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).
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