Splitting equilateral triangle into 5 equal parts
14
$begingroup$
Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable
from each other by a rigid motion) parts?
geometry dissection
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
asked Oct 29 '10 at 15:35
JaskaJaska
621518
$endgroup$
add a comment |
14
$begingroup$
Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable
from each other by a rigid motion) parts?
geometry dissection
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
asked Oct 29 '10 at 15:35
JaskaJaska
621518
$endgroup$
1
$begingroup$
Does "reflection" count as rigid motion?
$endgroup$
– kennytm
Oct 29 '10 at 17:20
$begingroup$
I think it does not leave the arrangement of triangle angles unchanged so no.
$endgroup$
– Jaska
Oct 29 '10 at 20:10
add a comment |
14
14
14
1
$begingroup$
Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable
from each other by a rigid motion) parts?
geometry dissection
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
asked Oct 29 '10 at 15:35
JaskaJaska
621518
$endgroup$
Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable
from each other by a rigid motion) parts?
geometry dissection
geometry dissection
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
asked Oct 29 '10 at 15:35
JaskaJaska
621518
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
asked Oct 29 '10 at 15:35
JaskaJaska
621518
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
edited Sep 13 '16 at 6:22
Ivan Neretin
9,02421635
9,02421635
asked Oct 29 '10 at 15:35
JaskaJaska
621518
asked Oct 29 '10 at 15:35
JaskaJaska
621518
asked Oct 29 '10 at 15:35
JaskaJaska
621518
621518
1
$begingroup$
Does "reflection" count as rigid motion?
$endgroup$
– kennytm
Oct 29 '10 at 17:20
$begingroup$
I think it does not leave the arrangement of triangle angles unchanged so no.
$endgroup$
– Jaska
Oct 29 '10 at 20:10
add a comment |
1
$begingroup$
Does "reflection" count as rigid motion?
$endgroup$
– kennytm
Oct 29 '10 at 17:20
$begingroup$
I think it does not leave the arrangement of triangle angles unchanged so no.
$endgroup$
– Jaska
Oct 29 '10 at 20:10
1
1
$begingroup$
Does "reflection" count as rigid motion?
$endgroup$
– kennytm
Oct 29 '10 at 17:20
$begingroup$
Does "reflection" count as rigid motion?
$endgroup$
– kennytm
Oct 29 '10 at 17:20
$begingroup$
I think it does not leave the arrangement of triangle angles unchanged so no.
$endgroup$
– Jaska
Oct 29 '10 at 20:10
$begingroup$
I think it does not leave the arrangement of triangle angles unchanged so no.
$endgroup$
– Jaska
Oct 29 '10 at 20:10
add a comment |
2 Answers
2
active
oldest
votes
5
$begingroup$
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
$endgroup$
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
1
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
1
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
add a comment |
15
+100
$begingroup$
The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html
edited Jan 6 at 19:46
naXa
1034
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
$endgroup$
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
5
$begingroup$
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
$endgroup$
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
1
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
1
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
add a comment |
5
$begingroup$
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
$endgroup$
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
1
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
1
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
add a comment |
5
5
5
$begingroup$
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
$endgroup$
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
edited Apr 30 '16 at 17:54
Grigory M
13.7k357104
13.7k357104
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
answered Oct 30 '10 at 1:54
Joseph MalkevitchJoseph Malkevitch
4,7051113
4,7051113
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
1
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
1
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
add a comment |
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
1
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
1
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
$begingroup$
In particular, look at the pinwheel tiling, which is for right triangles. See en.wikipedia.org/wiki/Pinwheel_tiling
$endgroup$
– lhf
Oct 30 '10 at 2:18
1
1
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
Umm. I was looking a solution for equilateral triangle so how right triangle helps me?
$endgroup$
– Jaska
Oct 30 '10 at 12:02
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
$begingroup$
It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."
$endgroup$
– Joel Reyes Noche
Nov 16 '11 at 3:59
1
1
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
$begingroup$
michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)
$endgroup$
– Lam Chau
Oct 24 '12 at 3:33
add a comment |
15
+100
$begingroup$
The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html
edited Jan 6 at 19:46
naXa
1034
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
$endgroup$
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
add a comment |
15
+100
$begingroup$
The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html
edited Jan 6 at 19:46
naXa
1034
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
$endgroup$
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
add a comment |
15
+100
15
+100
15
+100
$begingroup$
The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html
edited Jan 6 at 19:46
naXa
1034
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
$endgroup$
The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html
edited Jan 6 at 19:46
naXa
1034
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
edited Jan 6 at 19:46
naXa
1034
edited Jan 6 at 19:46
naXa
1034
edited Jan 6 at 19:46
naXa
1034
1034
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
answered Jan 26 '16 at 9:34
Sergey MarkelovSergey Markelov
34625
34625
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
add a comment |
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
$begingroup$
Note: one of the figures has to be reflected to match others. The OP says "I think it [reflection] does not leave the arrangement of triangle angles unchanged so no [reflection is not counted as rigid motion]."
$endgroup$
– naXa
Jan 6 at 18:52
add a comment |
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1
$begingroup$
Does "reflection" count as rigid motion?
$endgroup$
– kennytm
Oct 29 '10 at 17:20
$begingroup$
I think it does not leave the arrangement of triangle angles unchanged so no.
$endgroup$
– Jaska
Oct 29 '10 at 20:10