Lack of geometry

[David Cortesi <cbmvax!uunet!pucc.princeton.edu!infmx!godzilla!cortesi>]

I note that Lojban gismu are seriously lacking in terms for
basic mathematics and geometry. I don't see any easy way to
build tanru or lujvo for terms that are really fundamental not
only to elementary math but to astronomy, navigation, common surveying
and other fields.

English         Lojban

        polygons
triangle        ?
square          kurfa
rectangle       ?
rhombus         ?
polygon         ?

        conic  curves
circle          cukla tarmi     -- cukla is "circular", tarmi is "shape"
ellipse         ?
hyperbola       ?
parabola        ?
curve           kruvi

        points and angles

axis            jendu??
radius          ?
diameter        ?
degree          ?
radian          radno
angle           jganu
sine            sinso
tangent         tanjo
cosine          ?

        temperature
kelvin          kelvo
celcius         ?
fahrenheit      ?
degree          ?

There is clearly a shortage of words for measurable quantities.
We have lots of ways to say numbers, but only kelvo and radno
for units!

Granted, some of these can be made up by borrowings (though making
them is beyond me).  But I think some repairs could be still be
made in the gismu list.

Proposition 1: take back kurfa (square) and make it
        "polygon with x2 sides and x3 included angles"
Note that x2 and/or x3 could presumably be a set, for the
cases where the polygon is not regular and you really wanted
to describe it exactly.

This gives you triangles, squares, pentagons, hexagons, etc very
simply; any n-sided figure in casual speech; and accurate
description of any n-gon with some effort.

Proposition 2: take back the adjective cukla and make it

        "closed curve with major axis x2, minor axis x3"

With the assumption that when x3==zo'e it is the same as x2, i.e.
a circle.  This gives easy circles and ellipses with very little
effort. (x3 could be one of the generic numbers like "enough"
if you didn't want to be precise.)  cukla could still mean
"round" as a modifier; ellipses are "round."

Proposition 3: temperatures in Celsius are universal in all cultures
except the merkoids.  Yes, Kelvin is essentially the same, but it
is not convenient to have to mentally add 473 (is it?) before
stating the current temperature as it comes over the TV news (in
Europe and elsewhere).

We really need a gismu for degrees-Celsius.

Proposition 4: Navigators, astronomers, surveyors, and just about
everybody except geometry teachers measure angles in degrees, not
radians.  Yes you can convert between them but it is NOT something
you can do in your head when translating; and you risk error and
mis-translation by doing so.

We really need a gismu for angular degrees.

Proposition 5: it is nice to have sinso and tanjo but it makes no
sense to have them and not have cosines!  Either replace all three
with le'avla or else add a gismu for cosine.