3
votes
0answers
19 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
34 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
22 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
35 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
79 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
14 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
52 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
35 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
50 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
116 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
42 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
63 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 ...
7
votes
1answer
107 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
37 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
119 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
73 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
49 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
90 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
111 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, ...
3
votes
1answer
150 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
148 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
175 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
87 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
108 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
110 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
196 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
61 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
75 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
196 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
192 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
139 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?
1
vote
1answer
54 views

Higher dimensional analogue of an arc of a circle

What is the higher dimensional analogue for the arc of a circle? I'd like to work with the set of all points lying within a certain distance of a given point on an n-sphere, and I'd like to describe ...
1
vote
1answer
196 views

What is the name of the top of a hemisphere?

I need to refer to the "top" of a hemisphere - the "highest point" on a hemisphere. I am thinking it must be called the "apex" of the hemisphere, but I am not sure.
10
votes
2answers
373 views

Elementary Geometry Nomenclature: why so bad?

A long-ish wall of text, and I apologize. Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A ...
3
votes
4answers
5k views

What is the difference between normal and perpendicular?

What is the difference when a line is said to be normal to another and a line is said to be perpendicular to other?
0
votes
2answers
115 views

What does diameter mean in the sentence of Borsuk's conjecture?

What does diameter mean in the following sentence of Borsuk's conjecture? Sentence: Can every set $S \subseteq \Bbb R^d$ of bounded diameter $\operatorname{diam}(S)>0$ be partitioned into at most ...
-1
votes
1answer
1k views

Name of proof that area of square>area of rectangle of the same perimeter

What is the proof called for the fact that the area of a square is always greater than the area of a non-square rectangle of the same perimeter?
1
vote
1answer
158 views

What does “+ complete” mean?

I'm reading notes about Liapunov stability, and in the book of Abraham, Marsden and Ratiu I found the next definition: Let $m$ be a critical point of $X$. Then $m$ is stable (or Liapunov ...
0
votes
1answer
125 views

Parameter or independent variable?

I need an explanation of the difference between parameter and variable in the following example. In extremal geometric problems when we want to find the object having some extremal property, say ...
0
votes
1answer
187 views

Name of distance from center to side of rectangle

Is there a special name for the distance from the center of a rectangle to a side? I haven't done geometry in a while, but I thought there was an equivalent of a "radius" for regular polygons.
1
vote
1answer
112 views

simplex and power set

I read the following: Let $M$ be a set. The simplex on $M$ is the set of all subsets of $M$; we denote this by $\Delta_M$. We will sometimes refer to the elements of $M$ as vertices of $\Delta_M$. A ...
3
votes
1answer
274 views

What is the proper name of a “doughnut sector” or “curved trapezoid”?

What is the name of this shape? It is basically a sector with a doughnut hole cut out of it. Just wondering if it has a proper name.
8
votes
1answer
602 views

What are curves (generalized ellipses) with more than two focal points called and how do they look like?

An ellipse is usually defined as the locus of points so that sum of the distances to the two foci is constant. But what are curves called which are defined as the locus of points so that the sum of ...
3
votes
2answers
306 views

Notation for covariant derivative

I'm reading John M. Lee's book " Riemannian Manifolds". On page 57, the covariant derivative of $V$ along a curve $\gamma$ is defined, where $V$ is a vector field along $\gamma$. It is denoted by ...