Harish Chandra Rajpoot

application of hcrs theory of polygon hcr's formula for all five platonic solids inner radius application of hcr's theory of polygon mean radius outer radius dihedral angles between the adjacent faces hcr's theory of polygon hcr's 3d geometry identical circles touchig one another on a spheric all the parameters of a great rhombicuboctahedron truncated cube application hcr's formula hcr's inverse cosine formula hcr's derivations of 2d geometry hcr's solid geometry hcr's cosine formula spherical geometry arc radius total surface area covered & percentage of area co flat radius 2-d & 3-d geometry by hcr solid angle subtended by each face all the parameters of a great rhombicosidodecahedr uniform polyhedra normal distance of each face surface area surface area & volume of decahedron congruent right kite faces all the important parameters of a snub cube all the important parameters of a small rhombicubo inner truncated octahedron hcr's hand book solid angle subtended by a rectangular plane at an hcr formula of tetradecahedron non-uniform tetradecahedron hcr's formula for n-polyhedron non-uniform polyhedron hcr's formula for antiprism polygonal antiprism application of hcr's theory general formula of antiprism regular n-gonal antiprism geometry by h c rajpoot hcr's geometry solid angle of antiprism volume & surface area hcr's derivation of antiprism application of hcr's theory of formula of pentagonalantiprism regular pentagonal antiprism hcr's global distance formula min distance b/t two points great-circle distance formula hcr's formula for ci trapezium circuminscribed polygon formula of ci polygon ci trapezium by hcr circuminscribed(ci) trapezium 3d geometry by h c rajpoot formula of rhombicuboctahedron by hcr truncated rhombic dodecahedron by hcr hcr's polyhedron formula of rhombic dodecahedron by hc rajpoot catalan solid by h c rajpoot rhombic dodecahedron by hcr hcr's formula for rhombic dodecahedron paper model of flat container paper model of right pyramid paper model of pyramidal application of hcr's theorem and corollary hcr's corollary 3d-geometry by h c rajpoot rotation of coplanar planes about their edges hcr's theorem solid angle by rectangular right pyramid by hcr hcr's formula to solid angle by rectangular right solid angle by right pyramid by h c rajpoot solid angle subtended by regular n-gonal right pyr apollonius theorem for parallelogram proofs of apollonius theorem by h c rajpoot apollonius theorem hcr formula to compute area of spherical triangle archemedean twin circles by hcr archimedean circles formula for triangle square trapezium circles formula of advanced geometry by h.c. rajpoot solid angle subtended by regular heptagonal plane formula of advanced geometry disphenoid (isosceles tetrahedron) volume & circum-radius derived by hcr how to derive formula of volume of a disphenoid circum-center and centroid are coincident incenter solid geometry by h c rajpoot solid angle subtended by a tetrahedron at its vert solid angle subtended by a triangle solid geometry volume & surface area of cut cone cut cone with hyperbolic section flat ring test (frt) how to distinguish b/t surface of sphere & torus surface of a sphere vs surface of a torus 3d geometry by h.c. rajpoot minimum distance between two points on the sphere application of hcr's cosine formula angle between chords of two great circle arcs angle between the great circle arcs spherical surface three real positive numbers number theory hcr's inequality 3-d geometry regular spherical polygon topology spherical geometry volume of tetrahedron/pyramid bounded solid bounded by a plane & three orthogonal planes snugly packed spheres in the vertices of all five fillet radius sphere resting in the vertex of right pyramid & po right pyramid packing of spheres in the vertex of platonic solid analogous to archimedean solids archimedean solids photometry by hcr radiometry by hcr solid angle subtended by a beam with a rectangular circular profile of beam rectangular profile of beam reflection of point about a line & a plane soli truncated icosahedron truncated dodecahedron solid angles subtended by archimedean solids at th solid angle subtended by all five platonic solids solid angle subtended by any tetrahedron at the ve uniform polyhedral shells construction of uniform polyhedra platonic solids archimedean solid volume of uniform polyhedra regular polygonal faces trapezoidal faces generalized formula solid angle by each face volume all the parameters of a uniform tetradecahedron all the important parameters of a decahedron with inner radius mean radius circumradius all the important parameters of the elliptical pat major axis minor axis eccentricity & radius of the third tangent circle approximate value of solid angle subtended by a ci application of hcr's approximation formula for sym how to calculate radii of inscribed & circumscribe derivations of inscribed & circumscribed radii for interior angles of rectangle solid angle & area covered by a spherical rectangl all the important parameters of a spherical rectan solid angle & area covered by the spherical triang all the important parameters of a spherical triang all the parameters of any regular spherical polygo all the important parameters of any regular spheri solid angle interior angle length of side area covered by spherical polygon all the important parameters of a sm application of hcrs theory of polygon & newton ra newton-raphson method for snub cube all the important parameters of a truncated cuboct parameters of a truncated icosidodecahedron or gre all the parameters of a truncated icosidodecahedro all the important parameters of a rhombicosidodeca all the parameters of a rhombicosidodecahedron all the important parameters of an icosidodecahedr outer & mean radii of icosidodecahedron volume & surface area of icosidodecahedron icosidodecahedron parameters of cuboctahedron/archimedean solid analysis of cuboctahedron/archimedean solid outer & mean radii of truncated cube hcrs formula for all five platonic solids app truncated tetrahedron hcrs theory of polygon hcr's formula hcr's mathematical proofs hcr's or h. rajpoot formula for regular polyhedron mathematical analysis of regular n-polyhedrons hcr's dimensionless formula surface area & volume solution of internal & external angles of a tetrah intersecting planes & straight lines in the space hcr's series hcr's rank formula linear permutation linear algebra solid angle subtended by a torus at a point hcr's 3-d haikudeck advanced geometry hcr's derivations of solid angle 2013 solid angle subtended by any polygon at any point space science radiometry advanced geometry by h. c. rajpoot advanced geometry by h. c. rajpoot-2014 hcr's rank formula-2 calculation of rank of linear permutations of non- rank of circular permutations by hcr's rabk formul expansion of factorial by hcr's series verification of hcr's rank formula hcr's rank formula-2 for repetition of articles ranking of linear permutations application of hcr's rank formula on color propert analysis of oblique frustum of a right circular co hcr's deductions for cubic equation nature of real root & cubic curve 3-d geometry by h. c. rajpoot solid angle subtended by an elliptical plane hcr's approximation formula hcr's 3-d geometry solid angle subtended by rotatory solids 3-d geometry of h. c. rajpoot-2014 estimations of solid angle in solid state physics