How many non-congruent triangles are there on an $ntimes n$ dot grid? [closed]

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How many non-congruent triangles are there on a $3times 3$ and a $4times 4$ dot grid?

euclidean-geometry triangle

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edited Jul 17 at 17:41

Arthur

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asked Jul 17 at 17:31

PERCIVAL

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closed as off-topic by amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson Jul 18 at 0:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

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  I have posted the main question which this relates to.
  – PERCIVAL
  Jul 21 at 8:29
  
  

  
  
  
  

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up vote
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How many non-congruent triangles are there on a $3times 3$ and a $4times 4$ dot grid?

euclidean-geometry triangle

share|cite|improve this question

edited Jul 17 at 17:41

Arthur

98.9k793175

asked Jul 17 at 17:31

PERCIVAL

94

closed as off-topic by amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson Jul 18 at 0:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I have posted the main question which this relates to.
  – PERCIVAL
  Jul 21 at 8:29
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

How many non-congruent triangles are there on a $3times 3$ and a $4times 4$ dot grid?

euclidean-geometry triangle

share|cite|improve this question

edited Jul 17 at 17:41

Arthur

98.9k793175

asked Jul 17 at 17:31

PERCIVAL

94

How many non-congruent triangles are there on a $3times 3$ and a $4times 4$ dot grid?

euclidean-geometry triangle

share|cite|improve this question

edited Jul 17 at 17:41

Arthur

98.9k793175

asked Jul 17 at 17:31

PERCIVAL

94

share|cite|improve this question

share|cite|improve this question

edited Jul 17 at 17:41

Arthur

98.9k793175

edited Jul 17 at 17:41

Arthur

98.9k793175

edited Jul 17 at 17:41

Arthur

98.9k793175

98.9k793175

asked Jul 17 at 17:31

PERCIVAL

94

asked Jul 17 at 17:31

PERCIVAL

94

asked Jul 17 at 17:31

PERCIVAL

94

94

closed as off-topic by amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson Jul 18 at 0:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson Jul 18 at 0:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Parcly Taxel, Arthur, Alex Francisco, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I have posted the main question which this relates to.
  – PERCIVAL
  Jul 21 at 8:29
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I have posted the main question which this relates to.
  – PERCIVAL
  Jul 21 at 8:29
  
  

  
  
  
  

I have posted the main question which this relates to.
– PERCIVAL
Jul 21 at 8:29

I have posted the main question which this relates to.
– PERCIVAL
Jul 21 at 8:29

add a comment | 

1 Answer
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accepted

The 8 distinct triangles from a 3x3 grid can be described with 112, 125, 145, 158, 224, 255, 448, 455, with the first having edges $(sqrt1,sqrt1,sqrt2)$ and the last having edges $(sqrt4,sqrt5,sqrt5)$

Here are the 29 triangles from the 4 by 4 -- I only needed half the dots.

Here are the 79 triangles from the 5 by 5 -- I only needed half the dots.

Congruence classes of triangles which can be drawn using lattice points in n X n grid as vertices.

8, 29, 79, 172, 333, 587, 963, 1494.

This is OEIS sequence A028419.

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edited Jul 17 at 18:19

answered Jul 17 at 17:42

Ed Pegg

9,19732486

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
  – PERCIVAL
  Jul 17 at 17:45
  

  
  
  
  

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote



accepted

The 8 distinct triangles from a 3x3 grid can be described with 112, 125, 145, 158, 224, 255, 448, 455, with the first having edges $(sqrt1,sqrt1,sqrt2)$ and the last having edges $(sqrt4,sqrt5,sqrt5)$

Here are the 29 triangles from the 4 by 4 -- I only needed half the dots.

Here are the 79 triangles from the 5 by 5 -- I only needed half the dots.

Congruence classes of triangles which can be drawn using lattice points in n X n grid as vertices.

8, 29, 79, 172, 333, 587, 963, 1494.

This is OEIS sequence A028419.

share|cite|improve this answer

edited Jul 17 at 18:19

answered Jul 17 at 17:42

Ed Pegg

9,19732486

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
  – PERCIVAL
  Jul 17 at 17:45
  

  
  
  
  

add a comment | 

up vote
0
down vote



accepted

The 8 distinct triangles from a 3x3 grid can be described with 112, 125, 145, 158, 224, 255, 448, 455, with the first having edges $(sqrt1,sqrt1,sqrt2)$ and the last having edges $(sqrt4,sqrt5,sqrt5)$

Here are the 29 triangles from the 4 by 4 -- I only needed half the dots.

Here are the 79 triangles from the 5 by 5 -- I only needed half the dots.

Congruence classes of triangles which can be drawn using lattice points in n X n grid as vertices.

8, 29, 79, 172, 333, 587, 963, 1494.

This is OEIS sequence A028419.

share|cite|improve this answer

edited Jul 17 at 18:19

answered Jul 17 at 17:42

Ed Pegg

9,19732486

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
  – PERCIVAL
  Jul 17 at 17:45
  

  
  
  
  

add a comment | 

up vote
0
down vote



accepted

up vote
0
down vote



accepted

The 8 distinct triangles from a 3x3 grid can be described with 112, 125, 145, 158, 224, 255, 448, 455, with the first having edges $(sqrt1,sqrt1,sqrt2)$ and the last having edges $(sqrt4,sqrt5,sqrt5)$

Here are the 29 triangles from the 4 by 4 -- I only needed half the dots.

Here are the 79 triangles from the 5 by 5 -- I only needed half the dots.

Congruence classes of triangles which can be drawn using lattice points in n X n grid as vertices.

8, 29, 79, 172, 333, 587, 963, 1494.

This is OEIS sequence A028419.

share|cite|improve this answer

edited Jul 17 at 18:19

answered Jul 17 at 17:42

Ed Pegg

9,19732486

The 8 distinct triangles from a 3x3 grid can be described with 112, 125, 145, 158, 224, 255, 448, 455, with the first having edges $(sqrt1,sqrt1,sqrt2)$ and the last having edges $(sqrt4,sqrt5,sqrt5)$

Here are the 29 triangles from the 4 by 4 -- I only needed half the dots.

Here are the 79 triangles from the 5 by 5 -- I only needed half the dots.

Congruence classes of triangles which can be drawn using lattice points in n X n grid as vertices.

8, 29, 79, 172, 333, 587, 963, 1494.

This is OEIS sequence A028419.

share|cite|improve this answer

edited Jul 17 at 18:19

answered Jul 17 at 17:42

Ed Pegg

9,19732486

share|cite|improve this answer

share|cite|improve this answer

edited Jul 17 at 18:19

edited Jul 17 at 18:19

edited Jul 17 at 18:19

answered Jul 17 at 17:42

Ed Pegg

9,19732486

answered Jul 17 at 17:42

Ed Pegg

9,19732486

answered Jul 17 at 17:42

Ed Pegg

9,19732486

9,19732486

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
  – PERCIVAL
  Jul 17 at 17:45
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
  – PERCIVAL
  Jul 17 at 17:45
  

  
  
  
  

Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
– PERCIVAL
Jul 17 at 17:45

Thanks. So do you mean that for a 3x3 grid their are 8 different triangles?
– PERCIVAL
Jul 17 at 17:45

add a comment |