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- Advanced Geometry by HCR for the packing of the spheres (1)
- All the important parameters of a uniform decahedron are calculated by using HCR's Theory of Polygon (1)
- Area covered by spherical triangle (1)
- Derivations of inscribed & circumscribed radii for three externally touching circles (1)
- Ellipse between two circles (1)
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- Inner radius (1)
- Mean radius (1)
- Outer radius (1)
- Solid angle subtended at the center (1)
- Solid angle subtended by a tetrahedron at a vertex (1)
- Solid angle subtended by all the platonic solids at their vertices (1)
- Spherical triangle (1)
- Surface area & volume of a uniform tetradecahedron (1)
- Volume of tetrahedron/pyramid (1)
Articles 1 - 12 of 12
Full-Text Articles in Education
Derivation Of The Volume Of Tetrahedron/Pyramid Bounded By A Given Plane & The Co-Ordinate Planes, Harish Chandra Rajpoot Rajpoot Hcr
Derivation Of The Volume Of Tetrahedron/Pyramid Bounded By A Given Plane & The Co-Ordinate Planes, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
The article here deals with the derivation of a general expression to calculate the volume of tetrahedron/pyramid bounded by a given plane & the co-rdinate planes (i.e. XY-plane, YZ-plane & ZX-plane) using intercept form of equation of a plane in 3-D space. All the derivations are based on simple geometry. These are very useful to directly calculate the volume of the bounded tetrahedron/pyramid.
Mathematical Analysis Of Sphere Resting In The Vertex Of Right Pyramid & Polyhedron, Filleting Of The Faces & Packing Of The Spheres In The Vertex, Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Sphere Resting In The Vertex Of Right Pyramid & Polyhedron, Filleting Of The Faces & Packing Of The Spheres In The Vertex, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
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 Great Rhombicosidodecahedron (The Largest Archimedean Solid) By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Great Rhombicosidodecahedron (The Largest Archimedean Solid) By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the important parameters of a great rhombicosidodecahedron (the largest Archimedean solid), having 30 congruent square faces, 20 regular hexagonal faces, 12 congruent regular decagonal faces each of equal edge length, 180 edges & 120 vertices lying on a spherical surface with certain radius, have been derived by the author Mr H.C. Rajpoot by applying "HCR's Theory of Polygon" to calculate the solid angle subtended by each square face, regular hexagonal face & regular decagonal face & their normal distances from the center of great rhombicosidodecahedron, dihedral angles between the adjacent faces, inscribed radius, circumscribed radius, mean radius, surface area …
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 Uniform Decahedron Having 10 Congruent Faces Each As A Right Kite By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Uniform Decahedron Having 10 Congruent Faces Each As A Right Kite By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the important parameters of a decahedron having 10 congruent faces each as a right kite have been derived by the author by applying HCR's Theory of Polygon to calculate normal distance of each face from the center, inscribed radius, circumscribed radius, mean radius, surface area & volume. The formula are very useful in analysis, designing & modeling of polyhedrons.
Mathematical Analysis Of Elliptical Path In The Annular Region Between Two Circles, Smaller Inside The Bigger One (Ellipse Between Two Circles By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Elliptical Path In The Annular Region Between Two Circles, Smaller Inside The Bigger One (Ellipse Between Two Circles By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the articles have been derived by the author by using simple geometry & trigonometry. These articles are related to the analysis of the elliptical path in the annular region between two circle, smaller inside bigger one & their centers separated by a certain distance. These formula are used to calculate minor axis, major axis, eccentricity & the radius of the third tangent circle touching the smaller circle externally & the bigger one internally. These articles (formula) are very practical & simple to apply in case studies & practical applications of 2-D Geometry.
Mathematical Derivations Of Inscribed & Circumscribed Radii For Three Externally Touching Circles (Geometry Of Circles By Hcr), Harish Chandra Rajpoot Hcr
Mathematical Derivations Of Inscribed & Circumscribed Radii For Three Externally Touching Circles (Geometry Of Circles By Hcr), Harish Chandra Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
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 …
Mathematical Analysis Of Spherical Triangle (Spherical Trigonometry By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr
Mathematical Analysis Of Spherical Triangle (Spherical Trigonometry By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr
Harish Chandra Rajpoot H.C. Rajpoot
All the important parameters of a spherical triangle have been derived by Mr H.C. Rajpoot by using simple geometry & trigonometry. All the articles (formula) are very practical & simple to apply in case of a spherical triangle to calculate all its important parameters such as solid angle, covered surface area, interior angles etc. & also useful for calculating all the parameters of the corresponding plane triangle obtained by joining all the vertices of a spherical triangle by straight lines. These formula can also be used to calculate all the parameters of the right pyramid obtained by joining all the …