Federico Poloni's personal web page

Home

Here I have published a few unsorted documents about "olympiad-like" maths. All of these are in Italian. E-mails which point out errors and typoes and/or contain useful comments will be appreciated: my current addresses are fphthirtyseven@ngi.it or f.polonithirtyseven@sns.it. Please remove the number 37 to get the real addresses, I prefer not to publish them on the internet as they are to avoid spam. Anyway, I hope at least one of them is still active when you read this :) .

News:

09/10/2005: added ntbt.pdf
14/07/2004: added cp-pp.p*
13/07/2004: new version of arnesi.p*, with two minor corrections
26/06/2004: added arnesi.p*
21/03/2004: new versions of bt and olisyl
24/02/2004: added napo.ps & napo.pdf files, (a proof of Napoleon's theorem)

Please note that there are a few restrictions upon the usage of the following documents:

You may download these papers, print them, read them, use them privately and store them (unmodified) in any media or format.

Any other use (e.g. republicating them, printed or over the Internet, modifying or selling them, using them as teaching material in a course) is forbidden unless explicitly authorised by the author (i.e. ME!). Please write me a mail and ask my permission; actually, I am likely to say yes: I am adopting this restriction only because I want to keep track of how my work is used.

You are *NOT* free to redistribute these papers on your site, nor to put "deep links" to them directly in your web pages. PLEASE LINK ONLY TO THIS PAGE and not directly to the .ps/.pdf files.

There is no kind of copyright/licence information inside the documents themselves, and there is no restriction to their download. I know they would be useless, if you really want to break the rules I have set. You are kindly requested to follow them, and that should be enough, if you are fair.

If you find these documents published somewhere else on the internet and you think they may be stolen without my consent, please let me know.

For any kind of request or clarification, my mail address is written on the top of the page. If in doubt, ask.

ps	pdf	An incomplete and unofficial "syllabus", i.e. a programme which lists all the knowledge and theory you will need to know at the Italian Math Olympiads
ps	pdf	INCOMPLETE. A short essay on "pratical" problem-solving, titled "Barbatrucchi per il problem-solving". If you find it interesting, write me: if I get many enthusiastic and cheerful e-mails about it, I could even find the time/strength/will to finish it :)
	pdf	INCOMPLETE Some quick pratical notes and tricks in Number Theory (pre-IMO level). I have tried to write it in the same spirit as the previous "barbatrucchi". Please read the introduction for more information.
ps	pdf	My own (commented) solutions to problems 1,2,4 and 5 of IMO 2003 (I was not able to solve the others :) ) Hope you will like my style. :)
ps	pdf	"Arnesi per risolvere le equazioni funzionali" : a 20-pages paper on functional equations. It is the most complete work I have written up to now, it covers the subject quite fully.
ps	pdf	A short essay on Newton's and MacLaurin's inequalities. Short introduction and (analytic) proof. It uses some "quinta liceo" analysis.
ps	pdf	This is my high-school "tesina", titled "Una dimostrazione elementare dell'ellitticità delle orbite". It contains an original proof that orbits (in the classical two-body gravitational problem) are conics. Hope you'll find it interesting. It has never been reviewed since I wrote it (at the age of 18/19), so there could be lots of errors. Moreover, I think the introduction and the whole textual part would need a complete rewriting. Anyway, I think the proof itself works. Someone told me I could try to have it published on a "didactic-of-physics" journal, but I never cared to do it.
ps	pdf	A proof of Napoleon's theorem (given a triangle, erect equilateral triangles on its sides: then their centroids form another equilateral triangle) using complex numbers. It includes as well a short introduction on the use of complex numbers in geometry and their relationship with plane isometries. Read this only if you are already familiar with exponential form and complex roots of unity.
ps	pdf	This is my high-school "tesina", titled "Una dimostrazione elementare dell'ellitticità delle orbite". It contains an original proof that orbits (in the classical two-body gravitational problem) are conics. Hope you'll find it interesting. It has never been reviewed since I wrote it (at the age of 18/19), so there could be lots of errors. Moreover, I think the introduction and the whole textual part would need a complete rewriting. Anyway, I think the proof itself works. Someone told me I could try to have it published on a "didactic-of-physics" journal, but I never cared to do it.
ps	pdf	A short seminar paper about "covering and partitioning problems", which I had to do for the last univerisity term (it was my "Ricerca Operativa" oral exam). This is not, strictly speaking, elementary and olympic maths, but I think it might be interesting for someone, so I published it with the other docs. Moreover, all you need to know to read the paper is how to multiply vectors and matrices (plus understanding some tricky nonation on "breaking" matrices and vectors into parts).
	pdf	My Bachelor (laurea triennale) thesis. Disclaimer about non-olimpicity as above. Since I currently have no non-olimpic math zone to publish it, I have simply put it here. Enjoy.

This page has been hit times.

I have not "advertised" it in any way on search engines; you are encouraged to put links to it anywhere in your web sites!