Prove or disprove the non colinearity of three points
$begingroup$
Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $ABcap CD={E}$, $ACcap BD={F}$ and $ADcap BC={G}$. Then the points $E,F,G$ are not collinear.
I tried to prove by contradiction defining a graph on set ${A,B,C,D}$ with edge between two points if they lie on different sides of the line $EFG$ but couldn't arrive to a contradiction. Maybe there is a counterexample in Poincaré Geometry.
geometry
asked Dec 6 '18 at 21:31
user183294user183294
353
$endgroup$
add a comment |
$begingroup$
Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $ABcap CD={E}$, $ACcap BD={F}$ and $ADcap BC={G}$. Then the points $E,F,G$ are not collinear.
I tried to prove by contradiction defining a graph on set ${A,B,C,D}$ with edge between two points if they lie on different sides of the line $EFG$ but couldn't arrive to a contradiction. Maybe there is a counterexample in Poincaré Geometry.
geometry
asked Dec 6 '18 at 21:31
user183294user183294
353
$endgroup$
2
$begingroup$
The same question on MathOverflow: Prove or disprove the non colinearity of three points. For some advice on corss-posting see this answer on meta and other questions tagged cross-posting.
$endgroup$
– Martin Sleziak
Dec 7 '18 at 6:59
add a comment |
$begingroup$
Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $ABcap CD={E}$, $ACcap BD={F}$ and $ADcap BC={G}$. Then the points $E,F,G$ are not collinear.
I tried to prove by contradiction defining a graph on set ${A,B,C,D}$ with edge between two points if they lie on different sides of the line $EFG$ but couldn't arrive to a contradiction. Maybe there is a counterexample in Poincaré Geometry.
geometry
asked Dec 6 '18 at 21:31
user183294user183294
353
$endgroup$
Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $ABcap CD={E}$, $ACcap BD={F}$ and $ADcap BC={G}$. Then the points $E,F,G$ are not collinear.
I tried to prove by contradiction defining a graph on set ${A,B,C,D}$ with edge between two points if they lie on different sides of the line $EFG$ but couldn't arrive to a contradiction. Maybe there is a counterexample in Poincaré Geometry.
geometry
geometry
asked Dec 6 '18 at 21:31
user183294user183294
353
asked Dec 6 '18 at 21:31
user183294user183294
353
asked Dec 6 '18 at 21:31
user183294user183294
353
asked Dec 6 '18 at 21:31
user183294user183294
353
asked Dec 6 '18 at 21:31
user183294user183294
353
353
2
$begingroup$
The same question on MathOverflow: Prove or disprove the non colinearity of three points. For some advice on corss-posting see this answer on meta and other questions tagged cross-posting.
$endgroup$
– Martin Sleziak
Dec 7 '18 at 6:59
add a comment |
2
$begingroup$
The same question on MathOverflow: Prove or disprove the non colinearity of three points. For some advice on corss-posting see this answer on meta and other questions tagged cross-posting.
$endgroup$
– Martin Sleziak
Dec 7 '18 at 6:59
2
2
$begingroup$
The same question on MathOverflow: Prove or disprove the non colinearity of three points. For some advice on corss-posting see this answer on meta and other questions tagged cross-posting.
$endgroup$
– Martin Sleziak
Dec 7 '18 at 6:59
$begingroup$
The same question on MathOverflow: Prove or disprove the non colinearity of three points. For some advice on corss-posting see this answer on meta and other questions tagged cross-posting.
$endgroup$
– Martin Sleziak
Dec 7 '18 at 6:59
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3029074%2fprove-or-disprove-the-non-colinearity-of-three-points%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3029074%2fprove-or-disprove-the-non-colinearity-of-three-points%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
The same question on MathOverflow: Prove or disprove the non colinearity of three points. For some advice on corss-posting see this answer on meta and other questions tagged cross-posting.
$endgroup$
– Martin Sleziak
Dec 7 '18 at 6:59