2
votes
1answer
41 views

When does intersection of measure 0 implies interior-disjointness?

If there are two "nice" shapes in $R^2$, such as circles or polygons, whose intersection has area 0, then they must be interior-disjoint, as their intersection can only contain pieces of their ...
1
vote
1answer
25 views

Definition of a geodesic ball?

I think it goes along the lines of: a ball made of a series of flat sides. Also is a geodesic ball and geodesic dome the same thing?
1
vote
0answers
20 views

What's the name for a polygon with exactly two sets of side lengths?

Is there a name for the shape similar to a regular polygon, but using exactly $2$ side lengths (or $n$ side lengths) instead of one side length?
-1
votes
0answers
25 views

What does it mean to say “Resolving intersections”

Consider a surface (with boundary) $S$ with marked points on the boundary such that we may may triangulate the surface. Call a line joining two marked points in a triangulation an arc. Consider a ...
2
votes
2answers
41 views

What are a geometric system and a finite geometry?

Wikipedia says A finite geometry is any geometric system that has only a finite number of points. I wonder what a geometric system is? Is it some set system $(E, F)$, where $E$ is a set and $F ...
6
votes
1answer
61 views

Name of a shape that is intersected once by each ray that starts at a given point

Is there a particular name for a shape that is intersected exactly once by each ray that starts at a given point? To illustrate: I'm looking for a name for shapes like the left one in this image: ...
0
votes
2answers
60 views

Shapes bounded only by lines

What is a term for the set of geometric shapes in the plane, that are bounded by one or more continuous closed curves? This set contains simply-connected polygons and circles but also polygons with ...
4
votes
0answers
46 views

Name for a body that can be completely described using its silhouettes

I'm shooting blind over here because I have no background in this field of mathematics. I assume that if you have a body (in $\mathbb{R}^3$), you can call it convex if any segment from one point ...
1
vote
2answers
83 views

Can we define the normal set without $G$ being a group?

Let $X$ be a set in $G$ and $G$ be a group. A normal set is a set $X$ for which $gxg⁻¹∈X$ for every $x∈X,g∈G$. It's just like the normality condition for subgroups, except that $X$ doesn't have to be ...
0
votes
1answer
27 views

What is the “correct” label for quadrants?

Currently studying trigonometric functions and the book has the quadrants labeled for (+x,+y) is quadrant I, quadrant 2 is (+x,-y), quadrant 3 is (-x,-y), and quadrant 4 is (-x,y). While I ...
2
votes
3answers
67 views

What is linear, numerically and geometrically speaking?

For as simple as it is, I never fully grasped what mathematicians and physicists mean with linear . Intuitively anything that looks like a straight line is interpreted as linear, like something in ...
7
votes
3answers
89 views

Why do we say $n$ distinct points?

" Let's say we have $n$ distinct points... " , you see this every time you open a geometry textbook. Why not just $n$ points ? If the points are not distinct, they are not exactly $n$ points, are they ...
1
vote
0answers
19 views

Theorem about two quadrilaterals with parallel edges

I'm looking for a name for the following theorem: If $abAB$ lie on one line and $cdCD$ lie on another line, and furthermore $ac\Vert AC,ad\Vert AD,bc\Vert BC$, then $bd\Vert BD$. One can ...
3
votes
0answers
23 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
0
votes
1answer
36 views

2D is to face as 3D is to?

Essentially, if a point is a zero-dimensional component of an object, a line is a one-dimensional component, and a face is a two-dimensional component, what is a three-dimensional component? If there ...
0
votes
0answers
32 views

Name of this Formula [Spherical Earth projected to a plane]

I am using a formula to calculate the distance between two coordinates. Basically this is the Pythagorean theorem. I saw this formula on Wikipedia and it works perfectly for my use case. However I ...
2
votes
1answer
39 views

What is the name of the area formed by two intersecting circles?

When two circles intersect they form an area which is "ellipse-like" in shape. What is the name of this shape?
3
votes
0answers
83 views

What is this method of dividing a plane called?

I have an idea of a method for recursively dividing a plane, and as I'd like to do more research about this algorithm and the set of points that it produces, I'd like to know what it's formally known ...
0
votes
0answers
17 views

Family of transformations of a given shape

Let $s$ be a certain geometric shape. What term describes the set of all shapes that result from any combination of the following operations on $s$: translation rotation scaling reflections ...
2
votes
0answers
54 views

Is there a name to refers to anything that is a point, line, plane, etc?

I'm teaching my juniors in high school some beginning linear algebra, but I find there is some vocabulary I am missing. I want to say that points, lines, and planes are all related, but is there a ...
2
votes
0answers
152 views

What to call this kind of symmetry in a sphere?

Geometrically, if the two hemispheres of a spherical distribution of some kind (let's say a spherical gas cloud) are similar such that the properties of the gas as seen by a person standing on a ...
0
votes
1answer
46 views

Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
2
votes
4answers
54 views

Geometry terminology: concrete vs. continuous polygons?

I am trying to find the proper terminologies for 2 kinds of shapes: The first type of shape I'm calling "concrete polygons". They have a finite number of straight sides (connecting at vertices) and ...
2
votes
3answers
124 views

What is the correct English name of these lines?

Hello. I'm looking for the English name of these two lines in a two dimensional plane: they go through the origin they make angles of 45° and 135° with the $x$-axis, dividing the plane in two parts ...
0
votes
2answers
45 views

Naming general objects in more than 3 dimensions

In a paper I am writing, I need to talk about a general "object" formed by the points of a connected set in an $n$-dimensional euclidean space. I have found some suggestion here, but none fit my ...
2
votes
1answer
43 views

Notation for translating vectors

I'm completely new to vector geometry and recently encountered some new notation (and wholly unfamiliar) for the translation of vectors. $$T:Z \mapsto A + Z$$ The above is described as A ...
2
votes
2answers
98 views

What is the meaning of “integral point”?

While reading this paper (http://cowles.econ.yale.edu/P/cd/d04b/d0473.pdf) I encountered the concept of "integral point", used first in definition 5.1, on page 34. Does anybody know more details about ...
0
votes
1answer
51 views

term for a “squared simplex”

The set of points $$\{(x_0,...,x_n)|\forall{i}: x_i \in [0,1], \ and \ x_0+..+x_n=1\}$$ is an n-simplex. What can I call a set of points: $$\{(x_0,...,x_n,y_0,...,y_n)|\forall{i}: x_i,y_i \in ...
8
votes
1answer
132 views

Name of shape with constant distance to a line segment

For a computer graphics problem I have a shape that is defined by a constant distance to a line segment: I tried to find a name for this shape, but my Google skills have failed me. Does it have a ...
0
votes
1answer
42 views

Is there a different word for a line segment in 3D versus in 2D?

Many shapes have different terminology for them depending on how many dimensions. For example, a regular quadrilateral in two dimensions is a rectangle, but in 3D it is a box. Compare also circle ...
2
votes
1answer
170 views

How do you call the line y=0?

What do you call the line y=0 in a 2-dimensional plot? It's not the x-Axis, since i have the x-Axis below the plot. Is it called zero line?
0
votes
2answers
97 views

What is the $uv$ pair, or $uv$-plane, exactly?

Maybe the answer to this question is easier than computing $1+1$, but I often find this $uv$ pair on pretty much all the parametric equations that have something to do with 3D geometry and all the ...
3
votes
0answers
51 views

Curve of centers of curvature

I really can't find the English name of the curve of the centers of curvature of a curve. Formulated more precisely: Suppose $\alpha$ is a regular curve in $\mathbb{E}^2$ and $||\alpha(t)'||=1$. How ...
2
votes
2answers
98 views

Terminology for a rectangle whose width/height ratio is between $r$ and $1/r$?

What do you call a rectangle whose width/height ratio is between $r$ and $1/r$? I use the terminology "$r$-balanced rectangle". So, a $1$-balanced rectangle is a square, a $2$-balanced rectangle is a ...
1
vote
0answers
20 views

Terminology: interior subunits of polytope compounds

Edit: trying a better time of day. I'm trying to learn some geometry on my own and am getting drowned in terminology. The structures I'm looking to identify are those created by the overlap of two ...
1
vote
1answer
134 views

What is the definition of a “Circular Wedge”?

In Ahlfors' Complex Analysis, chapter 3, section 4, the author claims that a region whose boundary consists of two circular arcs with common end points is either a "circular wedge" or its complement, ...
4
votes
1answer
177 views

Maximal volume for given surface area of an $n$-hedron

Is there a term for a polyhedron with $n$ faces (or, similarly, $n$ vertices) that maximises the enclosed volume for a given surface area (equivalently, minimises the surface area for a given volume)? ...
2
votes
2answers
166 views

What is the technical term for certain circles?

I am writing up some notes on equilateral triangles. I have reached the point where I want to show that a triangle is equilateral if and only if the three circles P, Q, and R, in the above diagram ...
2
votes
1answer
202 views

Is there a term that means “the sum of the length, width, and height of a box”?

I seem to encounter this sum every time I fly (see this question, airline baggage restrictions) and am using it to limit the acceptable size of an object in an RFP. I have heard a variety of names ...
2
votes
1answer
98 views

Which polyhedra have an even number of faces touching each vertex?

A two-coloring of the faces of a polyhedron is always possible when an even number of faces meet at each vertex. http://www.georgehart.com/virtual-polyhedra/colorings.html Is there a name for ...
4
votes
1answer
110 views

What is the name of this geometric figure

Consider four lines $X_1, X_2, Y_1, Y_2$ pairwise parallel: $X_1$ is parallel with $X_2$ and $Y_1$ parallel with $Y_2$. The four intersection points form a square. Does this figure have a known name ? ...
1
vote
0answers
118 views

Is there a formal name for “Star” Polygons created by extending regular polygons

There exist Star Polygons created (for some $n$) by tracing a line along the consecutive vertices $V_0, V_1, \ldots, V_{n - 1}$ of a regular $n$-gon using $m$ steps, e.g. $$V_0 \rightarrow V_m ...
1
vote
2answers
215 views

What do you call the part of a plane “in front of or behind” a line segment?

This is a question of terminology. Suppose we have a line segment AB in a plane. The line segment forms three "zones" in the plane, where the "middle zone" is comprised of points for which some line ...
1
vote
2answers
64 views

Is the word “adjacent” being used correctly in this geometry problem?

I am trying to say Construct $\triangle ABC$ such that the extension of side CB is adjacent to side AB I am trying to avoid using poor ambiguous vocabularies like "to the right of AB" ...
1
vote
2answers
83 views

Geometry vocabulary.

Does anyone know how i can describe the point "x" that's in the picture? my best attempt so far is to say The point X is on the extended line segment of DE and lies outside $\triangle ABC$ and is ...
2
votes
1answer
81 views

What does 'the forward theorem' refer to?

I have seen the following in a circle geometry proof in a Cambridge textbook: We have proven that angles at the circumference standing on the same arc of a circle are equal. The converse of this ...
0
votes
1answer
209 views

Is there a name for position and dimension in the mathematics

I'm a Software Architect who looking for a corresponding term for position and dimensions of an object at the sametime. Is there a word or term for that in geometry or analytic geometry?
1
vote
1answer
128 views

What are the transformations of the plane called whose derivatives at each point are isometries?

Let $f:\Bbb R^2\to\Bbb R^2$ be a differentiable function. Are there names for the following two conditions? $Df(p)$ is an isometry at each point $p\in\Bbb R^2$; $Df(p)$ is a similarity at each point ...
3
votes
3answers
198 views

Naming quadrilaterals

Is there a rule for naming quadrilaterals in English? What I am expected to know about are: square, rhombus, rectangle, parallelogram, trapezium, kite. But how do we name other quadrilaterals?
2
votes
0answers
148 views

Formal name for polygon with hole

Is there a formal name for an irregular polygon that has 1 or more holes or cutouts in it? I've heard it refered to as a "swiss cheese polygon" or a "Donut polygon". Is this even strictly a polygon?