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Term for meshes bounding a non-degenerate tetrahedral mesh in 3D?

Is there a term in the literature referring to triangle meshes that are the closed boundary of some non-self-intersecting, non-degenerate tetrahedral mesh embedded in $R^3$? This class of triangle ...
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Show that the Minkowski sum of two triangles in 3D is the union of Minkowski sums of each triangle along the other's edges?

I'd like to show (or disprove) the claim that the Minkowski sum of two triangles with vertices in $\mathbb{R}^3$, $A+B$, is equal to the union of the unions of the Minkowski sums of $A$ along all ...
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Generalization of Stewart's theorem?

I'm curious about the generalization of Stewart's theorem to more dimensions. MathWorld mentions that there is a generalization done by Bottema, but I could not find much information on it. All I ...
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Triangle centers from curve shortening

The curve-shortening flow transforms curves in the plane by moving each point perpendicularly to the curve at a speed proportional to the curvature at that point. It is usually defined for smooth ...
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Maximum height of intersection of triangles

I'd like some advice regarding the following question, which I have been struggling with for long time. Let's call the shaded region in the below $S_3$. It is the union of three congruent isosceles ...
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Maximum possible number of similar three-colored triangles

I want to maximize the number of similar triangles with vertices from three fixed sets, one vertex from each set. For example, if you fix two points $X$, $Y$ (i.e. two sets with only one member), then ...
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Intersecting Sets of Pythagorean Triples with Common Hypotenuses

For any $r\in\mathbb{N}$, let $A_r$ denote the set of all natural numbers that are potentially a side of a Pythagorean triple with hypotenuse $r$. Given any $N\in\mathbb{N}$, does there exist $r,s$ ...
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About the 'minimum triangle' which includes a convex bounded closed set

Question : Is the following true? "Letting $K$ be a convex bounded closed set on a plane, then there exists a triangle $M$, which includes $K$, such that $|M|\le 2|K|$. Here, $|M|,|K|$ is the area of ...
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Relationship between triangle free graphs and their minimum degree

Let $T$ be a triangle-free graph on $n$ vertices with minimum degree $\delta$ (which can be $0$). How does one show that $n >2\delta -1$? It seems to be true for bipartite graphs, but I cannot see ...
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What is the best *general triangle*?

During courses on geometry it is sometimes necessary to draw a triangle on the blackboard that can easily be recognized as a general triangle. It must not be rectangular and must not have two or more ...
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Are there Heronian triangles that can be decomposed into three smaller ones?

Is there anything known about the existence of Heronian triangles ABC (i.e. with rational side lengths and rational area) that can be decomposed into three Heronian triangles ABD, BCD, CAD? ...
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Series for envelope of triangle area bisectors

The lines which bisect the area of a triangle form an envelope as shown in this picture It is not difficult to show that the ratio of the area of the red deltoid to the area of the triangle is \...
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Triangles with Congruent Corresponding Sides that Cannot fold into a Tetrahedron

I've been trying to find, without much success, 4 triangles whose corresponding sides are congruent that cannot be folded into a tetrahedron. Anyone has any clue how to approach this problem?
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Impossible Heronian Triangles (Ratio of 2 Sides)

There is no Heronian triangle (or simply consider triangles on an integer lattice which also have integer side lengths) for which one side is half the length of another side. What other "side-side ...
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4-regular graphs with every edge in a triangle

I am interested in regular graphs in which every edge lies in a triangle. For 3-regular graphs, only the complete graph $K_4$ has this property, so there's not much to see here. For 4-regular graphs,...
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Triangles, squares, and discontinuous complex functions

Is there some onto function $f:$ $\mathbb{C}$ $\rightarrow$ $\mathbb{C}$ such that for each triangle $T$ (with its interior), $f(T)$ is a square (with interior, too) ? I would have the same question ...
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Routh's theorem in three dimensions

The most well known case of Routh's triangle theorem is: If the sides BC, CA,and AB are trisected at the points D, E, and F, respectively, then the area of the inside triangle formed by AD, BE, ...
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Malfatti Circles - Limiting point

"Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles" (for a brief historical account on this topic, see ...
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find the collision of a particle with a swept triangle.

Given there is triangle: V in 3D space that transforms over time t -> t1 to V1, and a static point P is somewhere in 3d space, how can I determine if P ever collides with V, and if so at what value of ...
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How to compute the average distance till intersection within a triangle in R^2?

Lots of simple questions because I am a noob. You are given 3 points in R^2; A, B, C forming a triangle with area > 0. You pick an arbitrary point inside ABC and an arbitrary direction. After some ...
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Egalitarian measures

A question I got asked I while ago: If $T$ is a triangle in $\mathbb R^2$, is there a function $f:T\to\mathbb R$ such that the integral of $f$ over each straight segment connecting two points in the ...
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Side-Angle-Side Congruence and the Parallel Postulate

Is there a link between the side-angle-side congruence of triangles and the parallel postulate? Specifically, does it follow from Euclid's first four axioms alone? In fact, does it even follow from ...