Hodge-Podge
of Points:
- Did you include: kruvi, plita, sirji (especially in contrast
with linji; what are the differences
between these two words (how does one say “geodesic”?)), mokca, panra, cimde? plita
and karda/tapla (if the material
terbri is erased) are geometric too.
- We probably want to be able to
talk about tilings.
- We also lack an easy
way to specify the metric of the space.
- I have been wanting to
introduce Schläffi symbols in Lojban.
- One thing that one must be careful of in Lojban is distinguishing between
measures and objects. This comes up when one says in English "with diameter ____" or "with angle ____". A diameter is a line. So, “with diameter L” (where L is
defined to be some line) is proper (and follows the definition). On the other
hand, “with diameter 1 (unit)” is abusive and wrong: it should be “with
diameter measuring 1 unit”. Likewise for angles and their measures. I try to be
clear in English; Lojban needs to separate the two too. I propose that lujvo or
constructs with merli are employed
for the measures (the accuracy terbri thereof is sort of annoying in some
situations because in mathematical contexts, the accuracy is 1, but that could
probably be covered in the elliptical); the objects should be referenced by the
gismu.
- How does one
distinguish between a loop (closed, connected, simple (Jordan) curve), a spiral,
a ring/annulus, a torus, an ellipse, a sphere, a helix, and a whole bunch of
related concepts? We have words only for a few of them, with a lot of overlap.
- Is
there any implicit assumption that cukla/bolci-style
roundness implies convexity and connectedness?
A simple, closed, connected (Jordan) curve (= loop?) is basically a
circle, but is more generalized in the sense that it can be “variably curvy”.
General
Problems:
1) gismu list terbri for material/composition.
Examples: bolci, karda, tapla.
2) Many gismu improperly distinguish between
volumes and surfaces. Either we should
define (preferably all) geometric words to be surfaces and reference their
encompassed regions by lujvo with “area”/canlu (example: bolci means “sphere”, bolca’u means “ball”), or we should
define (preferably all) geometric words to be the encompassed volume and
specify the boundary/surface by lujvo with perhaps korbi (example: bolci
means “ball”, bolkoi means “sphere”).
Although, one must note that the encompassed (interior) region can depend on
interpret in some metrics; a small loop on the ground on Earth (an oblate
ellipsoidal surface) may be determined to have a small area or a large one- and
even the shape of that area depends on this interpretation.
An
Off-Topic Problem for Math in Lojban:
- There is no general term for “evaluate” (as
of, say, a function at a particular input value).