A star is born!

A

Amateur_geometer

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Hello, Mathematicians! I'm developing a theory and have run into a Geometry question that should be a snap to answer, but I can't seem to find this out.

Is there a named basic object in Geometry defined as "an infinite set of rays with a common point of origin"? I would think "Aster" would be it, but I cannot verify this. A "star" in Geometry seems to be reserved for 2 dimensional objects. The best I can do is couple "point" with "sheaf of rays". I would prefer to use "Aster."

Thanks for your help.

-Bob
 
Shouldn't we learn why we care before we go to the trouble to name it?
 
@JeffM

As far as I'm aware, a "star" in 2 dimensional geometry refers to a star shape similar to that made by a cookie cutter, generally with 5 or more points made of angles. An analogue or hyper-star in 3 dimensional space would not match my definition (the infinite set of rays sharing a common point of origin) at all. It would have pyramid shaped protuberances, not rays.

As far as definitions, in Biology there is: A star-shaped structure formed in the cytoplasm of a cell and having raylike fibers that surround the centrosome during mitosis.

This would be more like what I'm looking for in Geometry.

And a more complete etymology does in fact include "star": Latin ast
emacr.gif
r, a type of plant, from Greek, star, type of daisy.

Frankly, I'm quite surprised that this (what seems to me) most basic geometric element seems not to have been named! It is not a point, though obviously a close relative.

@tkhunny

Please bear with me, I cannot get into why this is important to me just yet. My question should be of interest to Mathematicians regardless. The object in question fills space entirely and can be described with simple math. Does it not already have a name?

-Bob
 
Well, if it fills space, isn't it just "Space". There are lots of ways to point to all of space. So what? They need descriptions, not fancy names.
 
@tkhunny

What an unbelievably aggressive, ignorant, unwarranted and unfriendly response. I can't imagine your other 7215 posts were like that.

As an amateur geometer I thought this, the freemathhelp forum, might be a friendly and knowledgeable place to find out what should be a simple question of geometry. Its a decent question and I'm not just trying to get someone to do my homework for free, like many others who post here. I should be welcomed.

At the moment, I would like to find the answer to my question. Later, we can discuss its significance and many ramifications.

@JeffM

The Oxford Old English Dictionary shows the primary definition of Aster (up to about 1650) was "star", though now it is obscure, with its roots in Greek. The Latin came after Greek.
 
replies...

I had responded previously, but for some reason my post never got past moderation. Thus, a second attempt:

@JeffM

The term "star" as commonly used in Geometry seems to indicate a cookie cutter shape, with 5 or more points made by angles. It can often be seen in the company of triangles, circles, squares, etc. on a two-dimensional plane. A hyper-star of this shape would likely suggest pyramidal projections rather than rays.

The Latin "astr" was apparently derived from the preexisting Greek, which is "Aster" and means star. The flower was named much later, obviously also a derivative of the Greek. The Greeks probably translated Babylonian to get their version.

I've moved on to exploring "pencil of rays" (see http://dictionary.die.net/pencil of rays), though that's not working well either, as a pencil does not necessarily indicate all of the rays which share a common point.

@tkhunny

First of all, if it's of no interest to you, you needn't reply. I personally find it quite odd that this shape, which is very basic yet significant, and most likely discovered ages ago, has no name in modern geometry.

Although "space" shares much with a complete pencil of rays, it is not at all a synonym, and in many instances the terms are not interchangeable.

I still prefer to use "Aster" as this shape's name, and in doing so, am possibly restoring a once used but now obscure term.
 
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