Mixing
The pattern of possible numbers of non-congruent triangles for different size dot grids.
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent).
If I start with nine dots, arranged in three rows of three to make a square, how many different (non-congruent) triangles is it possible to draw?
What if I start with a square formed of sixteen dots?
Can you generalise for n2 dots?
triangle
asked Jul 21 at 8:28
PERCIVAL
94
add a comment |Â
up vote
0
down vote
favorite
If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent).
If I start with nine dots, arranged in three rows of three to make a square, how many different (non-congruent) triangles is it possible to draw?
What if I start with a square formed of sixteen dots?
Can you generalise for n2 dots?
triangle
asked Jul 21 at 8:28
PERCIVAL
94
Do the triangles have to be made of as many dots as n+1
– Pi_die_die
Jul 21 at 10:45
Start with a simpler problem that you cannot yet solve: How many nondegenerate triangles are there in a grid of $n^2$ points?
– Christian Blatter
Jul 21 at 13:55
Can the triangles be turned in space? Or only in the plane? I.e., do you distinguish them according to chirality?
– joriki
Jul 21 at 14:38
The triangles you count for each number of dots can not be rotations of reflection of each other.
– PERCIVAL
Jul 22 at 13:28
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent).
If I start with nine dots, arranged in three rows of three to make a square, how many different (non-congruent) triangles is it possible to draw?
What if I start with a square formed of sixteen dots?
Can you generalise for n2 dots?
triangle
asked Jul 21 at 8:28
PERCIVAL
94
If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent).
If I start with nine dots, arranged in three rows of three to make a square, how many different (non-congruent) triangles is it possible to draw?
What if I start with a square formed of sixteen dots?
Can you generalise for n2 dots?
triangle
asked Jul 21 at 8:28
PERCIVAL
94
edited Jul 21 at 10:18
asked Jul 21 at 8:28
PERCIVAL
94
asked Jul 21 at 8:28
PERCIVAL
94
asked Jul 21 at 8:28
PERCIVAL
94
94
Do the triangles have to be made of as many dots as n+1
– Pi_die_die
Jul 21 at 10:45
Start with a simpler problem that you cannot yet solve: How many nondegenerate triangles are there in a grid of $n^2$ points?
– Christian Blatter
Jul 21 at 13:55
Can the triangles be turned in space? Or only in the plane? I.e., do you distinguish them according to chirality?
– joriki
Jul 21 at 14:38
The triangles you count for each number of dots can not be rotations of reflection of each other.
– PERCIVAL
Jul 22 at 13:28
add a comment |Â
Do the triangles have to be made of as many dots as n+1
– Pi_die_die
Jul 21 at 10:45
Start with a simpler problem that you cannot yet solve: How many nondegenerate triangles are there in a grid of $n^2$ points?
– Christian Blatter
Jul 21 at 13:55
Can the triangles be turned in space? Or only in the plane? I.e., do you distinguish them according to chirality?
– joriki
Jul 21 at 14:38
The triangles you count for each number of dots can not be rotations of reflection of each other.
– PERCIVAL
Jul 22 at 13:28
Do the triangles have to be made of as many dots as n+1
– Pi_die_die
Jul 21 at 10:45
Do the triangles have to be made of as many dots as n+1
– Pi_die_die
Jul 21 at 10:45
Start with a simpler problem that you cannot yet solve: How many nondegenerate triangles are there in a grid of $n^2$ points?
– Christian Blatter
Jul 21 at 13:55
Start with a simpler problem that you cannot yet solve: How many nondegenerate triangles are there in a grid of $n^2$ points?
– Christian Blatter
Jul 21 at 13:55
Can the triangles be turned in space? Or only in the plane? I.e., do you distinguish them according to chirality?
– joriki
Jul 21 at 14:38
Can the triangles be turned in space? Or only in the plane? I.e., do you distinguish them according to chirality?
– joriki
Jul 21 at 14:38
The triangles you count for each number of dots can not be rotations of reflection of each other.
– PERCIVAL
Jul 22 at 13:28
The triangles you count for each number of dots can not be rotations of reflection of each other.
– PERCIVAL
Jul 22 at 13:28
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2858330%2fthe-pattern-of-possible-numbers-of-non-congruent-triangles-for-different-size-do%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Do the triangles have to be made of as many dots as n+1
– Pi_die_die
Jul 21 at 10:45
Start with a simpler problem that you cannot yet solve: How many nondegenerate triangles are there in a grid of $n^2$ points?
– Christian Blatter
Jul 21 at 13:55
Can the triangles be turned in space? Or only in the plane? I.e., do you distinguish them according to chirality?
– joriki
Jul 21 at 14:38
The triangles you count for each number of dots can not be rotations of reflection of each other.
– PERCIVAL
Jul 22 at 13:28