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I am looking for a place to publish a research paper in Euclidean geometry. This is a fairly lengthy article (56 pages) in which I present a fundamental property of polygons. I have already been rejected in many journals, and all of them recognize that it is a valuable work, but that it is not suitable for their magazine. The last to refuse my job, after almost two and a half months of delay, was Annales of Henry Lebesgue (AHL). To exemplify the type of justifications that usually accompany the rejection of the work, I add this excerpt from the last Referee report on the manuscript from AHL:

"... The paper under review contains an observation in affine geometry that does not seem to be studied before (at least to my knowledge). It is written in great detail, with many beautiful figures, however in a somewhat verbose style. A more concise definition and statement of the main result in the beginning instead of the quite slow and cryptic exposition of the triangle case would maybe have been helpful for the reader. Even though the paper is of interest, it is clearly not suitable for a top tier generalist journal as the Annales Henri Lebesgue, hence I cannot recommend its publication and suggest submission to a journal more specialized in affine geometry. "

I am a retired professor and I no longer aspire to increase my curriculum vitae, but I find it disappointing that it was difficult to make available to the scientific community a work that has involved many hours of work and that, without a doubt, exposes an amazing result that lay. encrypted in the deep foundations of Geometry.

I would appreciate any suggestions that help me to bring this work to light, to make it known from a worthy place. Of course, I am not willing to pay fees to publish in open access.

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    $\begingroup$ if you wish to make your results available to the scientific community, wouldn't arXiv suffice? It is free, it is "open access", the only thing you would miss out on is the stamp of approval from a referee, but I understand from your message that this is not something you would miss. $\endgroup$ Mar 13, 2021 at 15:01
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    $\begingroup$ Possibly jcgeometry.org , if it still is active. (Forum Geometricorum has been discontinued, alas.) For smaller papers with an olympiad flair, Crux Mathematicorum is also an option. $\endgroup$ Mar 13, 2021 at 15:16
  • $\begingroup$ Thank you very much for your advices, Carlo Beenakker and Darij Grinberg. I have published some work on arXiv, but I have not had good experiences on that site. They tend to reject jobs without much judgment. That is the reason why viXra was created, as a counterpoint to arXiv. As for jcgeometry.org, the work does not meet the format conditions since they only accept black and grayscale images and my images are in color (necessary to differentiate different parts in a complex geometric construction), and I think that also exceeds the allowable size. $\endgroup$ Mar 14, 2021 at 22:17
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    $\begingroup$ Looking at the answer of AHL, it seems that there is place for you to publish your text in a mathematical journal. ArXiv is a place to put preprints, there is no judgement on the quality, only administrative requirements. Researchgate is essentially the Facebook of mathematics, and is not really a place to publish, but to make reference to published work. On this webpage you have plenty of nice journals, completely free: cimpa.info/en/node/62 . I might take time, but this deserves it. Another possibility would be the following journal: geombina.uccs.edu $\endgroup$ Mar 16, 2021 at 8:41
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    $\begingroup$ Interesting site! Thank you very much, Toni Mhax. $\endgroup$ Jun 23, 2021 at 16:59

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