An insanely huge locus!

A problem proposed by Thanos Kalogerakis leads to an insanely huge locus: an algebraic curve of the 30th degree whose equation occupies more than 16500 pages!

Read: An insanely huge locus!

Attachment: Source code and equation of the locus

El número 6174

Presentamos esta conocida propiedad del número 6174 acompañándolo todo con algunas instrucciones del programa Mathematica.

Descarga: 6174.pdf

Un Problema de Silver Samuel Palacios Paulino

Descarga: Un Problema de Silver Samuel Palacios Paulino

Sum of ratios into hyperbola

We generalize a relation involving ratios proposed by Thanos Kalogerakis and find a hyperbola as locus. We construct the hyperbola by using Pascal theorem and find other formulas.

Sum of ratios involving ratios

Another construction of an inconic with given perspector

Given a point $P$ with cevian triangle $A'B'C'$ we construct two extra points $M, N$ lying on the inconic tangent to $BC$, $CA$, $AB$ at $A', B', C'$ respectively.

Another construction of an inconic with given perspector

Sum of digit powers

Sum of digits powers

Four points on Euler Line

I introduce  four new points on Euler line:

I found these points trying to solve a problem proposed by Kadir Altintas.

Given a triangle ABC and a point P, call DEF its circuncevian triangle. The circumcenters of six triangles PBD, PDC, PCE, PEA, PAF and PFB lie on the same conic. When this conic is a circle?

Updated March, 1. Additions/corrections are in red.

Four points on Euler line