0
votes
1answer
56 views

Number of triangles formed by all chords between $n$ points on a circle

We have $n$ point on circumference of a circle. We draw all chords between this points. No three chords are concurrent. How many triangles exist that their apexes could be on circumference of ...
2
votes
2answers
72 views

Integer Triangles with Perimeter $n$

How many triangles are possible with positive integer side lengths for perimeter $n$? My attempt so far has been bashing for $n=1,\; 2, \cdots , 13$ and calculating how many triangles are ...
6
votes
2answers
96 views

Number of triangles in a graph based on number of edges

Given a graph $G(V,E)$, what is the maximum number of triangles that this graph can have in terms of $|E|$? I know that there is a triangle listing algorithm that lists all the triangles in ...
1
vote
2answers
49 views

Number of Equilateral triangles in circle with 42 evenly spaced points?

I know that the answer is 42/3 = 14 points, or in general for a circle with N points it is N/3, but I don't know why it actually works. Why is the number of equilateral triangles for a circle with N ...
1
vote
1answer
50 views

Number of ways to form isosceles triangle by picking points on a circle

Given a circle with 24 evenly spaced points, how would you find the number of possible isosceles triangles (which includes equilateral) that can by drawn using the points? My attempt was to say that ...
4
votes
2answers
609 views

Combinatorics. Inscribed Triangle in a decagon. No shared sides.

How many different triangles can be inscribed inside a regular decagon such that the triangle shares its vertices with the vertices of the decagon, but the triangle shares none of its sides? Here is ...
1
vote
1answer
482 views

Integer solutions to linear equation – Triangle with set perimeter

We have a triangle with the sides a, b and c where: ...
3
votes
0answers
72 views

How many unique centroids?

Possible Duplicate: How many positions for centroid of triangle? Suppose that we are given 40 points equally spaced around the perimeter of a square, so that four of them are located at the ...
0
votes
1answer
2k views

How many triangles can be formed from N points on a circle?

I have a circle with N points on it, and I want to determine how many triangles can be formed using these points. How can I do this? Thanks! Andrew
1
vote
2answers
794 views

What is the number of triangles with integer sides, given the length of the longest side?

Suppose $a,b,c \in\mathbb N$, and the value of $c$ is known and fixed, while $a$ and $b$ are unknown and are both smaller than $c$. What is the total number of unique triangles possible with $a, b$ ...
3
votes
1answer
3k views

How many triangles with integral side lengths are possible, provided their perimeter is $36$ units?

How many triangles with integral side lengths are possible, provided their perimeter is $36$ units? My approach: Let the side lengths be $a, b, c$; now, $$a + b + c = 36$$ Now, $1 \leq a, b, c ...
30
votes
6answers
13k views

How many triangles are there?

The question is how many triangles are there in the following picture? I have thought to solve it by creating a formula based on the angles of the lines starting from the bottom of each side. I ...