HCR's Principle of Polygon
This theory had been proposed by H.C. Rajpoot @ his college presently M.M.M. University of Technology, GKP273010 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:
harish , HCRs Theory of Polygon
By:
harishchandraraj
Science & Technology
63 months ago
Download


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 2D & 3D 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 Infiniteseries' published with IJMPSR
Tags:
Advanced , Book , Geometry , Hand , HCR
By:
harishchandraraj
Science & Technology
63 months ago
Download

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.
Tags:
Alltheparameters as solid angles , HCRsTheoryof Polygon and NR Met , Optimumsolutionby HCRs Theory of , Regularhexagonaland trapezoidal , Uniformtetradecahedron
By:
harishchandraraj
Education
59 months ago
Download



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:
Analysis , Application , HCR , Mathematical , Polygon
By:
harishchandraraj
Education
58 months ago
Download

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.
Tags:
Alltheparameters , Hexagonalandtrapezoidal faces , Table , Tetradecahedron , Uniform
By:
harishchandraraj
Education
59 months ago
Download

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:
Application , HCR , Polygon , REGULAR , Spherical
By:
harishchandraraj
Education
60 months ago
Download

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 & NewtonRaphson Method. It can be used in analysis, designing & modelling of uniform polyhedra.
Tags:
No tags for this presentation
By:
harishchandraraj
Education
60 months ago
Download
