Why are parallelograms defined as quadrilaterals? What term would encompass polygons with greater than two parallel pairs?What are curves (generalized ellipses) with more than two focal points called and how do they look like?Elementary Geometry Nomenclature: why so bad?Name of theorem about two quadrilaterals with parallel edgesIs there a term for two polygons with the same angles but different side lengths?What are equations with a degree more than 3 called?Which polygons are “mediogons” of simple polygons?What is the term for a function whose output is greater than its input, f(x) > x?Is there a term for functions which are greater than a bound?Name and number of “equilateral tessellations with same angles on all vertexes”ABCD and AECF are two parallelograms and side EF is parallel to AD . suppose AF and DE met at X and BF AND CE AT Y . prove that XY is parallel to AB
Cropping a message using array splits
What does formal training in a field mean?
Company threw a surprise party for the CEO, 3 weeks later management says we have to pay for it, do I have to?
How did Thanos not realise this had happened at the end of Endgame?
Renting a house to a graduate student in my department
Can 'sudo apt-get remove [write]' destroy my Ubuntu?
Ex-manager wants to stay in touch, I don't want to
Windows OS quantum vs. SQL OS Quantum
Improving Sati-Sampajañña (situative wisdom)
The meaning of a て-form verb at the end of this sentence
What is the name of meteoroids which hit Moon, Mars, or pretty much anything that isn’t the Earth?
What can cause an unfrozen indoor copper drain pipe to crack?
What was the plan for an abort of the Enola Gay's mission to drop the atomic bomb?
Has magnetic core memory been used beyond the Moon?
date to display the EDT time
Is it a good idea to copy a trader when investing?
Why is PerfectForwardSecrecy considered OK, when it has same defects as salt-less password hashing?
Why use steam instead of just hot air?
Why are low spin tetrahedral complexes so rare?
Why are parallelograms defined as quadrilaterals? What term would encompass polygons with greater than two parallel pairs?
Why should password hash verification be time constant?
Can the president of the United States be guilty of insider trading?
What was the notion of limit that Newton used?
Why did they go to Dragonstone?
Why are parallelograms defined as quadrilaterals? What term would encompass polygons with greater than two parallel pairs?
What are curves (generalized ellipses) with more than two focal points called and how do they look like?Elementary Geometry Nomenclature: why so bad?Name of theorem about two quadrilaterals with parallel edgesIs there a term for two polygons with the same angles but different side lengths?What are equations with a degree more than 3 called?Which polygons are “mediogons” of simple polygons?What is the term for a function whose output is greater than its input, f(x) > x?Is there a term for functions which are greater than a bound?Name and number of “equilateral tessellations with same angles on all vertexes”ABCD and AECF are two parallelograms and side EF is parallel to AD . suppose AF and DE met at X and BF AND CE AT Y . prove that XY is parallel to AB
$begingroup$
It seems the definition of a parallelogram is locked to quadrilaterals for some reason. Is there a reason for this? Why couldn't a parallelogram (given the way the word seems rather than as a mathematical/geometric construct) contain greater than two pairs of parallel sides? In a hexagon for example, all six sides are parallel to their opposing side. Is there a term for this kind of object?
It seems to me there must be some value in describing a polygon with even numbers of sides in which the opposing sides are parallel to each other. While a hexagon, octagon, decagon, etc. all match this rule, you could have polygons with unequal sides as well.
Edit 1: Object described by Mark Fischler
Zonogon:
terminology plane-geometry quadrilateral
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
It seems the definition of a parallelogram is locked to quadrilaterals for some reason. Is there a reason for this? Why couldn't a parallelogram (given the way the word seems rather than as a mathematical/geometric construct) contain greater than two pairs of parallel sides? In a hexagon for example, all six sides are parallel to their opposing side. Is there a term for this kind of object?
It seems to me there must be some value in describing a polygon with even numbers of sides in which the opposing sides are parallel to each other. While a hexagon, octagon, decagon, etc. all match this rule, you could have polygons with unequal sides as well.
Edit 1: Object described by Mark Fischler
Zonogon:
terminology plane-geometry quadrilateral
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Indeed, I see no reason why the word "parallelogram," which has origins in Middle French where it refers to "bounded parallel lines," should have come to mean specifically 4-sided plane figures. In solid geometry, again the term "parallelpiped" is reserved for six-sided figures, now with 3 pairs of parallel opposite faces.
$endgroup$
– Mark Fischler
6 hours ago
1
$begingroup$
@MarkFischler Yes basically! Also, your comment briefly hurt my brain at the switch from 2D to 3D terminology of 'sides' (2D: side = edge; 3D: side = face).
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
@ Mark Fischler What word did Euklid use for "parallelogramm"?
$endgroup$
– user
6 hours ago
$begingroup$
I have added an answer to what Euclid called them in my answer below; the comments don't seem to speak pasted Greek.
$endgroup$
– Mark Fischler
6 hours ago
add a comment |
$begingroup$
It seems the definition of a parallelogram is locked to quadrilaterals for some reason. Is there a reason for this? Why couldn't a parallelogram (given the way the word seems rather than as a mathematical/geometric construct) contain greater than two pairs of parallel sides? In a hexagon for example, all six sides are parallel to their opposing side. Is there a term for this kind of object?
It seems to me there must be some value in describing a polygon with even numbers of sides in which the opposing sides are parallel to each other. While a hexagon, octagon, decagon, etc. all match this rule, you could have polygons with unequal sides as well.
Edit 1: Object described by Mark Fischler
Zonogon:
terminology plane-geometry quadrilateral
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
It seems the definition of a parallelogram is locked to quadrilaterals for some reason. Is there a reason for this? Why couldn't a parallelogram (given the way the word seems rather than as a mathematical/geometric construct) contain greater than two pairs of parallel sides? In a hexagon for example, all six sides are parallel to their opposing side. Is there a term for this kind of object?
It seems to me there must be some value in describing a polygon with even numbers of sides in which the opposing sides are parallel to each other. While a hexagon, octagon, decagon, etc. all match this rule, you could have polygons with unequal sides as well.
Edit 1: Object described by Mark Fischler
Zonogon:
terminology plane-geometry quadrilateral
terminology plane-geometry quadrilateral
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 6 hours ago
duct_tape_coder
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
asked 6 hours ago
duct_tape_coderduct_tape_coder
1234
1234
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
duct_tape_coder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Indeed, I see no reason why the word "parallelogram," which has origins in Middle French where it refers to "bounded parallel lines," should have come to mean specifically 4-sided plane figures. In solid geometry, again the term "parallelpiped" is reserved for six-sided figures, now with 3 pairs of parallel opposite faces.
$endgroup$
– Mark Fischler
6 hours ago
1
$begingroup$
@MarkFischler Yes basically! Also, your comment briefly hurt my brain at the switch from 2D to 3D terminology of 'sides' (2D: side = edge; 3D: side = face).
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
@ Mark Fischler What word did Euklid use for "parallelogramm"?
$endgroup$
– user
6 hours ago
$begingroup$
I have added an answer to what Euclid called them in my answer below; the comments don't seem to speak pasted Greek.
$endgroup$
– Mark Fischler
6 hours ago
add a comment |
1
$begingroup$
Indeed, I see no reason why the word "parallelogram," which has origins in Middle French where it refers to "bounded parallel lines," should have come to mean specifically 4-sided plane figures. In solid geometry, again the term "parallelpiped" is reserved for six-sided figures, now with 3 pairs of parallel opposite faces.
$endgroup$
– Mark Fischler
6 hours ago
1
$begingroup$
@MarkFischler Yes basically! Also, your comment briefly hurt my brain at the switch from 2D to 3D terminology of 'sides' (2D: side = edge; 3D: side = face).
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
@ Mark Fischler What word did Euklid use for "parallelogramm"?
$endgroup$
– user
6 hours ago
$begingroup$
I have added an answer to what Euclid called them in my answer below; the comments don't seem to speak pasted Greek.
$endgroup$
– Mark Fischler
6 hours ago
1
1
$begingroup$
Indeed, I see no reason why the word "parallelogram," which has origins in Middle French where it refers to "bounded parallel lines," should have come to mean specifically 4-sided plane figures. In solid geometry, again the term "parallelpiped" is reserved for six-sided figures, now with 3 pairs of parallel opposite faces.
$endgroup$
– Mark Fischler
6 hours ago
$begingroup$
Indeed, I see no reason why the word "parallelogram," which has origins in Middle French where it refers to "bounded parallel lines," should have come to mean specifically 4-sided plane figures. In solid geometry, again the term "parallelpiped" is reserved for six-sided figures, now with 3 pairs of parallel opposite faces.
$endgroup$
– Mark Fischler
6 hours ago
1
1
$begingroup$
@MarkFischler Yes basically! Also, your comment briefly hurt my brain at the switch from 2D to 3D terminology of 'sides' (2D: side = edge; 3D: side = face).
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
@MarkFischler Yes basically! Also, your comment briefly hurt my brain at the switch from 2D to 3D terminology of 'sides' (2D: side = edge; 3D: side = face).
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
@ Mark Fischler What word did Euklid use for "parallelogramm"?
$endgroup$
– user
6 hours ago
$begingroup$
@ Mark Fischler What word did Euklid use for "parallelogramm"?
$endgroup$
– user
6 hours ago
$begingroup$
I have added an answer to what Euclid called them in my answer below; the comments don't seem to speak pasted Greek.
$endgroup$
– Mark Fischler
6 hours ago
$begingroup$
I have added an answer to what Euclid called them in my answer below; the comments don't seem to speak pasted Greek.
$endgroup$
– Mark Fischler
6 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Interesting question. Parallelograms are quadrilaterals for historical reasons. They could have been defined to include your examples, but weren't. Now the meaning is so common that it can't be changed.
I don't think there is a name for your class of polygons. The reason is in this:
It seems to me there must be some value in describing a polygon with
even numbers of sides in which the opposing sides are parallel to each
other.
If there were some value - if these polygons came up often in geometry - then someone would have named them. If you have interesting things to say about them and publish your thoughts you'll invent a name in your paper. If it's widely read the name will stick.
I thought parallelogon would be a good possibility, but that name is taken: https://en.wikipedia.org/wiki/Parallelogon .
The convex polygons whose sides come in equal parallel pairs are zonogons: https://en.wikipedia.org/wiki/Zonogon . Your polygons have zonogons as nontrivial Minkowski summands.
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
$endgroup$
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
add a comment |
$begingroup$
I'm going to propose, out of the blue, terms like "hexaparallelogram", "octaparallelogram", and so forth.
I'm wondering whether, for more than $4$ sides, you would like your definition of hexaparallelogram to be restricted to having 3 pairs of parallel and pairwise equal sides (as in your picture - evidently these have a name, zonogon), or would you include a hexagon with vertices at $(0,0), (12,0), (16,6), (4,12), (0,12), (-6,3)$ which has three pairs of parallel sides but no two sides of equal length?
Euclid, in proposition 34, introduces the term (παραλληλόγραμμα χωρία) which we can translate to "parallelogrammic area." So much for the etymology sites that trace the word only to Middle French. Euclid himself restricted the word to just four-sided figures. Proclus credits Euclid with having introduced the term "parallelogram," as opposed to bringing down that term from earlier works. So that tells us who to blame.
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
$endgroup$
1
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
1
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
add a comment |
Your Answer
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
);
);
duct_tape_coder is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3220273%2fwhy-are-parallelograms-defined-as-quadrilaterals-what-term-would-encompass-poly%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Interesting question. Parallelograms are quadrilaterals for historical reasons. They could have been defined to include your examples, but weren't. Now the meaning is so common that it can't be changed.
I don't think there is a name for your class of polygons. The reason is in this:
It seems to me there must be some value in describing a polygon with
even numbers of sides in which the opposing sides are parallel to each
other.
If there were some value - if these polygons came up often in geometry - then someone would have named them. If you have interesting things to say about them and publish your thoughts you'll invent a name in your paper. If it's widely read the name will stick.
I thought parallelogon would be a good possibility, but that name is taken: https://en.wikipedia.org/wiki/Parallelogon .
The convex polygons whose sides come in equal parallel pairs are zonogons: https://en.wikipedia.org/wiki/Zonogon . Your polygons have zonogons as nontrivial Minkowski summands.
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
$endgroup$
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
add a comment |
$begingroup$
Interesting question. Parallelograms are quadrilaterals for historical reasons. They could have been defined to include your examples, but weren't. Now the meaning is so common that it can't be changed.
I don't think there is a name for your class of polygons. The reason is in this:
It seems to me there must be some value in describing a polygon with
even numbers of sides in which the opposing sides are parallel to each
other.
If there were some value - if these polygons came up often in geometry - then someone would have named them. If you have interesting things to say about them and publish your thoughts you'll invent a name in your paper. If it's widely read the name will stick.
I thought parallelogon would be a good possibility, but that name is taken: https://en.wikipedia.org/wiki/Parallelogon .
The convex polygons whose sides come in equal parallel pairs are zonogons: https://en.wikipedia.org/wiki/Zonogon . Your polygons have zonogons as nontrivial Minkowski summands.
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
$endgroup$
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
add a comment |
$begingroup$
Interesting question. Parallelograms are quadrilaterals for historical reasons. They could have been defined to include your examples, but weren't. Now the meaning is so common that it can't be changed.
I don't think there is a name for your class of polygons. The reason is in this:
It seems to me there must be some value in describing a polygon with
even numbers of sides in which the opposing sides are parallel to each
other.
If there were some value - if these polygons came up often in geometry - then someone would have named them. If you have interesting things to say about them and publish your thoughts you'll invent a name in your paper. If it's widely read the name will stick.
I thought parallelogon would be a good possibility, but that name is taken: https://en.wikipedia.org/wiki/Parallelogon .
The convex polygons whose sides come in equal parallel pairs are zonogons: https://en.wikipedia.org/wiki/Zonogon . Your polygons have zonogons as nontrivial Minkowski summands.
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
$endgroup$
Interesting question. Parallelograms are quadrilaterals for historical reasons. They could have been defined to include your examples, but weren't. Now the meaning is so common that it can't be changed.
I don't think there is a name for your class of polygons. The reason is in this:
It seems to me there must be some value in describing a polygon with
even numbers of sides in which the opposing sides are parallel to each
other.
If there were some value - if these polygons came up often in geometry - then someone would have named them. If you have interesting things to say about them and publish your thoughts you'll invent a name in your paper. If it's widely read the name will stick.
I thought parallelogon would be a good possibility, but that name is taken: https://en.wikipedia.org/wiki/Parallelogon .
The convex polygons whose sides come in equal parallel pairs are zonogons: https://en.wikipedia.org/wiki/Zonogon . Your polygons have zonogons as nontrivial Minkowski summands.
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
edited 6 hours ago
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
answered 6 hours ago
Ethan BolkerEthan Bolker
47.5k556123
47.5k556123
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
add a comment |
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
Thank you for your answer. The zonogon concept is fascinating. The question was a bit more r/showerthoughts than math.SE (I'm no mathematician) and I'm quickly out of my depth but you've cut to the quick of my question. I think Mark's suggested object (I had to draw it to understand it so I've pasted it to my question) creates even more questions I can't answer.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
$begingroup$
I strongly recommend you reconsider the sentiment that "If there were some value ... then someone would have named them." Experimentation and exploration of math concepts should never be curtailed by that line of thinking.
$endgroup$
– Zimul8r
20 mins ago
add a comment |
$begingroup$
I'm going to propose, out of the blue, terms like "hexaparallelogram", "octaparallelogram", and so forth.
I'm wondering whether, for more than $4$ sides, you would like your definition of hexaparallelogram to be restricted to having 3 pairs of parallel and pairwise equal sides (as in your picture - evidently these have a name, zonogon), or would you include a hexagon with vertices at $(0,0), (12,0), (16,6), (4,12), (0,12), (-6,3)$ which has three pairs of parallel sides but no two sides of equal length?
Euclid, in proposition 34, introduces the term (παραλληλόγραμμα χωρία) which we can translate to "parallelogrammic area." So much for the etymology sites that trace the word only to Middle French. Euclid himself restricted the word to just four-sided figures. Proclus credits Euclid with having introduced the term "parallelogram," as opposed to bringing down that term from earlier works. So that tells us who to blame.
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
$endgroup$
1
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
1
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
add a comment |
$begingroup$
I'm going to propose, out of the blue, terms like "hexaparallelogram", "octaparallelogram", and so forth.
I'm wondering whether, for more than $4$ sides, you would like your definition of hexaparallelogram to be restricted to having 3 pairs of parallel and pairwise equal sides (as in your picture - evidently these have a name, zonogon), or would you include a hexagon with vertices at $(0,0), (12,0), (16,6), (4,12), (0,12), (-6,3)$ which has three pairs of parallel sides but no two sides of equal length?
Euclid, in proposition 34, introduces the term (παραλληλόγραμμα χωρία) which we can translate to "parallelogrammic area." So much for the etymology sites that trace the word only to Middle French. Euclid himself restricted the word to just four-sided figures. Proclus credits Euclid with having introduced the term "parallelogram," as opposed to bringing down that term from earlier works. So that tells us who to blame.
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
$endgroup$
1
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
1
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
add a comment |
$begingroup$
I'm going to propose, out of the blue, terms like "hexaparallelogram", "octaparallelogram", and so forth.
I'm wondering whether, for more than $4$ sides, you would like your definition of hexaparallelogram to be restricted to having 3 pairs of parallel and pairwise equal sides (as in your picture - evidently these have a name, zonogon), or would you include a hexagon with vertices at $(0,0), (12,0), (16,6), (4,12), (0,12), (-6,3)$ which has three pairs of parallel sides but no two sides of equal length?
Euclid, in proposition 34, introduces the term (παραλληλόγραμμα χωρία) which we can translate to "parallelogrammic area." So much for the etymology sites that trace the word only to Middle French. Euclid himself restricted the word to just four-sided figures. Proclus credits Euclid with having introduced the term "parallelogram," as opposed to bringing down that term from earlier works. So that tells us who to blame.
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
$endgroup$
I'm going to propose, out of the blue, terms like "hexaparallelogram", "octaparallelogram", and so forth.
I'm wondering whether, for more than $4$ sides, you would like your definition of hexaparallelogram to be restricted to having 3 pairs of parallel and pairwise equal sides (as in your picture - evidently these have a name, zonogon), or would you include a hexagon with vertices at $(0,0), (12,0), (16,6), (4,12), (0,12), (-6,3)$ which has three pairs of parallel sides but no two sides of equal length?
Euclid, in proposition 34, introduces the term (παραλληλόγραμμα χωρία) which we can translate to "parallelogrammic area." So much for the etymology sites that trace the word only to Middle French. Euclid himself restricted the word to just four-sided figures. Proclus credits Euclid with having introduced the term "parallelogram," as opposed to bringing down that term from earlier works. So that tells us who to blame.
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
edited 6 hours ago
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
answered 6 hours ago
Mark FischlerMark Fischler
34.9k12652
34.9k12652
1
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
1
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
add a comment |
1
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
1
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
1
1
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
$begingroup$
+1 interesting history. Your naming convention would require advance knowledge of the number of edges. What about "ultraparallelogram" or "megaparallelogram"?
$endgroup$
– Ethan Bolker
6 hours ago
1
1
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
Thank your for your answer as well. I've drawn (as best I understood it) and posted your object in the question. The zonogon was sort of what I was thinking originally (n-sides) but your object with sides of different lengths is even more fascinating. Thank you for the etymology as well.
$endgroup$
– duct_tape_coder
6 hours ago
add a comment |
duct_tape_coder is a new contributor. Be nice, and check out our Code of Conduct.
duct_tape_coder is a new contributor. Be nice, and check out our Code of Conduct.
duct_tape_coder is a new contributor. Be nice, and check out our Code of Conduct.
duct_tape_coder is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3220273%2fwhy-are-parallelograms-defined-as-quadrilaterals-what-term-would-encompass-poly%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
1
$begingroup$
Indeed, I see no reason why the word "parallelogram," which has origins in Middle French where it refers to "bounded parallel lines," should have come to mean specifically 4-sided plane figures. In solid geometry, again the term "parallelpiped" is reserved for six-sided figures, now with 3 pairs of parallel opposite faces.
$endgroup$
– Mark Fischler
6 hours ago
1
$begingroup$
@MarkFischler Yes basically! Also, your comment briefly hurt my brain at the switch from 2D to 3D terminology of 'sides' (2D: side = edge; 3D: side = face).
$endgroup$
– duct_tape_coder
6 hours ago
$begingroup$
@ Mark Fischler What word did Euklid use for "parallelogramm"?
$endgroup$
– user
6 hours ago
$begingroup$
I have added an answer to what Euclid called them in my answer below; the comments don't seem to speak pasted Greek.
$endgroup$
– Mark Fischler
6 hours ago