Education Commons^™

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

Harish Chandra Rajpoot H.C. Rajpoot

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

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 …

Mathematical Analysis Of Great Rhombicuboctahedron (An Archimedean Solid) By H.C. Rajpoot, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

All the important parameters of a great rhombicuboctahedron (an Archimedean solid), having 12 congruent square faces, 8 regular hexagonal faces, 6 congruent regular octagonal faces each of equal edge length, 72 edges & 48 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 the solid angle subtended by each square face, regular hexagonal face & regular octagonal face & their normal distances from the center of great rhombicuboctahedron, dihedral angles between the adjacent faces, inscribed radius, circumscribed radius, mean radius, surface area & volume. …

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

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 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 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 …