Received: from mail-pd0-f186.google.com ([209.85.192.186]:49851) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WvIMg-0000e5-NC for lojban-beginners-archive@lojban.org; Thu, 12 Jun 2014 20:41:37 -0700 Received: by mail-pd0-f186.google.com with SMTP id ft15sf423542pdb.23 for ; Thu, 12 Jun 2014 20:41:13 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20120806; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :x-original-sender:x-original-authentication-results:reply-to :precedence:mailing-list:list-id:list-post:list-help:list-archive :sender:list-subscribe:list-unsubscribe:content-type; bh=rnuqQ1LO9u/AZfoiy3Jl/aI664Ry/OV8uFOF2MguBXI=; b=oh2UoB7zwKgZcbYhQpzh8vfqVFZw5krwiG7lx69xlrH4XwGcesLi+44LZMaxFDUZTE gLkAchV9/nnVmtp5s1bd/0CstDzcvOYzFGJPDY+zHpcwQKbBTvjYpfYpIdCJjRXuemXu QJcHF8ggL7C+plVIivpUKnyp2jebkf6PntfWTzS+lNtBvv3FMYtuCXZRE0tTIJQxEduS sTdFknb4xX1Z3F2Oll8VHzFPNUS5M5sbvLdcOY4X7SG06cpTW0Df1lMAk2tNYBvZAY0y OFipcmwznrBU7lW0iHPOHLgb4gPbfW6Wc4zPP5NhmsfBAC+oksnCZNaSmDo/UROMHExX fG8Q== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:x-original-sender :x-original-authentication-results:reply-to:precedence:mailing-list :list-id:list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=rnuqQ1LO9u/AZfoiy3Jl/aI664Ry/OV8uFOF2MguBXI=; b=cLKytiWbec6G06YBNqkGSUjgJnPXPmiXrFWZea2nfGAHhlYmH00ss5KTklBtdexkGN ppBnPFvazYZWJratgRAR0RbXpficn4zRr1o8racKm9rrqpNaPcw1qjR/m+QggCQOOlNV 97vSL+IOopwz5n2NhnNuYOkcc0e/42qdT/G78P7dWLD2x5qsWH0NRHVVZBZ7T4tYRqRg 3qeB16PAGNoU1ZSGrKmd2NKyBbdh2D1Yoy+AC9KpfzEi9t1ReIFuYELKIkn2E28zsK1r hShiKG0gkQSmlNyh9YV2BMIOrP1CfeZXPosVVdKLGvre+pm3+ILQwcewj9Ueps47fHx9 smiQ== X-Received: by 10.182.20.204 with SMTP id p12mr89obe.29.1402630872932; Thu, 12 Jun 2014 20:41:12 -0700 (PDT) X-BeenThere: lojban-beginners@googlegroups.com Received: by 10.182.47.196 with SMTP id f4ls1435090obn.5.gmail; Thu, 12 Jun 2014 20:41:11 -0700 (PDT) X-Received: by 10.182.186.103 with SMTP id fj7mr26115obc.9.1402630870994; Thu, 12 Jun 2014 20:41:10 -0700 (PDT) Received: from mail-qc0-f172.google.com (mail-qc0-f172.google.com [209.85.216.172]) by gmr-mx.google.com with ESMTPS id x7si630423qcd.3.2014.06.12.20.41.10 for (version=TLSv1 cipher=ECDHE-RSA-RC4-SHA bits=128/128); Thu, 12 Jun 2014 20:41:10 -0700 (PDT) Received-SPF: none (google.com: ross@rossogilvie.id.au does not designate permitted sender hosts) client-ip=209.85.216.172; Received: by mail-qc0-f172.google.com with SMTP id o8so3470047qcw.3 for ; Thu, 12 Jun 2014 20:41:10 -0700 (PDT) X-Gm-Message-State: ALoCoQlhIU6uLLUxCc2OiEzzFKTjFELl1rAWaGpwnqNbDSelCVGs3KpMCNdZc3PJDznh/mxODWG0 X-Received: by 10.140.24.196 with SMTP id 62mr16156qgr.45.1402630870553; Thu, 12 Jun 2014 20:41:10 -0700 (PDT) MIME-Version: 1.0 Received: by 10.96.87.5 with HTTP; Thu, 12 Jun 2014 20:40:40 -0700 (PDT) X-Originating-IP: [129.78.95.84] In-Reply-To: References: From: Ross Ogilvie Date: Fri, 13 Jun 2014 13:40:40 +1000 Message-ID: Subject: Re: [lojban-beginners] Re: {konju} and its place structure To: lojban-beginners X-Original-Sender: ross@rossogilvie.id.au X-Original-Authentication-Results: gmr-mx.google.com; spf=neutral (google.com: ross@rossogilvie.id.au does not designate permitted sender hosts) smtp.mail=ross@rossogilvie.id.au 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=001a11c13bfeca6bf404fbaf7230 X-Spam-Score: -1.9 (-) X-Spam_score: -1.9 X-Spam_score_int: -18 X-Spam_bar: - Content-Length: 9065 --001a11c13bfeca6bf404fbaf7230 Content-Type: text/plain; charset=UTF-8 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 . 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. 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-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. > -- 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. --001a11c13bfeca6bf404fbaf7230 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Getting my math nerd on, the= re'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.wikiped= ia.org/wiki/Cone_%28topology%29 . If you wanted a predicate for a gener= al cone like this, I'd go with: x1 is a cone with base x2 and vertex x3= . 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 k= onju be lo cibjgatai
a triangular pyramid

Compare als= o to {pirmidi}.

-- Ross


On 13 June 2014 00:06, <len.budney@= 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"= definition. 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. (geom= etry) A surface of revolution formed by rotating a segment of a line around= another line that intersects the first line.
2. (geometry) A sol= id of revolution formed by rotating a triangle around one of its altitudes.=

I think neither meaning of "cone" reflects {k= onju}. I think {konju} describes a *segment* of a line (possibly infinite t= hus identical to a line in such case) revolving around another linear segme= nt 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.=C2=A0but 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 only the surf= ace of an object made after the revolution of a triangle. That's why ko= nju3 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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