Τετάρτη 27 Μαρτίου 2024

Cosmology of Plane Geometry: Concepts and Theorems

Alexander Skutin,Tran Quang Hung, Antreas Hatzipolakis, Kadir Altintas: Cosmology of Plane Geometry: Concepts and Theorems>

ΨΗΦ. Cosmology of Plane Geometry: Concepts and Theorems
ΨΗΦ. Cosmology of Plane Geometry: Concepts and Theorems

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ΨΗΦ. Cosmology of Plane Geometry: Concepts and Theorems
ΨΗΦ. Cosmology of Plane Geometry: Concepts and Theorems

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Τρίτη 26 Μαρτίου 2024

Fermat-Torricelli and Napoleon Points

Thanasis Gakopoulos, Debabrata Nag: Fermat-Torricelli and Napoleon Points of a Triangle
A PLAGIOGONAL Approach

ΨΗΦ Fermat-Torricelli and Napoleon Points

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Σάββατο 9 Μαρτίου 2024

A PROOF OF MORLEY THEOREM

Thanasis Gakopoulos - Debabrata Nag, Morley Theorem ̶ PLAGIOGONAL Approach of Proof

Abstract: In this work, an attempt has been made by the authors to present a PLAGIOGONAL approach to prove the Morley Theorem involving the intersecting trisectors of the angles of a scalene triangle. The objective of the present work is to also establish the non-orthogonal coordinates of the vertices of Morley triangle.

Gakopoulos - Nag

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ETC1

X(73056) = X(2)X(58726)∩X(5)X(5422) Barycentrics    a^2*(a^14 - 5*a^12*b^2 + 9*a^10*b^4 - 5*a^8*b^6 - 5*a^6*b^8 + 9*a^4*b^10 - 5*a^2*b^12 +...

  • EUCLID 4404
  • HOMOTHETIC TRIANGLES and EULER LINES
    Theorem 1. Let ABC be an equilateral triangle and P a point. The Euler lines of the triangles PBC,PCA,PAB are concurent.Denote the point ...
  • ANOPOLIS CIRCLE
    Let ABC be a triangle. Denote: (N1),(N2), (N3) = the NPCs of IBC, ICA, IAB, resp. (12), (13) = the reflections of (N1) in BI, CI, resp. ...