Geodesic
Theorems on Two Tetrahedrons Intersecting a Sphere
Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 219-227 Cet article a éte moissonné depuis la source Heldermann Verlag

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We describe three-dimensional theorems of two tetrahedrons intersecting a sphere. These theorems can be considered as generalizations of the two-dimensional Pascal's hexagon and Steiner's theorems. We first restructure the original version of the two-dimensional Pascal's hexagon theorem, and prove it synthetically using a simple lemma. In the proving process, we found the essential nature of Pascal's theorem that leads to the synthetic generalization in three-dimensional space. In order to focus on visual representations, we only use a synthetic method in the generalization process.
Classification : 51M04, 51M35
Mots-clés : Triangles and tetrahedrons in perspective, extension of Pascal's hexagon and Steiner's theorems 
@article{JGG_2018_22_2_JGG_2018_22_2_a5,
     author = {K. Morita },
     title = {Theorems on {Two} {Tetrahedrons} {Intersecting} a {Sphere}},
     journal = {Journal for geometry and graphics},
     pages = {219--227},
     year = {2018},
     volume = {22},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a5/}
}
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K. Morita . Theorems on Two Tetrahedrons Intersecting a Sphere. Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 219-227. http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a5/