Perfect Prism Problem- A Better Way of Representing Perfect Cuboid Problem

Jayaram A S

doi:https://doi.org/10.14445/22315373/IJMTT-V67I4P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 4 | Year 2021 | Article Id. IJMTT-V67I4P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I4P507

Perfect Prism Problem- A Better Way of Representing Perfect Cuboid Problem

Jayaram A S

Citation :

Jayaram A S, "Perfect Prism Problem- A Better Way of Representing Perfect Cuboid Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 4, pp. 47-50, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I4P507

Abstract

This paper illustrates that the perfect cuboid problem, which is also known as perfect Euler brick problem, can be easily and conveniently represented by a prism instead of a cuboid. This will make the concept simpler and easier to understand. It eliminates the use of solid diagonal of the cube, which used to be a hidden line. It makes the same line to be represented on the surface of the prism as face diagonal. All the seven lines representing the integer numbers are on the surfaces and on the edges. This eliminates repeated extra lines and makes the simpler visual meaning of the problem. The aim of this paper is not to prove or disprove the problem but to clearly illustrate that the key factor is common numbers in Pythagorean triplets, finally converting the whole problem into 2D with a set of triangles.

Keywords

Perfect Euler brick problem, Perfect cuboid problem, Prism representation, Pythagoras theorem, Seven integers.

References

[1] Maiti, S., The Non-existence of Perfect Cuboid., arXiv preprint arXiv:2005.07514 (2020).
[2] Sharipov, R. A., Symmetry-Based Approach to the Problem of a Perfect Cuboid., Journal of Mathematical Sciences 252.2 (2021) 266-282.
[3] Masharov, A. A., and R. A. Sharipov., A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture., arXiv preprint arXiv:1504.07161 (2015).
[4] Gallyamov, R. R., I. R. Kadyrov, D. D. Kashelevskiy, N. G. Kutlugallyamov, and R. A. Sharipov., A fast modulo primes algorithm for searching perfect cuboids and its implementation., arXiv preprint arXiv:1601.00636 (2016).
[5] Reiter, C., and J. Tirrell., Pursuing the perfect parallelepiped., JP Jour. Algebra Number Theory & Appl 6(2006) 279-274.
[6] Nguhi, Alex, and Cleophas Kweyu., On the Pythagorean Triples’ Equations and the Perfect Cuboid Problem., OSF Preprints. April 4 (2021).
[7] Dawit, Bambore., The Proof for Non-existence of Perfect Cuboid., (2014).
[8] DRAGAN, VALERIU.,Notes on a Particular Class of Perfect Cuboids., WSEAS TRANSACTIONS ON MATHEMATICS 13(2014) 811-819.
[9] Druzhinin, V., It is impossible for a perfect cuboid to exist., Norwegian Journal of Development of the International Science 18-1 (2018).
[10] Sharipov, Ruslan., On a pair of cubic equations associated with perfect cuboids., arXiv preprint arXiv:1208.0308 (2012).
[11] Ortan, Alexandra, and Vincent Quenneville-Bélair., Euler’s brick., Delta Epsilon, McGill Undergraduate Mathematics Journal 1 (2006): 30-33.
[12] Sawyer, Jorge, and Clifford Reiter., Perfect parallelepipeds exist., Mathematics of computation 80(274)(2011) 1037-1040.
[13] Jayaram A S, Shifting of Maximum Stress from a critical section., International Journal of Engineering Applied Sciences and Technology, 9 (2019) 164-167.
[14] Jayaram A S., Effect of Stress Concentration Factor on Maximum Stress for A Rectangular Plate With Cutout, Subjected to Tensile Load” International Journal of Innovative Science and Research Technology, 9(2017) 294-297.