# 2363 presentation(s) on 'hcrs theory'

Subscribe to HCR's Principle of Polygon This theory had been proposed by H.C. Rajpoot @ his college presently M.M.M. University of Technology, GKP-273010 in Oct, 2013, for finding out the solid angle subtended by any polygonal plane at any point in the space. It gives the simplest, easiest & the most versatile methods for calculating the mathematically correct value of solid angle subtended by any plane bounded by the straight lines like triangle, quadrilateral like rectangle, square, rhombus, trapezium etc., any regular or irregular polygon like pentagon, hexagon, heptagon, octagon etc.) at any point in the space. It is the unified theory applied for any polygon by using one standard formula only. This can derive expression for solid angle subtended by any plane bounded by the straight lines. This theory is equally applicable for atomic distances & stellar distances in the Universe. Tags: 75 Views Science & Technology 63 months ago All the important parameters of cuboctahedron/Archimedean solid by HCR Table of all the important parameters of a cuboctahedron (Archimedean solid having 8 congruent equilateral triangular & 6 congruent square faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons. 80 Views Education 61 months ago HCR's Hand Book (Formula of Advanced Geometry) All the standard formula from 'Advanced Geometry' by the author Mr H.C. Rajpoot have been included in this book. These formula are related to the solid geometry dealing with the 2-D & 3-D figures in the space & miscellaneous articles in Trigonometry & Geometry. These are useful the standard formula to be remembered for case studies & practical applications. Although, all the formula for the plane figures (i.e. planes bounded by the straight lines only) can be derived by using standard formula of right triangle that has been explained in details in "HCR's Theory of Polygon" published with International Journal of Mathematics & Physical Sciences Research in Oct, 2014.And the analysis of oblique frustum of right circular cone has been explained in his research paper 'HCR's Infinite-series' published with IJMPSR Tags: 56 Views Science & Technology 63 months ago Mathematical Analysis of Uniform Tetradecahedron by HCR All the important parameters of a uniform tetradecahedron, having 2 congruent regular hexagonal faces, 12 congruent trapezoidal faces & 18 vertices lying on a spherical surface with certain radius, have been derived by the author by applying "HCR's Theory of Polygon" to calculate solid angle subtended by each regular hexagonal & trapezoidal face & their normal distances from the center of uniform tetradecahedron, inscribed radius, circumscribed radius, mean radius, surface area & volume. These formula are very useful in analysis, designing & modeling of various uniform polyhedra. 228 Views Education 59 months ago All the important parameters of a truncated dodecahedron Table of all the important parameters of a truncated dodecahedron (having 20 congruent equilateral triangular & 12 congruent regular decagonal faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons. Tags: 50 Views Education 61 months ago All the important parameters of a snub cube (an Archimedean solid) Table of the important parameters of a snub cube (an Archimedean solid having 32 congruent equilateral triangular & 6 congruent square faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's Theory of Polygon & Newton-Raphson Method. It can be used in analysis, designing & modelling of uniform polyhedra. 200 Views Education 60 months ago Mathematical Analysis of Tetrahedron (solid angle by tetrahedron) All the articles have been derived by the author Mr H.C. Rajpoot by using HCR's Inverse cosine formula & HCR's Theory of Polygon. These formula are very practical & simple to apply in case of any tetrahedron to calculate the internal (dihedral) angles between the consecutive lateral faces meeting at any of four vertices & the solid angle subtended by it (tetrahedron) at the vertex when the angles between the consecutive edges meeting at the same vertex are known. These are the generalized formula which can also be applied in case of three faces meeting at the vertex of various regular & uniform polyhedrons to calculate the solid angle subtended by polyhedron at its vertex. Tags: 35 Views Education 58 months ago Table of the important parameters of a uniform tetradecahedron by HCR Table of the important parameters of a uniform tetradecahedron, having 2 congruent regular hexagonal faces, 12 congruent trapezoidal faces & 18 vertices lying on a spherical surface with certain radius, derived by the author H.C. Rajpoot by applying "HCR's Theory of Polygon" to calculate solid angle subtended by each regular hexagonal & trapezoidal face & their normal distances from the center of uniform tetradecahedron, inscribed radius, circumscribed radius, mean radius, surface area & volume. These formula are very useful in analysis, designing & modeling of various uniform polyhedrons. 50 Views Education 59 months ago Mathematical Analysis of Regular Spherical Polygons by HCR All the parameters of a regular spherical polygon such as solid angle subtended at the center, area, length of side, interior angle etc. have been derived by Mr H.C. Rajpoot by using simple geometry & trigonometry. All the formula are very practical & simple to apply in case of any regular spherical polygon to calculate all its important parameters such as solid angle, surface area covered & length of each side etc. & also all the parameters of the corresponding regular plane polygon obtained by joining all the vertices of the regular spherical polygon by straight lines. These formula can also be used to calculate all the parameters of the right pyramid obtained by joining all the vertices of a regular spherical polygon to the center of sphere such as normal height, angle between the consecutive lateral edges, area of regular polygonal base etc. All these results are also the shortcuts for calculating the various complex problems related to the regular spherical polygons. Tags: 127 Views Education 60 months ago All the important parameters of a snub dodecahedron by HCR Table of the important parameters of a snub dodecahedron (an Archimedean solid having 80 congruent equilateral triangular & 12 congruent regular pentagonal faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's Theory of Polygon & Newton-Raphson Method. It can be used in analysis, designing & modelling of uniform polyhedra. Tags: No tags for this presentation 101 Views Education 60 months ago 