Abstract
At the request of the Editor-in-Chief, the Journal of Mathematics and Statistics has decided to retract the manuscript titled "Application of Sivasubramanian Kalimuthu Hypothesis to Triangles" authored by M. Sivasubramanian, published in Volume 5, Issue 2 with the page numbering 90-92. The authors have falsified findings and the article contains unsubstantiated claims and was accepted because of an administrative error. In accordance with recommendations from COPE we have retracted all affected published articles, including this one. Apologies are offered to readers of the journal that this was not detected during the submission and review process.
Highlights
For two thousand years, many attempts were made to prove the parallel postulate using Euclid's first four postulates
If the order the postulates were listed in the Elements is significant, it indicates that Euclid included this postulate only when he realised he could not prove it or proceed without it
Ibn Al-Haytham (Alhazen) (965-1039), an Iraqi mathematician, made the first attempt at proving the parallel postulate using a proof by contradiction, where he introduced the concept of motion and transformation into geometry
Summary
Many attempts were made to prove the parallel postulate using Euclid's first four postulates. Ibn Al-Haytham (Alhazen) (965-1039), an Iraqi mathematician, made the first attempt at proving the parallel postulate using a proof by contradiction, where he introduced the concept of motion and transformation into geometry. Omar Khayyám (1050-1123) made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate and he was the first to consider the cases of elliptical geometry and hyperbolic geometry, though he excluded the latter The Khayyam-Saccheri quadrilateral was first considered by Omar Khayyam in the late 11th century in Book I of Explanations of the Difficulties in the Postulates of Euclid.
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