Conveners
Geometry
- Zdenka Kolar-Begović
In this talk, we study the Brocard triangles of a triangle in the isotropic plane. We present some statements about the first and the second Brocard triangle in the isotropic plane and consider the relationships between Brocard triangles and some other objects related to a triangle in the isotropic plane. We also investigate some interesting properties of these triangles and consider...
Any triangle in an isotropic plane has a circumcircle $u$ and an incircle $i$. It turns out that there are infinitely many triangles with the same circumcircle $u$ and incircle $i$. This one-parameter family of triangles is called a poristic system of triangles.
We prove that all triangles in a poristic system share the centroid and the Feuerbach point. The symmedian point and the...
In this talk, we observe a one-parameter triangle family,
where two vertices are fixed and the third vertex lies on
a given line. For this family of triangles, we observe the
loci of centroids, orthocenters, circumcenters, incenters,
excenters and some triangle elements associated to these
triangle points.
We describe refinements of Euler's inequality that the circumradius is at least n times larger than the inradius of an n-simplex T, provide explicit refinements for n = 2,3,4 and a recursive procedure for higher dimensions. We describe probability application in astrophysics. The final remarks are on Grace-Danielsson-Drozdev theorem (2024) on the upper bound of the distance between the...
