[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [lojban] Geometry shapes categorization
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.
>
> Warning: me not using geometry IRL for a long time can lead to mistakes
> below.
>
> 1. konju - 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 formed by a linear segment rotating around an
> "imaginary" linear segment such that they they intersect with each other
> 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 which
(except the tangent ones) is an ellipse. I think that "konclupa" was intended
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 (= jincla); (usage
> has been for near-circles, such as tight spirals, even if not closed
> loops). Also band, belt, encircle (= jinsru). See also clupa, cukla, dasri,
> karli, sovda, sruri, konju. *Is it terete in cross-section? How to specify
> 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 emphasis
> on roundness means that the concept may include 'ring'. See also djine,
> ranji, bolci, tarmi. *Okay, so a more general than ring concept. Seems that
> we don’t need a diameter place*
lo cukla is a circle, filled in or not, but having only one radius. lo djine
has two radii, the inner and the outer.
> 4. mijgresirji - x1 is a diameter between x2 and x3 of x4. *Diameter –
> do we need it as a separate brivla?*
"mijgresirji" means "line passing through the middle". "Diameter" can also
mean "length of a line segment passing through the middle" (of a circle, the
length is independent of which line segment one measures).
> 5. linji x1 is a line/among lines [1-dimensional shape/form] defined by
> set of points x2. Ray/vector (farli'i or porli'i). See also kruvi, sirji,
> 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’t need to be solid and can be made out of soft
> 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
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 two
> meanings of “angle”:*
>
> A. A. (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. “the angle between lines A and B”
>
> B. B. (geometry) The measure of such a figure. In the case of 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 the
> surface area to the square of the radius of the section of a sphere. E.g.
> “The angle between lines A and B is π/4 radians, or 45 degrees.”
>
> *Seems that we can’t express three-planes angle.*
I'd say "ligjga" for a solid angle. There are dihedral angles.
Pierre
--
ve ka'a ro klaji la .romas. se jmaji
--
You received this message because you are subscribed to the Google Groups "lojban" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lojban+unsubscribe@googlegroups.com.
To post to this group, send email to lojban@googlegroups.com.
Visit this group at http://groups.google.com/group/lojban.
For more options, visit https://groups.google.com/d/optout.