We show that a natural hybridation construction of lattices in SU(n, 1) to produce (non-arithmetic) lattices in SU(n + 1, 1) fails when n = 1 for most triangle groups in SU(1, 1).

We study Euler’s problem of determination of a triangle from its circumcenter, orthocenter, and incenter as a problem of geometric construction. While it cannot be solved using ruler and compass, we construct the vertices by intersecting a circle with a rectangular hyperbola, both easily constructed from the given triangle centers.

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. We interprete some of the so-called Lyapunov exponents of the Kontsevich–Zorich cocycle as normalize...

The SQuad data structure represents the connectivity of a triangle mesh by its “S table” of about 2 rpt (integer references per triangle). Yet it allows for a simple implementation of expected constant-time, random-access operators for traversing the mesh, including in-order traversal of the triangles incident upon a vertex. SQuad is more compact than the Corner Table (CT), which stores 6 rpt, ...

Most of the previous multiresolution models use exclusively the triangle graphic primitive both in the data structure and in the rendering stage. Only a few models use another graphic primitive in this rendering process and just one uses the triangle fan as the basic primitive of the model. In this paper we present the first multiresolution model, Multiresolution Triangle Strips, that uses the ...

Given a triangle center we can draw line segments from each vertex through the triangle center to the opposite side, this splits the triangle into six smaller triangles called daughters. Consider the following problem: Given a triangle S and a rule for finding a center find a triangle T , if possible, so that one of the daughters of T , when using the rule is S. We look at this problem for the ...

Is it possible that the lengths of two sides of a primitive Heron triangle have a c ommon factor? The triangle with sides 9, 65, 70 and area 252 shows that this is possible. But notice that the common factor 5 is a prime of the form 4+1. Surprisingly, however, such a common factor cannot be a prime of the form 4 ; 1. Heron's name is familiar to anyone who has used the formula = p s(s ; a)(s ; b...