# Tagged Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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" ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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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?
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### 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?
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### 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 ...
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### 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.
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### 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 ...
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### 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?
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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.
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### 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 ...
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### 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.
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 ...