For questions about triangles
2
votes
2answers
244 views
0
votes
2answers
58 views
A question on Trigonometry (bisector)
If two bisector of a triangular is equal, then it is Isosceles triangular.
0
votes
2answers
54 views
Calculating meeting point where line intersects arch
How do I find the point $p$ where the arch meets the red line if the angle of the blue are is known and the height of the yellow?
3
votes
1answer
152 views
Algebra question about Triangle Interiors
I was reading about Triangle Interiors on Wolfram Alpha:
http://mathworld.wolfram.com/TriangleInterior.html
and they have a simple equation:
$$\mathbf{v} = \mathbf{v}_0 + a\mathbf{v}_1 + ...
2
votes
1answer
50 views
Does the orthocenter have any special properties?
Each of the commonly known triangle centers I know has some sort of special property. For example:
The incenter is the center of the inscribed circle.
The circumcenter is the center of the circle ...
2
votes
1answer
90 views
Altitude of tetrahedron?
I'm really curious to know any relationships between the altitude of a tetrahedron and how the foot of this altitude splits the base triangle. For example if you have a tetrahedron PABC with apex P, ...
1
vote
1answer
33 views
P is a point in triangle $ABC$, what is $[APC]$?
Moderator Note: This question is part of an ongoing contest on Brilliant.org, and will be unlocked in 1 week.
P is a point in triangle $ABC$. The lines $AP$,$BP$, and $CP$ intersect the sides ...
1
vote
1answer
122 views
Geometry - optimal 2D mesh between X expendable points
Say you have X points on a plane.
If you connect two points, you form a line. Connecting three points forms a triangle.
A line cannot cross a line, and a smaller triangle cannot be created inside a ...
1
vote
1answer
72 views
Prove $(b-c)\sin A+(c-a)\sin B+(a-b)\sin C=0$
Prove the following equation, when you consider it as $BC=a$, $CA=b$, and $AB=c$ in a triangle $ABC$.
$(b-c)\sin A+(c-a)\sin B+(a-b)\sin C=0$
0
votes
1answer
51 views
Gergonne Point of a triangle coinciding with other triangle centers
I am trying to prove the following:
Let $T$ be the Gergonne point (the intersection of the lines that connect the points of tangency of the incircle with the vertices of the triangle) of $\triangle ...
0
votes
1answer
38 views
Triangle $z$-index interpolation between the vertices
I got a $2$D triangle, each vertex has a $2$D coordinate with a $z$-index value (NOT a $z$ coordinate!). The $z$-index value indicates whether a vertex lays on, in front of, or behind your screen ...
0
votes
1answer
152 views
Squares in a triangle?
I've got some trouble...
IJKL is a square and B, I, J, C are aligned (alternatively, |IJ| is confounded with |BC|.
h is the height of acute $\triangle$ ABC from A to side BC.
C1 is the red ...
0
votes
1answer
113 views
Barycentric coordinates of a triangle
I have to do what described in the picture below.
Any ideas on how to do this?
0
votes
1answer
58 views
how to find(measure,calculate) the distance (height,length) of an object?
I am trying to develope code ,so i need a mathematics help to proceed,please help me to find distance of an object using trigonometry r any applicable maths without using any sensors r external ...
2
votes
0answers
73 views
triangles in a grid of $n\times n$ with positive coordinates
I need to count the number of triangles formed in a grid of $n\times n$ with positive integer coordinates $(0..n)$. For example for $n = 1$ the answer is 4.
2
votes
0answers
253 views
Euler's Line of a medial triangle
I have the following problem with a comment below on the steps that I took so far. Here is the example: Let triangle ABC be any triangle. The midpoints of the sides in Triangle ABC are labeled $A', ...
2
votes
0answers
157 views
Does “triangle” in English exclude degenerate triangles?
Just for fun read few problems on the projeteuler.net website.
Number 276 found interesting:
Consider the triangles with integer sides a, b and c with a ≤ b ≤ c.
An integer sided triangle ...
1
vote
0answers
32 views
Proving that the circumcenter is the centroid
Given a triangle and its centroid, we know that the 3 line segments between the centroid and each of the vertices of the triangle divide the triangle into three smaller triangles. Prove that the ...
1
vote
0answers
21 views
maximum length of a scaled vector in a triangle (simplex)
Given a triangle (or, in general, a simplex) $T$ and a vector $\vec{s}$, I'd like to compute the quantity
$$
\max\{|x-y|: x,y\in T, x-y = \alpha \vec{s}, \alpha\in\mathbb{R}\}
$$
i.e., the maximum ...
1
vote
0answers
114 views
Finding side and angle of isosceles triangle inside two circles
I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something i'm struggling with for a project. :)
Basically, there are two circles, represented ...
1
vote
0answers
31 views
Two coloured plane
Can you prove that For any two angles $θ,ϕ$ there exists a monochromatic triangle that has angles $θ,ϕ,180−(θ+ϕ)$ in two coloured plane?
1
vote
0answers
58 views
How to find the inverse position inside a triangle
If i were standing in a triangle - How do i calculate the inverse of my position? Can it be done? It's easy inside a rectangle, but I can't think of how you would do it inside of a triangle.
I'm ...
1
vote
0answers
34 views
Triangular exponentation logarithm and inverse
The generalized formula of triangular exponentation on real numbers field is
$x ^ {\triangle y} = \frac {1} {y \cdot B (x, y)} = \frac {\Gamma(x + y)} {\Gamma(x) \cdot \Gamma(y + 1)} $
It's my ...
1
vote
0answers
326 views
General formula for computing triangular gaussian quadrature.
While this is a simple question, I'm totally lost. Is there any general formula for generation of n-point gaussian quadrature over a triangle?
I'll use this formula to generate a variable-point (7, ...
0
votes
0answers
37 views
Law sines in Spherical Triangle $\rightarrow$ Law sines in plane triangle
Could any one tell me how to estimate or get law of sines in Spherical Triangle to The Law of Sines in Plane Triangle? i.e $\frac{\sin a}{\sin A}=\frac{sin b}{\sin B}=\frac{\sin c}{\sin C}$ to ...
0
votes
0answers
55 views
Finding a formula for perimeter of triangles in triangle
I hope you are familiar with counting triangles in triangle problem. I've studied it a little recently. Now i want to find a formula for sum of perimeters of this all triangles but i don't know how to ...
0
votes
0answers
55 views
Sum of angles in a hyperbolic triangle with one ideal angle
I want to calculate the sum of the angles of the triangle formed in the hyperbolic plane from the points $(-1,1), (0,1)$, and $(1,1)$. This forms an angle at the origin which has an infinite slope for ...
0
votes
0answers
54 views
Figuring out angles of a second triangle based off of one side of a first
My friend and I are developing some image tracking software for a robot we are creating and we have this right here:
...
0
votes
0answers
80 views
Unknown depth issue: Triangle, Pyramid, Rotation, Translation, Zoom?
Edit: Had to delete the 2nd picture
Another tricky question. What you can see here is my physical pyramid built with 3 leds which form a triangle in 1 plane and another led in the mid center, about ...
0
votes
0answers
63 views
Determining a point in 3D space
So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
0
votes
0answers
31 views
Looking for different (analytical) approaches to a problem
Given 5 points in the plane any three of which are vertices of a triangle. Prove that among these triangles there is an obtuse triangle.
I was able to prove it by examining all possible cases. I ...
0
votes
0answers
33 views
Rotate a triangle to next 'visible' side
I have a triangle along the y/z axis (I can only see the flat side facing me).
How do I rotate it around the x axis so that the next side faces me?
0
votes
0answers
130 views
pixels in a projection of a triangle in 3d space onto a 3d plane through a pinhole camera
I have a triangle in 3d space. The x and y components of its vertices make a 2d right isoceles triangle. I am projecting it through a pinhole onto a plane. The projected triangles on the plane are now ...
0
votes
0answers
75 views
Get value of angle with 45 degrees as maximum and 0 and 90 degrees as minimum
I want the calculate the "value" of an angle in such a way that:
The angle of 45 degrees corresponds with the maximum value of 1
The angles of 0 and 90 degrees correspond with the minimum value of 0
...
0
votes
0answers
129 views
Uniform Random Points on a triangle using only edge plane normals
For a triangle $ABC$ in 3D (each point has x, y, z coordinates) is it possible to generate uniform random points on the triangle from only the following data:
Normal of the triangle plane $N = ...
0
votes
0answers
161 views
How to find the last coordinate of an isosceles triangle
I'm having some trouble trying to find out how to find the final coordinate on an isosceles triangle.
Here's a list of information that I have:
The length of the two equal sides (A and B)
The angle ...
0
votes
0answers
177 views
problem finding a 2D Point in a triangle
I have a Triangle with 3 Points - A, B and C and the angle alpha
A and B are fixed. C is any point at the side of 'b'
Alpha has at A and B the same size
I need to find any Point on side 'a' except B
...
