Received: from mail-ie0-f189.google.com ([209.85.223.189]:49005) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WvQnc-0003EO-K7 for lojban-beginners-archive@lojban.org; Fri, 13 Jun 2014 05:41:50 -0700 Received: by mail-ie0-f189.google.com with SMTP id lx4sf549217iec.16 for ; Fri, 13 Jun 2014 05:41:34 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20120806; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=Z6OVoR79kV1W1arWe7NLzBOSjn0XIobRtRJ8zN50wOI=; b=C94ZcS/e54nk91UeBm5te5T9mU+tIWjNQ6YUWwWaupx9VUMPeq6gZCqylYjxQrYMqC E+RZ8aBmlx8kOJuiQh+8YiRQxFs26cWAmbAVr0Vuz1FhQCPiw4dqxKQ3I8MDwC4+IG9N gMSZJsKIFe7/IEE1kp5jN5ytWC4i0W2x3JfX6kJfMHtonQFHeg9GN0bT/7ubhujW8oTi UHfp0i3eTyzDWfEeMLBDK4nnNKBn1vY93g2Uj0lDj8hloltHRgKJ29PkM9E1ldEuTgG6 uCJ26OzVZ5wnwDiYx3rkb6yrjH3fbgQuGH1YI/r3YBqsBCSJ7CCBNepC6NHIbLQvsojZ X1pw== DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=Z6OVoR79kV1W1arWe7NLzBOSjn0XIobRtRJ8zN50wOI=; b=U/hMGdVe3T0I+RSCQiRHqi0KaeAuVrhE5Sd5M7KqrG8av5SsS7kLoLUbEF5UA/SxYu BdJcw0xlUkA7d/8pXexyr2h/fxoOA+wsjfhUp8Iq3mG8OY/kmnxu7k3E6LM7ZcCKK3eS bYG3TJZNVPbc7fBAT7MDBBIBWwoxxwlUT4DblAJEexXhSaB3O60RXLHMDvx+RWAMLRDJ 2OwifQVWPQsmv1rvCVXlb1783KUg1SLBEuCmSXkIsaLRZ3DQsh0CFfK01C8vVXyoDqg2 A5f58SBTTDx/gfPCRsYWXueleYatTtmD9gD3f+6sRB9Zzofx0xpswbZCZbgmLrdNIHCI Em4g== X-Received: by 10.140.49.67 with SMTP id p61mr1756qga.21.1402663294516; Fri, 13 Jun 2014 05:41:34 -0700 (PDT) X-BeenThere: lojban-beginners@googlegroups.com Received: by 10.140.23.7 with SMTP id 7ls3546476qgo.60.gmail; Fri, 13 Jun 2014 05:41:33 -0700 (PDT) X-Received: by 10.140.21.233 with SMTP id 96mr21215qgl.19.1402663293394; Fri, 13 Jun 2014 05:41:33 -0700 (PDT) Date: Fri, 13 Jun 2014 05:41:32 -0700 (PDT) From: len.budney@gmail.com To: lojban-beginners@googlegroups.com Message-Id: <3b60a090-6dbb-4730-9caf-9200b53a0b27@googlegroups.com> In-Reply-To: References: Subject: Re: [lojban-beginners] Re: {konju} and its place structure MIME-Version: 1.0 X-Original-Sender: lenbudney@gmail.com Reply-To: lojban-beginners@googlegroups.com Precedence: list Mailing-list: list lojban-beginners@googlegroups.com; contact lojban-beginners+owners@googlegroups.com List-ID: X-Google-Group-Id: 300742228892 List-Post: , List-Help: , List-Archive: Sender: lojban-beginners@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: multipart/alternative; boundary="----=_Part_69_1269519.1402663292753" X-Spam-Score: -2.0 (--) X-Spam_score: -2.0 X-Spam_score_int: -19 X-Spam_bar: -- Content-Length: 13262 ------=_Part_69_1269519.1402663292753 Content-Type: text/plain; charset=UTF-8 On Thursday, June 12, 2014 11:41:13 PM UTC-4, Ross Ogilvie wrote: > > Getting my math nerd on, there's no reason the region has to be connected, > or has to be embedded in R^N for that matter, but the idea is right. The > formal definition is https://en.wikipedia.org/wiki/Cone_%28topology%29. > Hats off to you, sir. That's the most general definition of a cone all right. I shied away from giving that one because it's mind-bending without a bit of a background in point-set topology. Also, it's homeomorphic to some things we would not consider cones if we saw them embedded in R^3--like the one with a cylindrical surface as its base, and the midpoint of its axis as the vertex. > If you wanted a predicate for a general cone like this, I'd go with: x1 is > a cone with base x2 and vertex x3. > I would consider that to be more or less the ideal definition for {konju}. You can add an x4 to specify the material, but in that case it would create ambiguity whether we're talking about the mathematical abstraction of "cone," or simply a conical object. I guess we could say {konju da'i} for an abstract cone and {konju da'inai} for a conical object? I'm reaching here. --Len > Obviously you could swap the last two places, but this way it's more > compatible with the current konju and also allows you to easily specify the > type of cone, eg > 1) lo konju be lo cukla > a circular cone > > 2) lo konju be lo cibjgatai > a triangular pyramid > > Compare also to {pirmidi}. > > -- Ross > > > On 13 June 2014 00:06, > wrote: > >> 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 : >>> >>> 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? >>>> >>> >>> -- >> You received this message because you are subscribed to the Google Groups >> "Lojban Beginners" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to lojban-beginne...@googlegroups.com . >> To post to this group, send email to lojban-b...@googlegroups.com >> . >> Visit this group at http://groups.google.com/group/lojban-beginners. >> For more options, visit https://groups.google.com/d/optout. >> > > -- You received this message because you are subscribed to the Google Groups "Lojban Beginners" group. To unsubscribe from this group and stop receiving emails from it, send an email to lojban-beginners+unsubscribe@googlegroups.com. To post to this group, send email to lojban-beginners@googlegroups.com. Visit this group at http://groups.google.com/group/lojban-beginners. For more options, visit https://groups.google.com/d/optout. ------=_Part_69_1269519.1402663292753 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
On Thursday, June 12, 2014 11:41:13 PM UTC-4, Ross Ogilvie= wrote:

= Getting my math nerd on, there's no reason the region has to be connected, = or has to be embedded in R^N for that matter, but the idea is right. The fo= rmal definition is https://en.wikipedia.org/w= iki/Cone_%28topology%29.
=

Hats off to you, sir. That's the most gene= ral definition of a cone all right. I shied away from giving that one becau= se it's mind-bending without a bit of a background in point-set topology. A= lso, it's homeomorphic to some things we would not consider cones if we saw= them embedded in R^3--like the one with a cylindrical surface as its base,= and the midpoint of its axis as the vertex.
 
<= div>
If you wanted a predicate for a general cone like this, I'd go wi= th: x1 is a cone with base x2 and vertex x3.
<= /div>

I would consider that to be mor= e or less the ideal definition for {konju}. You can add an x4 to specify th= e material, but in that case it would create ambiguity whether we're talkin= g about the mathematical abstraction of "cone," or simply a conical object.= I guess we could say {konju da'i} for an abstract cone and {konju da'inai}= for a conical object? I'm reaching here.

--Len

 
Obviously you could s= wap the last two places, but this way it's more compatible with the current= konju and also allows you to easily specify the type of cone, eg
1) lo konju be lo cukla
a circular cone

2) lo k= onju be lo cibjgatai
a triangular pyramid

Compare als= o to {pirmidi}.

-- Ross


On 13 June 2014 00:06, <len.b...@gmail.com> wrote:
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.


On Friday, May 23, 2014 4:00:01 PM UTC-4, la gleki wrote:
There are two main definitions of "cone":
1. (geometry) A su= rface of revolution formed by rotating a segment of a line around another l= ine that intersects the first line.
2. (geometry) A solid of revo= lution formed by rotating a triangle around one of its altitudes.

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.

This explains why only vertex is specified. but ko= nju2 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>:

The definition of {kon= ju} is rather cryptic.

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.

either o= nly 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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You received this message because you are subscribed to the Google Groups &= quot;Lojban Beginners" group.
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