Proof the Dot Conjecture
Clash Royale CLAN TAG#URR8PPP
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I was reading the book Fermat's Last Theorem Simon Singh and in chapter 3 he mentions the "Dot Conjecture", and gives a proof in the appendix.
However, the "proof" seems to me as a just more elaborate way of stating that the proof is obvious and trivial. I was talking with a friend and she is also clueless. Furthermore, I couldn't even find any reference to it by googling.
I realise that, since this is a pop-math book, he might not be using the "official" name of this conjecture.
If somebody could explain it to me or at least give some link or further reading, I'd be very grateful.
first mention of the dot conjecture
the "proof"
graph-theory proof-explanation network
asked Aug 8 at 20:08
fazan
164
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up vote
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favorite
I was reading the book Fermat's Last Theorem Simon Singh and in chapter 3 he mentions the "Dot Conjecture", and gives a proof in the appendix.
However, the "proof" seems to me as a just more elaborate way of stating that the proof is obvious and trivial. I was talking with a friend and she is also clueless. Furthermore, I couldn't even find any reference to it by googling.
I realise that, since this is a pop-math book, he might not be using the "official" name of this conjecture.
If somebody could explain it to me or at least give some link or further reading, I'd be very grateful.
first mention of the dot conjecture
the "proof"
graph-theory proof-explanation network
asked Aug 8 at 20:08
fazan
164
Look up this wiki article. It's a well known theorem, but the proof that you've given is actually quite recent. There were some harder proofs before that one popped up (by Kelly). I wouldn't say that it is in any way trivial. What makes you think that ?
– Kolja
Aug 8 at 20:12
1
Neither of these links works for me. What is the "dot conjecture?"
– saulspatz
Aug 8 at 20:47
@saulspatz it is impossible to draw a dot diagram such that every line has at least three dots on it, and every dot is connected with every other dot by a line
– fazan
Aug 9 at 0:44
This is Sylvester's Theorem. Look at this : ics.uci.edu/~eppstein/junkyard/sylvester.html
– saulspatz
Aug 9 at 7:43
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I was reading the book Fermat's Last Theorem Simon Singh and in chapter 3 he mentions the "Dot Conjecture", and gives a proof in the appendix.
However, the "proof" seems to me as a just more elaborate way of stating that the proof is obvious and trivial. I was talking with a friend and she is also clueless. Furthermore, I couldn't even find any reference to it by googling.
I realise that, since this is a pop-math book, he might not be using the "official" name of this conjecture.
If somebody could explain it to me or at least give some link or further reading, I'd be very grateful.
first mention of the dot conjecture
the "proof"
graph-theory proof-explanation network
asked Aug 8 at 20:08
fazan
164
I was reading the book Fermat's Last Theorem Simon Singh and in chapter 3 he mentions the "Dot Conjecture", and gives a proof in the appendix.
However, the "proof" seems to me as a just more elaborate way of stating that the proof is obvious and trivial. I was talking with a friend and she is also clueless. Furthermore, I couldn't even find any reference to it by googling.
I realise that, since this is a pop-math book, he might not be using the "official" name of this conjecture.
If somebody could explain it to me or at least give some link or further reading, I'd be very grateful.
first mention of the dot conjecture
the "proof"
graph-theory proof-explanation network
asked Aug 8 at 20:08
fazan
164
asked Aug 8 at 20:08
fazan
164
asked Aug 8 at 20:08
fazan
164
asked Aug 8 at 20:08
fazan
164
164
Look up this wiki article. It's a well known theorem, but the proof that you've given is actually quite recent. There were some harder proofs before that one popped up (by Kelly). I wouldn't say that it is in any way trivial. What makes you think that ?
– Kolja
Aug 8 at 20:12
1
Neither of these links works for me. What is the "dot conjecture?"
– saulspatz
Aug 8 at 20:47
@saulspatz it is impossible to draw a dot diagram such that every line has at least three dots on it, and every dot is connected with every other dot by a line
– fazan
Aug 9 at 0:44
This is Sylvester's Theorem. Look at this : ics.uci.edu/~eppstein/junkyard/sylvester.html
– saulspatz
Aug 9 at 7:43
add a comment |Â
Look up this wiki article. It's a well known theorem, but the proof that you've given is actually quite recent. There were some harder proofs before that one popped up (by Kelly). I wouldn't say that it is in any way trivial. What makes you think that ?
– Kolja
Aug 8 at 20:12
1
Neither of these links works for me. What is the "dot conjecture?"
– saulspatz
Aug 8 at 20:47
@saulspatz it is impossible to draw a dot diagram such that every line has at least three dots on it, and every dot is connected with every other dot by a line
– fazan
Aug 9 at 0:44
This is Sylvester's Theorem. Look at this : ics.uci.edu/~eppstein/junkyard/sylvester.html
– saulspatz
Aug 9 at 7:43
Look up this wiki article. It's a well known theorem, but the proof that you've given is actually quite recent. There were some harder proofs before that one popped up (by Kelly). I wouldn't say that it is in any way trivial. What makes you think that ?
– Kolja
Aug 8 at 20:12
Look up this wiki article. It's a well known theorem, but the proof that you've given is actually quite recent. There were some harder proofs before that one popped up (by Kelly). I wouldn't say that it is in any way trivial. What makes you think that ?
– Kolja
Aug 8 at 20:12
1
1
Neither of these links works for me. What is the "dot conjecture?"
– saulspatz
Aug 8 at 20:47
Neither of these links works for me. What is the "dot conjecture?"
– saulspatz
Aug 8 at 20:47
@saulspatz it is impossible to draw a dot diagram such that every line has at least three dots on it, and every dot is connected with every other dot by a line
– fazan
Aug 9 at 0:44
@saulspatz it is impossible to draw a dot diagram such that every line has at least three dots on it, and every dot is connected with every other dot by a line
– fazan
Aug 9 at 0:44
This is Sylvester's Theorem. Look at this : ics.uci.edu/~eppstein/junkyard/sylvester.html
– saulspatz
Aug 9 at 7:43
This is Sylvester's Theorem. Look at this : ics.uci.edu/~eppstein/junkyard/sylvester.html
– saulspatz
Aug 9 at 7:43
add a comment |Â
1 Answer
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Taking back the proof from where it stops, imagine that there is a third point on that line (call it $ AB $ where $ A $ is on the left and $ B $ on the right, and call the "closest point" below $ P $), if the third point, say $ C $ is on the left of the picture, then the distance from $ A $ to $ PC $ is shorter than the dashed segment. You get a similar contradiction if $ C $ is on the right, or between $ A $ and $ B $.
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Taking back the proof from where it stops, imagine that there is a third point on that line (call it $ AB $ where $ A $ is on the left and $ B $ on the right, and call the "closest point" below $ P $), if the third point, say $ C $ is on the left of the picture, then the distance from $ A $ to $ PC $ is shorter than the dashed segment. You get a similar contradiction if $ C $ is on the right, or between $ A $ and $ B $.
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
add a comment |Â
up vote
0
down vote
Taking back the proof from where it stops, imagine that there is a third point on that line (call it $ AB $ where $ A $ is on the left and $ B $ on the right, and call the "closest point" below $ P $), if the third point, say $ C $ is on the left of the picture, then the distance from $ A $ to $ PC $ is shorter than the dashed segment. You get a similar contradiction if $ C $ is on the right, or between $ A $ and $ B $.
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Taking back the proof from where it stops, imagine that there is a third point on that line (call it $ AB $ where $ A $ is on the left and $ B $ on the right, and call the "closest point" below $ P $), if the third point, say $ C $ is on the left of the picture, then the distance from $ A $ to $ PC $ is shorter than the dashed segment. You get a similar contradiction if $ C $ is on the right, or between $ A $ and $ B $.
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
Taking back the proof from where it stops, imagine that there is a third point on that line (call it $ AB $ where $ A $ is on the left and $ B $ on the right, and call the "closest point" below $ P $), if the third point, say $ C $ is on the left of the picture, then the distance from $ A $ to $ PC $ is shorter than the dashed segment. You get a similar contradiction if $ C $ is on the right, or between $ A $ and $ B $.
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
answered Aug 8 at 20:34
Arnaud Mortier
19.2k22159
19.2k22159
add a comment |Â
add a comment |Â
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Look up this wiki article. It's a well known theorem, but the proof that you've given is actually quite recent. There were some harder proofs before that one popped up (by Kelly). I wouldn't say that it is in any way trivial. What makes you think that ?
– Kolja
Aug 8 at 20:12
1
Neither of these links works for me. What is the "dot conjecture?"
– saulspatz
Aug 8 at 20:47
@saulspatz it is impossible to draw a dot diagram such that every line has at least three dots on it, and every dot is connected with every other dot by a line
– fazan
Aug 9 at 0:44
This is Sylvester's Theorem. Look at this : ics.uci.edu/~eppstein/junkyard/sylvester.html
– saulspatz
Aug 9 at 7:43