Science and Mathematics 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 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

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

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

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

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 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.