ABSTRACT In this article we compute volume and surface area of the torus, volume of a slice of a ... more ABSTRACT In this article we compute volume and surface area of the torus, volume of a slice of a 3-ball. Besides this we discuss some interesting facts like ‘derivative of the area of a circle with respect to its radius is its perimeter, derivative of the volume of the sphere with respect to its radius is its surface area and derivative of the volume of the torus with respect to the radius of its meridian circle is its surface area’.
Some Ζ 2 -actions on the Torus
Journal of Mathematics Research, Oct 9, 2013
In this article we discuss some Ζ 2 -actions on the 2-Torus and describe the corresponding orbit ... more In this article we discuss some Ζ 2 -actions on the 2-Torus and describe the corresponding orbit space by using combinatorial techniques.
We demonstrate a well known topological fact that the space obtained by identifying diagonally op... more We demonstrate a well known topological fact that the space obtained by identifying diagonally opposite points of the 3-sphere is homeomorphic to the 3-sphere.
In this article we discuss some Ζ 2 -actions on the 2-Torus and describe the corresponding orbit ... more In this article we discuss some Ζ 2 -actions on the 2-Torus and describe the corresponding orbit space by using combinatorial techniques.
Z Actions on the 3-SPHERE
In this article, we discuss some 2 Z actions on the 3-sphere and give triangulations of the actio... more In this article, we discuss some 2 Z actions on the 3-sphere and give triangulations of the action maps. We also discuss the corresponding quotient spaces by using simplicial complexes.
Topology in Chemistry
In this article we discuss the importance of topological and combinatorial concepts to count the ... more In this article we discuss the importance of topological and combinatorial concepts to count the number of isomers of a chemical compound. We have considered molecules of the kind (CH) 2n in this article but the same game can be played with any other chemical compound.
Special Triangulations of 3-DIMENSIONAL Lens Spaces
JP Journal of Geometry and Topology
In this article, we give some special triangulations of infinitely many 3-dimensional lens spaces... more In this article, we give some special triangulations of infinitely many 3-dimensional lens spaces, say (). 1 , d L The specialty in these triangulations is that a suitable vertex labeling of any of these gives a simplicial map whose geometric realization is homeomorphic to an 1 S -bundle projection map 1 () . 1 , : 2 S d L p → We also give for each N ∈ d a triangulation of a d-fold covering map ().
Calculus and geometry
Resonance, 2013
ABSTRACT In this article we compute volume and surface area of the torus, volume of a slice of a ... more ABSTRACT In this article we compute volume and surface area of the torus, volume of a slice of a 3-ball. Besides this we discuss some interesting facts like ‘derivative of the area of a circle with respect to its radius is its perimeter, derivative of the volume of the sphere with respect to its radius is its surface area and derivative of the volume of the torus with respect to the radius of its meridian circle is its surface area’.
For any d (resp. for almost all d) we compute the least number (d) of vertices which a triangulat... more For any d (resp. for almost all d) we compute the least number (d) of vertices which a triangulation K of the 2-sphere (resp. any other orientable surface) must have in order that there exists a degree d simplicial map from K to the 4-vertex 2-sphere. We also prove an analogous result for uniquely 4-colourable Ks.
In this article we discuss some Geometric and Topological properties of the polyhedrons and refor... more In this article we discuss some Geometric and Topological properties of the polyhedrons and reformulate Polyhedral Gauss Bonnet Theorem.
Keywords Sphere-Cylinder Theorem, volume and surface area of the torus, volume and surface area o... more Keywords Sphere-Cylinder Theorem, volume and surface area of the torus, volume and surface area of a slice of a solid sphere. The author earned his PhD degree in mathematics (topology), in 2000, from Panjab University, Chandigarh and since then he has been teaching analysis, algebra, calculus and discrete mathematics at DES-MDRC, Panjab University. His areas of interest are combinatorial topology, algebraic topology, differential topology, braid groups, knot theory and graph theory.
Marcelo Alberto Aguilar, Aziz El Kacimi Alaoui, KK Azad, Alex Chigogidze, Bruno Colbois, Antonio ... more Marcelo Alberto Aguilar, Aziz El Kacimi Alaoui, KK Azad, Alex Chigogidze, Bruno Colbois, Antonio Conde, Ana Pereira do Vale, Michael Falk, Sergey Finashin, Maximilian Ganster, Hubert Gollek, Haydee Herrera, Richard Hitt, Howard T. Iseri, Masaharu Ishikawa, Gwon Soo Jeong ...
An application of Graph Theory to Algebra
MATHEMATICS NEWSLETTER, Jan 1, 2008
On Branched Coverings
International Journal of Applied Mathematics & …, Jan 1, 2009
... On Branched Coverings. Keerti Vardhan Madahar. Abstract. We construct, for almost all permiss... more ... On Branched Coverings. Keerti Vardhan Madahar. Abstract. We construct, for almost all permissible degrees d, a minimal simplicial branched covering map of degree d from each closed, suitably triangulated, 2-manifold onto the 6-vertex Real Projective Plane. ...
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