The Journal of the Indian Mathematical Society

R. C. Bose ¹

Affiliations
1 Calcutta, IN

Abstract

In Hyperbolic Geometry the angle of parallelism corresponding to a distance a is generally denoted by TT (»), while the distance of parallelism corresponding to the angle a is denoted by ∇ ( a).

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R. C. Bose

Abstract

James Singer by using the Finite Projective Geometry PG(2,pⁿ), proved the following theorem of the 'theory of numbers': Given an integer m≥2 of the form pⁿ (p being a prime) we can find m+I integers

d₀, d₁, d₂,..., d_m.

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R. C. Bose ¹

Affiliations
1 Calcutta, IN

Abstract

It has been shown by Ganapati that all the cyclic points of a convex oval cannot lie on the same circle. The object of this note is to establish the following similar theorems:

THEOREM (A). The tangents to the oval at the cyclic points cannot all touch the same circle.

This theorem may in a sense be regarded as the dual of Ganapati's theorem, but is not derivable from his theorem by polar reciprocation.

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R. C. Bose ¹

Affiliations
1 Calcutta, IN

Abstract

The object of this note is to prove the following theorem, connecting the perimeter of a convex curve, with the perimeter of convex equiangular polygons circumscribing it.

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R. C. Bose ¹

Affiliations
1 Calcutta, IN

Abstract

If r=r(s) is the vector equation of a plane curve V, s denoting the affine length, then r₁=r'(s) and r₂=r"(s), are the vector equations of what have been called the tangent and curvature forms of V, the dashes denoting differentiation with respect to s.

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