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Srinivasiengar, C. N.
- On a Particular Type of Scrolls
Authors
1 Central College, Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 19 (1932), Pagination: 44-48Abstract
The highest order of multiplicity that is possible for a multiple curve on a surface of degree n is n - 1, and in this case the multiple curve is a straight line and the surface is ruled.
- Remarks on Spurious Correlation
Authors
Source
The Journal of the Indian Mathematical Society, Vol 19 (1932), Pagination: 251-252Abstract
The expression obtained by Mr. N. K. Adyanthaya for the correlation (according to the usual definition) between any two functions f( x1 , x2) and Φ (x3 , x4) where the variables may be inter-correlated [J.I. M.S. Vol XIX, p. 163, equation (7)] is of considerable theoretical interest.- Some Properties of Developable Surfaces
Authors
1 Central College, Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 193-200Abstract
Preliminary. On a surface referred to a system of parametric curves p = const, and q = const, consider a point at which the fundamental magnitudes of the second order L, M, N all vanish. At such a point, the equation
Ldp 2 + 2M dpdq + Ndq2 = 0
determining the inflexional directions becomes an identity. There are two possibilities.
- The Theory of Envelopes of Plane Curves
Authors
Source
The Journal of the Indian Mathematical Society, Vol 17 (1928), Pagination: 71-76Abstract
Ths envelope of a family of plane curves f (x, y, c) = 0 is defined in many text-books as the locus of the ultimate intersections of f(x, y, c) = 0 and f(x, y, c + δc) = 0. This definition has one serious disadvantage; for, it is easily prove J that if the family possess any double points, these will appear in the c-discriminant.- On the Quartic Developable
Authors
1 Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 127-130Abstract
The quartic developable is generated by the tangents of a twisted cubic. Taking the cubic as
x = t3, y = t2, z = t,w = I, (I)
the equation of the developable is
f(x,y,z,w)=6xyzw-4y3w-4xz3+3y2z2-x2w2 = 0. (2)
The object of this paper is to obtain a remarkable property regarding the first polar surfaces of this developable.
- The Linear Line - Congruence
Authors
1 Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 73-91Abstract
A linear congruence of lines is formed by the lines common to two linear line-complexes. The lines of such a congruence possess two transversals, and the congruence is called hyperbolic, elliptic or parabolic according as these transversals are real and distinct, imaginary and distinct, or coincident.- The Lines of Striction on a Quadric
Authors
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 19-24Abstract
It is well known that the line of striction of a regulus on a quadric is a rational quartic of type (1,3) cutting every generator of the regulus at a single point and every generator of the other regulus in three points. The rational quartic curve R4 in [3] has been studied in detail from the projective point of view. In this paper, the metrical specialisations consequent to the metrical definition of the line of striction, and a few allied problems are considered.- On the Zeros of Weierstrass's Non-Differentiable Function
Authors
1 Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 114-117Abstract
The zeros of certain standard non-differentiable functions have been the subject-matter of a few papers-mostly of an introductory and numerical type.- A Note on Harmonic Curves
Authors
1 Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 2 (1937), Pagination: 302-307Abstract
The equations of a rational curve which lies on a quadric surface and whose tangents belong to a linear complex can be expressed in the form
x:y:z:w=tm+n:tm:tn:1 (1)
where m and n are integers prime to each other.
- The Asymptotic Curves of the Cubic and Quartic Scrolls
Authors
1 Central College, Bangalore, IN
Source
The Journal of the Indian Mathematical Society, Vol 1 (1935), Pagination: 251-258Abstract
The asymptotic curves of the cubic scroll of the first type are rational quartic curves which cut every generator in two points harmonically separating the intersections of the generator with the directrix lines.
This theorem was first proved by Wilczynski who deduced it from his well-known differential equations of a ruled surface. It is the object of this section to employ the theory of correspondence to discuss the asymptotic curves.