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

A construction of X8056

From a interpretation of a system of linear equations we arrive to a construction of the point X8056 and a property of circumconics.

A construction of X8056

Circumconics with asymptotes making a given angle

This is an updated version of my recent article published in Forum Geometricorum (Volume, 18 (2018) 367--370.

Circumconics with asymptotes making a given angle

A property of the circle (O,K)

This is a generalization of a formula given by Kadir Altintas:


A property of circle (O, K).

José María Pedret, in memoriam

Bisección de un cono

Queremos dividir con un plano un cono en dos partes, de manera que el plano corte a la base en un punto y ambas partes tengan el mismo volumen.


Fijado un punto de la base bastaría saber cuál es el punto sobre la generatriz opuesta por el que debería pasar el plano. Para ver la solución de este problema, pulsa aquí:

Bisección de un cono