. None of all the above alternatives does that! Nobody, zero. Because in the end all these subscriptions and memberships cost. Quantum had everything in one package. And to be honest, my feeling is that the american version was probably better than the russian one while it lasted mostly because I think the Quantoon column (collected in Quantoons) was an american addition to the magazine (the other reason for being better, is that they had 20+ years of Kvant issues from which to select the best articles to be translated  ). This is part of the heritage left by the american Quantum, and Quantoons is worth every penny if you are a high school student, or a guy like Corribus who teaches Physics every now and then.
I am telling you Binabik (and it makes me sad); when the circulation of Quantum stopped, we made a significant step backwards; both here and in Greece.
Addition (Euclid)
Of course, in every country the equivalent mathematical society has at least one high-school magazine. Which gives me the opportunity to say something for any greek young guys that might follow the conversation. Here is the webpage with the relevant information for the three magazines by the the Hellenic Mathematical Society (for ages up to 18): small Euclid, Euclid A', and Euclid B'. Subscription costs about 12 euro per year for each series (4 issues), and my guess is that small Euclid is for primary school children, Euclid A' is for junior high, and Euclid B' for high school students. As a note, if one of your parents has a degree in sciences, you can get both Euclid A' and B' for 21 euro/year; relevant info on the same page.
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The empty set
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Binabik
Responsible
Legendary Hero
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posted August 03, 2010 08:12 AM |
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Nah, it's not a disappointment. Scientific American was never meant to be the same kind of magazine as Quantum. It just happened to have some puzzles in the back that I enjoyed. To my knowledge we never had anything like Quantum here. And even if we did I probably wouldn't have read it. I didn't want to study, I just wanted to do fun puzzles. Although depending on what it was I might have dug in and studied it.
Looking back I think that when I got advanced enough in math that I had to start studying, is when I quit enjoying it as much. I guess another way of looking at it was that I wanted something easy to learn, but with complex and/or challenging puzzles.
Maybe that's why I like circuit boards. The basic idea behind it is pretty simple, but finding the solution can sometimes be a total brain meltdown. There is certainly knowledge involved, but the ultimate result of that knowledge is to put additional constraints on the puzzle, making it more difficult.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted August 04, 2010 03:18 AM |
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Edited by dimis at 03:34, 04 Aug 2010.
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted August 04, 2010 09:28 AM |
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Awesome video
Very talented guy/girl..
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Better judged by 12 than carried by 6.
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ihor
Supreme Hero
Accidental Hero
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posted August 04, 2010 10:25 AM |
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Really awesome.
I wonder how much time he spent to create this.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted August 04, 2010 03:22 PM |
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Edited by dimis at 15:23, 04 Aug 2010.
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From the youtube description:
"This is the final piece for my AS art course, a flipbook made entirely out of biro pens. It's something like 2100 pages long, and about 50 jotter books. I'd say I worked on and off it for roughly 3 weeks."
And apparently, the guy/girl is using this to sell clothes and make money. I didn't know that either when I posted the video. But in any case, I love the video!
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted August 04, 2010 04:45 PM |
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Edited by dimis at 16:46, 04 Aug 2010.
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By the way, the Gazette seems very interesting. I went through one of their samples, Irrational Thoughts, by Marty Ross (available online), and I believe this is precisely what 15-16 year olds should get. They are not supposed to follow everything, but they get a glimpse of many "undefined" notions and some associations/applications of them. In the end, this gives motivation to come back to the article in the future.
Just like with all stories, when you read them again, you find something that you didn't realize in the first read. Also, it has a good amount of historical gossiping with references. Irrational thoughts is a perfect example.
Ask me in a year about Gazette.
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted August 04, 2010 07:03 PM |
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Edited by dimis at 08:13, 05 Aug 2010.
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A bit of history on Kvant/Quantum
This is probably my last post on Kvant/Quantum. I just want you Binabik to understand the level of our stupidity on this matter. So, I will just mention a few names and awards that are closely related to the magazine.
Russian Version
(I apologize that I mention only one thing next to each of the following names; but I want to be brief)
The whole idea started from Kapitsa (1978 Nobel in Physics), and the first chief editors were Kikoin (Hero of Socialist Labour) and Kolmogorov (well ... what to mention here? Ok, Stalin prize).
American Version
NY Times article, October 1989 - before the publication starts.
After the publication started, within its first 5 years, it was accompanied with the following awards/distinctions:
- Folio award (1995), announcement in the magazine. The announcement is 1-page, and from the Mission Statement: "Some articles are elegant expositions of sophisticated concepts, and some give an unexpected twist to a well-known idea or phenomenon; others show that there is no such thing as a silly question."
* Judges comment: "The articles are dense with information, but are written in an engaging, somewhat informal style using rhetorical examples, which I suspect teenagers can relate to. Laced with wonderful illustrations and interesting riddles."
- Apex award (1995).
- Distinguished Public Service Medal (NASA, 1995): "The award is granted only to individuals whose distinguished accomplishments contributed substantially to the NASA mission. The contribution must have been so extraordinary that other forms of recognition by NASA would be inadequate. This is the highest honor that NASA confers on a non-Government individual."
* Announcement from the magazine; recipient is the publisher; Bill Aldridge.
* I couldn't find a list of 1995 recipients in NASA's History Division to double-check, but I hardly believe this is a fraud. Volume 4 (1969-1978) of NASA's Historical Data Book has an appendix with the recipients. However, the appropriate volume which contains 1995 (volume 6) does not have such entries. Neither does vol. 5.
Now we have, what we deserve.
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The empty set
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Binabik
Responsible
Legendary Hero
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posted August 27, 2010 06:16 AM |
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Stacking Firewood
OK, so I had a large part of a tree fall the other day. As I was stacking the resulting logs I was thinking about the optimum way to stack logs of different sizes. I didn't think very hard about it and just threw them on the stack as I picked them up. But I thought there should be some neat geometry questions in it.
For simplicity let's say that the logs have diameters of 10, 15, 20, 25 and 30 cm. Also for simplicity we'll work with circles instead of cylinders.
1) My initial question was to minimize the contact area with the ground because I didn't want the logs to rot. I'll say that "contact area" is within 2 cm of the ground due to grass, weeds, moisture etc.
So for a given length in the bottom row, am I better off using large logs or small logs, or possibly some combination? In other words, let's say the bottom row will be (approx) 2m long, so is it better to place 10*20cm logs, or 20*10cm logs, or 10*10cm + 5*20cm, etc?
A variation of the above, but would be very tedious to figure out: With a variable length bottom row, and 10 each of the log sizes, how would you minimize the ground contact area and still place all logs on the stack in a stable way?
2) A 10cm and 20cm log are laying on the ground (flat surface). They are rolled toward each other until they touch. What is the angle of the line through the center points of the circles (relative to the ground)? Is there a general formula to calculate the angle given different log diameters?
3) The 10cm (A) and 20cm (B) logs are on the ground and touching, as above. A 3rd log (C) is placed on the stack where it comes to rest due to gravity, just touching the other logs at one point each (working in 2D here). What is the maximum diameter of C for it to remain in place without rolling off?
4) Starting with the above 3 logs, and using the maximum diameter of C: as the diameter of C decreases linearly, trace the path of the center point of C. What will the shape be?
That's all for now, although I can think of tons of questions about this. BTW, I don't have all the answers myself, but I just thought I'd throw these out there because if I've ever done this type of geometry problems I don't remember it. The first Q is intuitive without crunching numbers, and I think the 4th one is also intuitive, but I'm not 100% confident with that one.
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Binabik
Responsible
Legendary Hero
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posted September 01, 2010 10:10 AM |
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Can you see a full moon?
Can you see a new moon?
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Ecoris
Promising
Supreme Hero
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posted September 01, 2010 10:35 AM |
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Yes to both?
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Binabik
Responsible
Legendary Hero
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posted September 01, 2010 10:44 AM |
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Is it so simple? I'm not so sure. Think about it more. I'm really not entirely sure of the answer, but I think it's no to both.
Off to bed though. I have a bad habit of posting just before bed.
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Ecoris
Promising
Supreme Hero
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posted September 01, 2010 11:01 AM |
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You can see a new moon at a solar eclipse.
At a lunar eclipse, the moon is still visible.
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Corribus
Hero of Order
The Abyss Staring Back at You
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posted September 01, 2010 03:49 PM |
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By the way, your firewood questions were nice ones, Bin. I didn't post any solutions so as to allow others to try.
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Binabik
Responsible
Legendary Hero
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posted September 01, 2010 09:59 PM |
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@Ecoris, it becomes a matter of semantics, but you got the point, it can only happen during an eclipse. Personally I don't call an eclipse actually "seeing" it though. I call a full moon a bright white moon and that's not the case with a lunar eclipse. A solar eclipse would blind you. If I remember right, even using a pin hole you don't see more than an outline. But again, it's a matter of semantics.
@Corribus, go for it. Dimis sent me a pm about it and said he wanted to get to it but was busy with rl stuff atm. He thought I should have posted pictures to make it more clear, but I thought that would make it too obvious.
Also, the log problems reminded me of an old toy I had when I was a kid. Does anyone remember the Spirograph or similar toy? There are some links at the bottom of the article. I like the graphics in this one and this one. Here are some pictures of the toy itself. There are some on Ebay also. I thought about getting one if it's cheap.
There are also several youtube videos, but most of them are software versions, not the kid's toy. The software would allow for more experimentation, but I don't think it would be as good of a learning tool for kids as the hands-on toy.
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Corribus
Hero of Order
The Abyss Staring Back at You
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posted September 02, 2010 01:49 AM |
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Actually some of your log problems are closely related to some classical (and I mean - Greek era classical) problems on circles (e.g., Apollonian Kissing Circles and Japanese Temple Problems). I'll post some solutions in a while.
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Ecoris
Promising
Supreme Hero
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posted September 02, 2010 10:39 AM |
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In space you can see a full moon.
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Binabik
Responsible
Legendary Hero
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posted September 02, 2010 12:25 PM |
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Your head would get in the way and block all the light.
But maybe....
stand to the side and wait for the light to go past you. Then while you're waiting for it to get to the moon and reflect back hurry and jump out there so you can see the full moon.
That reminds me, I missed Perseids again....I forget almost every year.
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mvassilev
Responsible
Undefeatable Hero
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posted September 05, 2010 11:30 PM |
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Quick question:
Suppose f(x) is growing at a constant positive rate, g, that is, suppose f'(x)/f(x) = g for all x, where g>0. What does the graph of ln f(x) look like?
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Eccentric Opinion
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This thread is pages long: 
