https://gphjournal.org/index.php/m <p style="font-family: 'Segoe UI', sans-serif; font-size: 16px; color: #333;"><strong>GPH-International Journal of Mathematics (e-ISSN&nbsp;<a href="https://portal.issn.org/resource/ISSN/3050-9629" target="_blank" rel="noopener">3050-9645</a>)</strong> is a peer-reviewed, open-access journal dedicated to advancing research in mathematics. The journal publishes original research articles, comprehensive reviews, and survey papers covering both pure and applied mathematics, including topics such as algebra, analysis, geometry, number theory, and mathematical modeling. It provides a global platform for mathematicians and researchers to share innovative ideas, foster interdisciplinary collaboration, and contribute to the advancement of mathematical knowledge.</p> Global Publication House en-US GPH-International Journal of Mathematics 3050-9645 <p>The authors and co-authors warrant that the article is their original work, does not infringe any copyright, and has not been published elsewhere. By submitting the article to <a class="is_text" title="GPH - International Journal of Mathematics" href="https://www.gphjournal.org/index.php/m/index">GPH - International Journal of Mathematics</a>, the authors agree that the journal has the right to retract or remove the article in case of proven ethical misconduct.</p> https://gphjournal.org/index.php/m/article/view/2449 <p><strong>a...</strong> The Unsolvability of the Three famous Ancient Greek Problems—Doubling the Cube, Trisecting the Angle, and Squaring the Circle -- <strong>Stands on the Base justification</strong> of the <strong>Algebraic Field Theory (specifically GaloisTheory)</strong> and the <strong>Theory of Constructible Numbers</strong>, which were developed in the 19th century.</p> <p><strong>b...</strong> The Greeks often used other Techniques <strong>(like Conic sections orMechanical tools)</strong> to Solve these Problems, But <strong>their self-imposed</strong> "Euclidean" constraint, with a <strong>Ruler and a Compass</strong> ,(straightedge and compass) made these Specific Problems impossible to solve.</p> <p><strong>c...</strong> In the Published Articles [123],[124],[126] , it is <strong>clearly evident</strong> that the Solution of the Ancient , Unsolved Greek Problems, using <strong>a Ruler and a Compass</strong> , as the constraint has been set by Euclid], <strong>Has Become Possible</strong>, and is in the Critique of Both , <strong>Human Logic Thinking and , The Artificial Intelligence</strong> when it uses <strong>The Path of Knowledge</strong> to the Truths of Nature, and which is the <strong>Dialectic Logic</strong> of Euclidean Geometry.</p> <p><strong>d...</strong> From the Published Articles [123] , [124] , [126] , All Steps Follow the Restrictions set by Euclid which are <strong>&lt; By A Ruler and a Compass &gt;</strong></p> <p><strong>In the New Article [125] the Proof is repeated , Both of the Squaring of the circle and the Doubling of the Cube using only a Ruler and a Compass , as well as the Bellow-motion of the Photon with The Photon`s Cloning Method.</strong></p> Markos Georgallides ##submission.copyrightStatement## https://creativecommons.org/licenses/by-nc-nd/4.0 2026-06-01 2026-06-01 9 5 01 23 10.5281/zenodo.20492443 https://gphjournal.org/index.php/m/article/view/2453 <p>This research investigates the Lie-derivative and Berwald covariant derivatives of the conformal curvature tensor in the generalized fifth recurrent Finsler space. The study focuses on the mathematical properties and interrelations of these tensors, exploring the behavior of the conformal curvature tensor under various differential operators, including the Lie derivatives and Berwald covariant derivatives. This paper builds upon the definition for the conformal curvature tensor under the Lie derivative in generalized BK-fifth recurrent Finsler space. We study the relations between the mentioned curvature tensors and Rᶦⱼₖₕ by Lie-derivative. The Lie-derivative for the conformal curvature tensor Cᵢⱼₖₕ and the fifth-order Berwald covariant derivatives are mutually commutative. In addition, we prove that the conformal curvature tensor Cᵢⱼₖₕ behaves as a fifth recurrent under certain conditions. In conclusion, we demonstrate that applying the fifth-order Berwald covariant derivative to the Lie derivative of the curvature scalar R is vanishing.</p> Adel M. Al-Qashbari Alaa A. Abdallah Saeedah M. Baleedi ##submission.copyrightStatement## https://creativecommons.org/licenses/by-nc-nd/4.0 2026-05-31 2026-05-31 9 5 24 33 10.5281/zenodo.20558308