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[lojban] Geometry shapes categorization



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
  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
  4. mijgresirji - x1 is a diameter between x2 and x3 of x4. Diameter – do we need it as a separate brivla?
  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?
  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.

  1. bolci x1 is a ball/sphere/orb/globe [shape/form] of material x2; x1 is a spherical object [made of x2]. Also round. See also bliku, cukla, bidju, gunro. Radius or if ellipsoid or geoid then what?
  2. tanbo x1 is a board/plank [3-dimensional long flat rectangle] of material x2. See also bliku, kubli.

 

  1. bliku x1 is a block [3-dimensional shape/form] of material x2, surfaces/sides x3. x3 sides/surfaces should include number, size, and shape; also polyhedron (= pitybli having flat/planar sides/surfaces). regular polyhedron (= kubybli, blikubli), brick (= kitybli); See also tapla, kubli, tanbo, canlu, kojna, sefta, bolci, kurfa, tarmi.
  2. kurfa x1 is a right-angled shape/form defined by set of vertices x2, dimensions x3 (default 2). Also rectangle, square, rectilinear; square (= kubykurfa, pitkubykurfa), cube (= kurkubli), rectangle (= clakurfa), rhombus/diamond (= sa'orkurfa, sa'orpitkubli). See also bliku, kubli, tapla, salpo, tarmi.
  3. kubli x1 is a cube/regular polyhedron/polygon of dimensions x2 (def. 3), surfaces/sides x3 (def. 6). (cf. kurfa - needed for 'cube', bliku for a physical object; tanbo, tapla, tarmi). Seems that bliku3 is better to express with kubli2 and kubli3? For tanbo it seems to be the only option.

Also I wish to have examples of kubli2, kubli3, kurfa2 fiile dwith something sclearly specified.

 

Many important shapes are not in gimste. E.g. pyramid. It was suggested

pirmidi - x1 is a pyramid of base/side x2 and height x3

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