Titles and Short Summaries of the Talks

26 Geometry
9:20–12:00
Geometry
March 20th (Wed) Conference Room III
Final: 2013/2/7
1 Hirotaka Ebisui (Oval Research Center) ♯ Saround theorem of famous theorem in history · · · · · · · · · · · · · · · · · · · · · 5
Summary: We know there are many theorem in history. For example, there are Papus, Meneraus,
Pascal, Simson, Napoleon, Morley, Fractal, etc. We show attached theorem of them as researching
saround them. These theorem is somehow similar researches as adding new conditions to famous
theorem-composition.
2 Hirotaka Ebisui (Oval Research Center) ♯ On some square infinty-chain expansion-compositions of Phytagoras 2
area theorem and 6 perpendiculars-concurrence theorem, which show
the existance of infinity parallel space · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
Summary: We show the title context using CAD figures and one proof of area theorem by some
output results of Maple soft Promram Code.
3 Noriko Zaitsu (Eigakuin) About rigidity and infinitesimal rigidity of Polyhedron · · · · · · · · · · · · · · 10
Summary: Square pyramid is rigid, but the polyhedron excluding the bottom there is flexible.
This paper is consider about rigidity and infinitesiml rigidity of Polyhedron. December, 1992 “the
polyhedron which infinitesimal flexible however has rigidity exists” I discovered the theorem under
a captain Mr. Osamu Kobayasi. (figure 1) Then, while it was careless, the point was exceeded to
Mr. Kuan of China, but since the example was different, it carried out by noticing that there is
another meaning later. First, “does an infinitesimal flexible polyhedron exist at 2 or n points in one
motion?” The conjecture was considered. (figure 2) Behind, the polyhedoron foldable at both ends
which moves very truly and near flexible polyhedron were discovered from the little cause in 2005
or 2006. (figure 3)
4 Kiyohisa Tokunaga
(Fukuoka Inst. of Tech.)
♯ The divergence theorem of a triangular integral · · · · · · · · · · · · · · · · · · · · 10
Summary: This divergence theorem of a triangular integral demands the antisymmetric symbol
to derive the inner product of the nabla and a vector. Replacing a cuboid (a rectangular solid) by
a tetrahedron (a triangular pyramid) as the finite volume element, a single limit is only demanded
for triple sums in our theory of a triple integral. The divergence theorem of a triangular integral
is derived by substituting the total differentials into our new method of a triangular integral. We
thus infer that our new method of a triangular integral must be the inverse operation of the total
differential.
5 Sadahiro Maeda (Saga Univ.) ♯ Characterizations of the homogeneous real hypersurface of type (B)
Katsufumi Yamashita (Saga Univ.) having two constant principal curvatures in a complex hyperbolic space
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We characterize the homogeneous real hypersurface M of type (B) having two constant
principal curvatures in a complex hyperbolic space CH n (c) by investigating its contact form η, its
shape operator A and the extrinsic shape of some geodesics on M in the ambient space CH n (c).