cover image: Bulletin of the Calcutta Mathematical Society  September  1941

Premium

20.500.12592/35n7pt

Bulletin of the Calcutta Mathematical Society September 1941

1941

Denoting the vectors of the set by p1 p2 p the (7.) co-ordinates of the multisector referred to the basis a are given by the scalar determinants a 1. a.. [...] Unifying the results of this article and of the foregoing one we can enunciate the final proposition in the following manner:— The cylinctroid represents Mt only type of (real) cubic scroll whose section made by the plane at infinity consists of two (imaginary) tangents to the circle at infinity and their (real) chord of contact. [...] 5. It is remarkable that when a cylindroid is to be defined as above as a special varietS of right conoid of the third degree the qualifying clause to he introduced is that the section of the s-urface by the plane at Do should consist of the ee rt. [...] Hessian whose equation is given in the well-known deter antal form is of degree 4(n-2) and the locus of the vertices of the conical polar quadrics answering to different points on it is another surface which is called the Steinerian and which coincides with the Hessian if and only if the original surface II is a cubic. [...] Furthermore reliance being placed on the known theorem that the parabolic curve of a surface II is its partial curve of intersection with its own Hessian—the residual curve of intersection being possibly the multiple curve or curves (if any) of II—the legitimate inference is that the parabolic curve of the cylindroid is a degenerate twisted curve of the second degree consisting of the two rt.
technology medicine science
Pages
58
Published in
India
SARF Document ID
sarf.120023
Segment Pages Author Actions
Frontmatter
i-ii S.N. Bose, F.W. Levi, C.V.H. Rao view
On the Properties of the Functions which are Self-Reciprocal in Hankel’s Transform
93-98 D.P. Banerjee view
Properties of a Certain Confluent Hyper Geometric Function
99-104 B. Mohan view
Dyadics and Muitidyadics in Hyperspace
105-118 N.N. Ghosh view
The Enumeration of the Latin Rectangle of Depth Three by means of a Difference Equation
119-128 S.M. Kerawala view
Cylindroid and Kindred Surfaces
129-148 Haridas Bagchi view

Related Topics

All