Date: Thu, 12 Jun 2014 07:06:42 -0700 (PDT)
From: len.budney@gmail.com
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Subject: [lojban-beginners] Re: {konju} and its place structure
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The definition more prevalent in higher math is: the object created by 
taking a connected region in N dimensions, and a point outside that region 
in N+1 dimensions, and including all lines between that point and any point 
in the region. I would consider that the "standard" definition. Both of 
yours are special cases where N=2 and the region is circular. Pyramids and 
ellipsoidal cones are also legit cones.


On Friday, May 23, 2014 4:00:01 PM UTC-4, la gleki wrote:
>
> There are two main definitions of "cone":
> 1. (geometry) A surface of revolution formed by rotating a segment of a 
> line around another line that intersects the first line.
> 2. (geometry) A solid of revolution formed by rotating a triangle around 
> one of its altitudes.
>
> I think neither meaning of "cone" reflects {konju}. I think {konju} 
> describes a *segment* of a line (possibly infinite thus identical to a line 
> in such case) revolving around another linear segment thus forming a 
> *surface*. As for konju1 it describes an object (possibly immaterial) with 
> *a property* of such cone-ness.
>
> This explains why only vertex is specified. but konju2 seems to be 
> superflous then since it is not always necessary.
>
>
> 2014-05-23 12:11 GMT+04:00 Gleki Arxokuna <gleki.is...@gmail.com 
> <javascript:>>:
>
>> The definition of {konju} is rather cryptic.
>>
>> x1 is a cone [shape/form] of material x2 with vertex x3. Also ellipse, 
>> ellipsoid (= konclupa). See also jesni, djine, sovda, kojna, jganu.
>>
>> "Cone" is this object: https://en.wiktionary.org/wiki/File:PovCone.jpg
>> either only the surface of an object made after the revolution of a 
>> triangle. That's why konju3 seems strange. Why only vertex is defined?
>>
>> Definitely cone it's not an ellipse.
>>
>> Could you please explain this?
>>
>
>

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<div dir=3D"ltr">The definition more prevalent in higher math is: the objec=
t created by taking a connected region in N dimensions, and a point outside=
 that region in N+1 dimensions, and including all lines between that point =
and any point in the region. I would consider that the "standard" definitio=
n. Both of yours are special cases where N=3D2 and the region is circular. =
Pyramids and ellipsoidal cones are also legit cones.<div><br><br>On Friday,=
 May 23, 2014 4:00:01 PM UTC-4, la gleki wrote:<blockquote class=3D"gmail_q=
uote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;pad=
ding-left: 1ex;"><div dir=3D"ltr"><div>There are two main definitions of "c=
one":</div><div>1. (geometry) A surface of revolution formed by rotating a =
segment of a line around another line that intersects the first line.</div>=
<div>2. (geometry) A solid of revolution formed by rotating a triangle arou=
nd one of its altitudes.</div>
<div><br></div><div>I think neither meaning of "cone" reflects {konju}. I t=
hink {konju} describes a *segment* of a line (possibly infinite thus identi=
cal to a line in such case) revolving around another linear segment thus fo=
rming a *surface*. As for konju1 it describes an object (possibly immateria=
l) with *a property* of such cone-ness.</div>
<div><br></div><div>This explains why only vertex is specified.&nbsp;but ko=
nju2 seems to be superflous then since it is not always necessary.</div></d=
iv><div><br><br><div class=3D"gmail_quote">2014-05-23 12:11 GMT+04:00 Gleki=
 Arxokuna <span dir=3D"ltr">&lt;<a href=3D"javascript:" target=3D"_blank" g=
df-obfuscated-mailto=3D"PyhQIa1yyscJ" onmousedown=3D"this.href=3D'javascrip=
t:';return true;" onclick=3D"this.href=3D'javascript:';return true;">gleki.=
is...@gmail.com</a>&gt;</span>:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex"><div dir=3D"ltr"><div>The definition of {kon=
ju} is rather cryptic.</div><div><br></div><div>x1 is a cone [shape/form] o=
f material x2 with vertex x3. Also ellipse, ellipsoid (=3D konclupa). See a=
lso jesni, djine, sovda, kojna, jganu.</div>

<div><br></div><div>"Cone" is this object:&nbsp;<a href=3D"https://en.wikti=
onary.org/wiki/File:PovCone.jpg" target=3D"_blank" onmousedown=3D"this.href=
=3D'https://www.google.com/url?q\75https%3A%2F%2Fen.wiktionary.org%2Fwiki%2=
FFile%3APovCone.jpg\46sa\75D\46sntz\0751\46usg\75AFQjCNHE25NEv-UTed7Kqst9OB=
RPZVYgYQ';return true;" onclick=3D"this.href=3D'https://www.google.com/url?=
q\75https%3A%2F%2Fen.wiktionary.org%2Fwiki%2FFile%3APovCone.jpg\46sa\75D\46=
sntz\0751\46usg\75AFQjCNHE25NEv-UTed7Kqst9OBRPZVYgYQ';return true;">https:/=
/en.wiktionary.<wbr>org/wiki/File:PovCone.jpg</a></div><div>either only the=
 surface of an object made after the revolution of a triangle. That's why k=
onju3 seems strange. Why only vertex is defined?</div>

<div><br></div><div>Definitely cone it's not an ellipse.</div><div><br></di=
v><div>Could you please explain this?</div></div>
</blockquote></div><br></div>
</blockquote></div></div>

<p></p>

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