Geometry

2006 Submissions

[6] viXra:2006.0269 [pdf] submitted on 2020-06-30 11:55:41

On a Special Family of Right Triangles

Authors: Juan Moreno Borrallo
Comments: 5 Pages.

In this brief paper they are studied the right triangles (a,b,c) such that c-b=b-a, showing the maths behind their most remarkable special property.
Category: Geometry

[5] viXra:2006.0241 [pdf] replaced on 2020-08-22 01:05:13

Pythagoras Theorem is an Alternate Form of Ptolemy’s Theorem

Authors: Radhakrishnamurty Padyala
Comments: 5 pages 4 Figures

Generally, the proofs given to demonstrate Ptolemy’s theorem prove Pythagoras theorem as a special case of Ptolemy’s theorem when certain special conditions are imposed. We prove in this article, that Pythagoras theorem follows from Ptolemy’s theorem in all cases. Therefore, we may say that Pythagoras rediscovered Ptolemy’s theorem.
Category: Geometry

[4] viXra:2006.0197 [pdf] replaced on 2020-11-11 08:53:33

Triple Cosines Lemma and π-Sums of Arccosines

Authors: Yuly Shipilevsky
Comments: 6 Pages.

We obtain a relationship between cosines of two independent angles and cosine of the angle that depends on them in 3D space and then we use that relationship to obtain π-sums of Arccosines
Category: Geometry

[3] viXra:2006.0108 [pdf] submitted on 2020-06-13 07:48:45

On the Existence of Triangles

Authors: Volker Thürey
Comments: 2 Pages.

We formulate criterions about the existence of triangles depending on its sidelengths.
Category: Geometry

[2] viXra:2006.0095 [pdf] submitted on 2020-06-11 17:00:55

Pappus Chain and Division by Zero Calculus

Authors: Hiroshi Okumura
Comments: 6 Pages.

We consider circles touching two of three circles forming arbeloi with division by zero and division by zero calculus.
Category: Geometry

[1] viXra:2006.0050 [pdf] replaced on 2021-03-04 08:19:24

L’inverso Della Sezione Aurea e la Sorella Speculare Della Spirale Aurea. the Reverse of the Golden Ratio and the Mirror Sister of the Golden Spiral.

Authors: Dante Servi
Comments: 10 Pages. Copyright by Servi Dante.

Le spirali logaritmiche (r=ae^bθ), partendo da un punto di distanza (a) dalla loro origine si possono sviluppare allontanandosi (se b > 0) oppure avvicinandosi (se b < 0) ad essa, questo provo a dire che vale anche per la spirale aurea. Ho corretto la proposta per semplificare la costruzione della spirale aurea basata sui rettangoli aurei. The logarithmic spirals (r=ae^bθ), starting from a point of distance (a) from their origin, can develop by moving away (if b > 0) or approaching (if b < 0) to it, this I try to say that also applies to the golden spiral. I corrected the proposal to simplify the construction of the golden spiral based on the golden rectangles.
Category: Geometry