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[2] viXra:2104.0039 [pdf] submitted on 2021-04-08 17:26:13
Authors: Harish Chandra Rajpoot
Comments: 9 Pages. Original Research Work
The author derives mathematical formula to analytically compute the V-cut angle (δ) required for rotating through the same angle (θ) the two co-planar planes, initially meeting at a common edge bisecting the angle (α) between their intersecting straight edges, about their intersecting straight edges until their new straight edges (generated after removing V-shaped planar region) coincide. As a result, we get a point (apex) where three planes intersect one another out of which two are original planes (rotated) & third one is their co-plane (fixed).
This theorem is very useful for making specific pyramidal flat containers with polygonal (regular or irregular) base using sheet of paper, cardboard, polymer, metal or alloy which can be easily bent and butt-joined at the mating edges, closed right pyramids/bi-pyramids & polyhedrons having two regular n-polygonal & 2n congruent trapezoidal faces. The author has also presented some paper models for making pyramidal flat containers with regular pentagonal, heptagonal and octagonal bases.
Category: Geometry
[1] viXra:2104.0009 [pdf] submitted on 2021-04-03 07:32:25
Authors: Antoine Balan
Comments: 2 pages, written in french
We show that a conformally isometric application of the space is an isometry composed with an homothety.
Category: Geometry
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