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I am currently researching on Recreational Mathematics - Mathematical Tricks and I have come across this article: Ten Amazing Mathematical Tricks .

This article is of free style and does not follows the pattern/format I have seen in all the other articles/research paper so far.

My question is: Is this a research paper? Is it a paper? If not, what is it? Can such a paper be cited as a reference? I want to know more about these freestyle articles.

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A number of people have correctly told you (I can see the article) that this is a collection of mathematical puzzles, rather than a research paper. So let me tell you a little more about this type of article. Martin Gardner is considered by many to be the biggest popularizer of recreational mathematics in the 20th century (perhaps ever). For 25 years (1956-1981), he wrote a column for Scientific American called Mathematical Games. Many of his columns have been collected into books (such as Martin Gardner's Mathematical Games). Some other well-known examples of similar writing include that of Douglas Hofstadter, Ian Stewart, and Keith Devlin.

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  • I am so glad this question was asked, because I hadn't heard of Ian Stewart and Keith Devlin. I'm looking forward to reading their works.
    – mhwombat
    Jul 22, 2015 at 13:07
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I can't see the actual article, but if it's an MAA article by Martin Gardner, it's probably a list of interesting puzzles. Peter Winkler also writes a column of this kind.

These might not be "research papers" in the sense of proving new theorems on a topic, but they're interesting communications. You can of course cite such a paper as a reference if you use some material from it (and you should!)

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This is the description of the Journal:

Math Horizons is intended primarily for undergraduates interested in mathematics. Thus, while we especially value and desire to publish high-quality exposition of beautiful mathematics, we also wish to publish lively articles about the culture of mathematics. We interpret this quite broadly—we welcome stories of mathematical people, the history of an idea or circle of ideas, applications, fiction, folklore, traditions, institutions, humor, puzzles, games, book reviews, student math club activities, and career opportunities and advice.

So, it don't contain research papers.

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As the others have stated, what you refer to is an article in a magazine, and not a research paper in a journal. If your goal is to show that you came upon an idea while reading this article, then you should cite the article. (Research papers do sometimes include magazine articles in their bibliographies.)

However, research papers usually cite sources where ideas were first published, and it is rare for original ideas to be first published in magazines as articles. So there is a good chance that the ideas you found in the article were published earlier. I recommend that you search for earlier sources and cite them also.

I also recommend that you read a few issues of the three publications I mentioned in this answer to see how they cite work in recreational mathematics. (In my opinion, the most prestigious place to publish work on recreational mathematics is the American Mathematical Monthly.)

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    And just in case you didn't know, Martin Gardner (en.wikipedia.org/wiki/Martin_gardner) is considered a giant in the field of popularizing recreational mathematics.
    – JRN
    Jun 30, 2012 at 22:13
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    And if you really didn't know about Martin Gardner, I envy you. You get to read all his columns for the first time!!
    – JeffE
    Jun 30, 2012 at 22:39
  • @JeffE I really didn't knew, I have learned it only recently.
    – user557
    Jul 1, 2012 at 3:06

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