Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1501.03104

Range of magic constant on Hexagonal Tortoise Problem

Donghwi Park
View original source ↗Read source document ↗Export metadata ↓

Abstract

Hexagonal tortoise problem (HTP), also known as Jisuguimundo or Jisugwimundo, is a magic square variety which was invented by medieval Korean Mathematician and minister Suk-Jung Choi (1646-1715).[1] Choi showed pattern 30 vertices 3 by 3 diagonal shape which has 93 as its magic constant. Unlike magic square, vertices in Jisugwimundo counted one times, twice or three times. This change makes magic constant of Hexagonal Tortoise Problem could be vary. We consider a range of hexagonal sums in various Jisugwimundo. In this paper, we decomposed vertices on Jisugwimundo to some groups. by this way we found the range of magic constant on several HTP.

Explore related subjects

math.HOmath.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Donghwi Park. 2015-01-11. Range of magic constant on Hexagonal Tortoise Problem. https://arxiv.org/abs/1501.03104

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis

Powerful artificial intelligence is weakening the traditional relationship between mathematical output and evidence of mathematical expertise. In particular, the production of an original theorem or a polished dissertation can no longer, by itself, certify the intellectual formation of its nominal author. I argue that graduate mathematical education should therefore be organized around the formation of intellectual agency: internal technical competence, mathematical judgment, understanding, and responsible participation in a shared intellectual culture. I distinguish productive from premature cognitive offloading, propose complementary independent and AI-augmented modes of training, and suggest a corresponding reformulation of the role of the PhD thesis and dissertation defense. More broadly, I argue that academic mathematics should understand itself increasingly as an institution for the reproduction and stewardship of human mathematical expertise rather than primarily as a mechanism for producing theorems.

math.HO↗
arXiv2026

The Stairs of Reconciliation: A Mathematical Tourist in Graz

Inside the Grazer Burg, two late-Gothic stone flights rise about distinct spindles, overlap, share several treads, and separate again. Their plan is governed not by a coaxial double helix but, to first approximation, by two intersecting circles. This elementary geometry yields a model of recurrent meeting and makes explicit the compatibility conditions that meeting requires. It also leads to a second object that geometers call a double spiral staircase - the helicoid - and to a useful distinction between resemblance and identity. The staircase becomes a meditation on how paths, models, and disciplines can meet without becoming the same.

math.HO↗
arXiv2026

On the Reconstruction of SAS from Other Triangle Congruence Criteria

Starting from a Hilbert plane and removing the Side-Angle-Side (SAS) congruence axiom, we investigate to what extent SAS can be recovered synthetically from the remaining classical triangle congruence criteria. We show that the Angle-Side-Angle criterion, together with a ray correspondence principle corresponding to Theorem 13 of Hilbert's \emph{Grundlagen der Geometrie}, suffices to reconstruct SAS. We further show that both the Side-Side-Side and the Side-Angle-Angle criteria also suffice, once combined with the ray correspondence principle and suitable auxiliary principles -- the existence of midpoints and a hypotenuse-angle criterion for right triangles in the first case, and the existence of angle bisectors, the congruence of supplements of congruent angles, and the Pons Asinorum in the second. Although the two routes rely on auxiliary principles of different character, we show that they converge on a single final argument once a common hypotenuse-angle criterion is established. A metamathematical analysis, based on an explicit model adapted from Hilbert's own independence construction, complements these reconstructions: it shows that the ray correspondence principle alone cannot reconstruct any of the classical criteria, and that the Pons Asinorum and the hypotenuse-angle criterion are each independent of the remaining auxiliary principles used in their respective reconstructions. The resulting picture is not a formal hierarchy of the congruence criteria, but it does show that the Angle-Side-Angle reconstruction rests on a provably more economical basis than those obtained from Side-Side-Side or Side-Angle-Angle.

math.HO↗