For the origin of new geometry
The author of this paper has published, both as a single author and aided and abetted by \textit{M. Sivasubramanian}, in a variety of journals published by vanity presses, short notes which purport to prove out of thin air the Euclidean parallel postulate (which, we are told in one of the papers in the bibliography, all authored by himself with or without \textit{M. Sivasubramanian}, he has studied for more than 25 years), as well as the trisection of an angle of \(60^{\circ}\). The current paper --- which together with \textit{M. Sivasubramanian} [Appl. Math. Lett. 23, No. 9, 1137--1139 (2010; Zbl 1200.51011)], constitute the first examples this reviewer is aware of in which rubbish by authors whose mathematical sophistication is firmly stuck in a confused pre-high school phase has penetrated a bona fide research journal (for true believers in the ``impact factor'', this journal's is 0.978) --- consists of (1) a ``proof'' via 7 statements that there is a spherical rectangle, with unequal opposite sides, and that this is ``a contradiction'', (2) two figures occupying half a page, (3) a half page of English text with an abundance of keywords to impress the uneducated, but unrelated to (1), a genuine and a fake Einstein quotation. It is not entirely clear whether the author's acknowledgement, thanking `` the anonymous referees for their suggestions for the revision and refinement of this paper'' corresponds to an actual state of affairs. After receiving several letters, the editor of the journal has retracted \textit{M. Sivasubramanian}'s paper, and the current one will likely meet the same fate. Editorial remark: As expected by the reviewer, after two years the paper has been ``retracted at the request of the Editor-in-Chief and Publisher. This paper does not meet the minimum research and mathematical standards of Applied Mathematics Letters; for example, some of this paper's constructions and arguments make no sense mathematically. Though handled by the previous editorial office, the available records lead us to believe its publication was the result of an administrative oversight and apologies are offered to readers of the journal that this was not detected earlier.''
scientific article; zbMATH DE number 5810844