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Identical Circles Touching One Another On The Spherical Polyhedrons Analogous To Archimedean Solids, Harish Chandra Rajpoot Rajpoot Hcr
Identical Circles Touching One Another On The Spherical Polyhedrons Analogous To Archimedean Solids, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
The formula, derived here by the author H.C. Rajpoot, are applicable on a certain no. of the identical circles touching one another at different points, centered at the identical vertices of a spherical polyhedron analogous to an Archimedean solid for calculating the different parameters such as flat radius & arc radius of each circle, total surface area covered by all the circles, percentage of surface area covered etc. These formula are very useful for tiling, packing the identical circles in different patterns & analyzing the spherical surfaces analogous to all 13 Archimedean solids. Thus also useful in designing & modelling …
Identical Circles Touching One Another On A Whole (Entire) Spherical Surface, Harish Chandra Rajpoot Rajpoot Hcr
Identical Circles Touching One Another On A Whole (Entire) Spherical Surface, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the articles discussed & analysed here are related to all five platonic solids. A certain no. of the identical circles are touching one another on a whole (entire) spherical surface having certain radius then all the important parameters such as flat radius & arc radius of each circle, total surface area & its percentage covered by all the circles on the sphere have been easily calculated by using simple geometry & table for the important parameters of all five platonic solids by the author Mr H.C. Rajpoot. These parameters are very useful for drawing the identical circles on a …
Reflection Of A Point About A Line & A Plane In 2-D & 3-D Co-Ordinate Systems, Harish Chandra Rajpoot Rajpoot Hcr
Reflection Of A Point About A Line & A Plane In 2-D & 3-D Co-Ordinate Systems, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the articles are related to the reflection of any point about a line in 2-D co-ordinate system and about a line & a plane in 3-D co-ordinate system. Point of reflection about a line or a plane can be easily determined simply by applying the procedures explained or by using formula derived here. These formulas are also useful to determine the foot of perpendicular drawn from a point to a line or a plane in 3-D space. All these derivations are based on the application of simple geometry.
Solid Angles Subtended By The Platonic Solids (Regular Polyhedra) At Their Vertices, Harish Chandra Rajpoot Rajpoot Hcr
Solid Angles Subtended By The Platonic Solids (Regular Polyhedra) At Their Vertices, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
The solid angles subtended at the vertices by all five platonic solids (regular polyhedrons) have been calculated by the author Mr H.C. Rajpoot by using standard formula of solid angle. These are the standard values of solid angles for all five platonic solids i.e. regular tetrahedron, regular hexahedron (cube), regular octahedron, regular dodecahedron & regular icosahedron useful for the analysis of platonic solids.
Mathematical Analysis Of Tetrahedron (Solid Angle Subtended By Any Tetrahedron At Its Vertex), Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Tetrahedron (Solid Angle Subtended By Any Tetrahedron At Its Vertex), Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
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 …
Mathematical Analysis Of A Uniform Tetradecahedron With 2 Congruent Regular Hexagonal Faces, 12 Congruent Trapezoidal Faces & 18 Vertices Lying On A Spherical Surface By Hcr, Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of A Uniform Tetradecahedron With 2 Congruent Regular Hexagonal Faces, 12 Congruent Trapezoidal Faces & 18 Vertices Lying On A Spherical Surface By Hcr, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
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 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 polyhedra.
Mathematical Analysis Of Spherical Rectangle By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Spherical Rectangle By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the articles 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 spherical rectangle to calculate all its important parameters such as solid angle, surface area covered, interior angles etc. & also useful for calculating all the parameters of the corresponding plane rectangle obtained by joining all the vertices of a spherical rectangle by the 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 spherical rectangle …