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From: Pierre Abbat <phma@bezitopo.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] Geometry shapes categorization
Date: Tue, 27 May 2014 09:22:13 -0400
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On Tuesday, May 27, 2014 11:11:33 Gleki Arxokuna wrote:
> Let's list most important geometry shapes and see if we can specify their
> defining parameters without resorting to metaphors or tanru.
>=20
> Warning: me not using geometry IRL for a long time can lead to mistakes
> below.
>=20
>    1. konju  - x1 is a cone [shape/form] of material x2 with vertex x3.
>    Also ellipse, ellipsoid (=3D konclupa). See also jesni, djine, sovda,
> kojna, jganu. *Cone is formed by a linear segment rotating around an
>    "imaginary" linear segment such that they they intersect with each oth=
er
> on one of their ends. Cone forms a surface, it is not solid. We need to
> specify a). the length of the linear segment and b). either the bottom of
> the cone (which is a circle) or the angle between the two linear segments=
*

An ellipse is a conic section. An ellipsoid is a solid, any section of whic=
h=20
(except the tangent ones) is an ellipse. I think that "konclupa" was intend=
ed=20
to mean "ellipse" and put in the definition of "konju" by mistake.

> 2. djine  - x1 is a ring/annulus/torus/circle [shape/form] of material x2=
,
> inside diam. x3, outside diam. x4. Also ellipse, oval (=3D jincla); (usag=
e
> has been for near-circles, such as tight spirals, even if not closed
> loops). Also band, belt, encircle (=3D jinsru). See also clupa, cukla, da=
sri,
> karli, sovda, sruri, konju. *Is it terete in cross-section? How to specif=
y
> parameters of circles-ellipses?*
>    3. cukla x1 is round/circular [2-dimensional shape/form]; x1 is a
>    disk/circle/ring. Normally used for a filled-in circle/disk, but empha=
sis
> on roundness means that the concept may include 'ring'. See also djine,
> ranji, bolci, tarmi. *Okay, so a more general than ring concept. Seems th=
at
> we don=E2=80=99t need a diameter place*

lo cukla is a circle, filled in or not, but having only one radius. lo djin=
e=20
has two radii, the inner and the outer.

>    4. mijgresirji - x1 is a diameter between x2 and x3 of x4. *Diameter =
=E2=80=93
>    do we need it as a separate brivla?*

"mijgresirji" means "line passing through the middle". "Diameter" can also=
=20
mean "length of a line segment passing through the middle" (of a circle, th=
e=20
length is independent of which line segment one measures).

>    5. linji x1 is a line/among lines [1-dimensional shape/form] defined b=
y
>    set of points x2. Ray/vector (farli'i or porli'i). See also kruvi, sir=
ji,
> jganu, kantu, mokca.  *Seems to be okay?*
>    6. clupa  - x1 is a loop/circuit of x2 [material]. *Is it the same as
>    djine? Or it doesn=E2=80=99t need to be solid and can be made out of s=
oft
>    materials? Do we need its length or radius?*

lo clupa, in the geometric sense, is a closed curve. It can also be a loop =
in=20
a program, in which case its material is immaterial (mucti).

>    7. jganu - x1 is an angle [2-dimensional shape/form] from vertex x2
>    subtended by lateral [segment] x3. Also (adjective:) x1 is angular; x2
>    corner; (segment x3 can be defined by interval). See also kojna, linji=
,
>    konju, mokca. *Okay, so jganu2 specifies the measure of the angle and
>    jganu3 specifies the length of its sides. Wiktionary says there are tw=
o
>    meanings of =E2=80=9Cangle=E2=80=9D:*
>=20
> A.   =E2=80=8BA. (geometry) A figure formed by two rays which start from =
a common
> point (a plane angle) or by three planes that intersect (a solid angle).
> E.g. =E2=80=9Cthe angle between lines A and B=E2=80=9D
>=20
> B.   B.   =E2=80=8B(geometry) The measure of such a figure. In the case o=
f a plane
> angle, this is the ratio (or proportional to the ratio) of the arc length
> to the radius of a section of a circle cut by the two rays, centered at
> their common point. In the case of a solid angle, this is the ratio of th=
e
> surface area to the square of the radius of the section of a sphere. E.g.
> =E2=80=9CThe angle between lines A and B is =CF=80/4 radians, or 45 degre=
es.=E2=80=9D
>=20
> *Seems that we can=E2=80=99t express three-planes angle.*

I'd say "ligjga" for a solid angle. There are dihedral angles.

Pierre
--=20
ve ka'a ro klaji la .romas. se jmaji

--=20
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