# Questions tagged [triangles]

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### Interesting geometry problem [closed]

Let n be a natural number and let M be the set of points located on the border or inside the triangle OAB , where A(n,0) and B(0,n). Find the maximum cardinality of a subset S of M with the property ...
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### Force–Balance Matrix for FEM [closed]

Consider 4 vertices that are grouped into 2 triangles: I need to construct a system of equations $$\mathbf{A} f = -f^\text{ext}$$ such that the forces $f$ balance the external forces and satisfy ...
1 vote
59 views

### Partitioning polygons into obtuse isosceles triangles

Ref: Partitioning polygons into acute isosceles triangles Partition of polygons into 'strongly acute' and 'strongly obtuse' triangles https://math.stackexchange.com/questions/1052063/...
1 vote
59 views

### Cutting off odd numbers of equal area triangles from a unit square

Two earlier related posts: Cutting the unit square into pieces with rational length sides On a possible variant of Monsky's theorem Question: for odd n, how does one cut the unit square into n ...
1 vote
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### Tiling the plane with pair-wise non-congruent and mutually similar triangles

Question: Is it possible to tile the plane with triangles that are (1) mutually similar, (2) pairwise non-congruent and (3)non-right? No other constraints. Note 1: Reg requirement 3 above: since any ...
1 vote
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### How many convex polygons can be made from $n$ identical right angle triangles?

Whilst working on a Tangram problem, I came across the need to find the total number of convex shapes that can be produced from $16$ identical (isosceles) right angle triangles (since the Tangram can ...
93 views

### Is Morley’s observation complete?

Morley’s observation states that in a triangle the intersections of trisectors proximal to a (triangle) side lie six by six on three triples of parallel lines that make angles of 60° with each other. ...
173 views

### Do the heights of an acute triangle intersect at a single point (in neutral geometry)?

A well-known result of the Euclidean planimetry says that the heights of any triangle have a common point called the orthocentre of the triangle. This result is not true in neutral geometry (i.e., ...
130 views

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### The 4th vertex of a triangle?

I was immensely surprised and amused by the idea of the fourth side of a triangle that was introduced by B.F.Sherman in 1993. 'Sherman's Fourth Side of a Triangle' by Paul Yiu is available here. ...
283 views

### Constructing an equilateral triangle using Tarski's axioms for geometry

In Euclid's first geometry proposition, he constructs an equilateral triangle given an arbitrary line segment. I was wondering if it was possible to prove this straight from Tarski's axioms for ...
264 views

### Need help with finding all angles of 11 sided 3D object [closed]

Question: I'm an artist trying to build a hendecahedron for a project (Image below to see the shape). This object consists of 5 pentagons at the base, 1 pentagon on the bottom, then 5 quadrilaterals ...
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### Three circles intersecting at one point

Can you provide a proof for the following proposition: Proposition. Let $\triangle ABC$ be an arbitrary triangle with nine-point center $N$ and circumcenter $O$. Let $A',B',C'$ be a reflection points ...