Tagged Questions
1
vote
0answers
51 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
75 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
57 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
44 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
76 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
55 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
82 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
51 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
75 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
56 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
157 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
125 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
145 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
104 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
47 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
158 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
265 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
3answers
850 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
91 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
749 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
132 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
82 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
105 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.
0
votes
1answer
76 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 ...
2
votes
1answer
122 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
274 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
252 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 ...
1
vote
1answer
95 views
Point travels around curve
I wonder what does this mean: Point travels around curve. I try to figure out some math explanation in the book and I can't move forward because I can't understand these words.
I can understand when ...
3
votes
2answers
106 views
What's the most concise way to refer to this shape?
What would you call this shape?
Not the shape in green, I mean the entire object.
0
votes
1answer
88 views
Essentials of Plane Geometry: Need Help Understanding Wording of Question
Could someone explain to me what this simple problem is asking me to do?
Draw three straight lines intersecting by twos?
Does this mean that each line in the set of three has to be intersected ...
1
vote
4answers
203 views
What is the name for a maximal convex set of points contained in another set of points?
What is the name for a maximal convex set of points contained in another set of points X?
Maximal in terms of inclusion. For the desired set to be unique, X can be restricted to be a simple polygon ...
6
votes
1answer
166 views
What is the term for the projection of a vector onto the unit cube?
Normalizing a vector sets its magnitude to $1$ and retains its direction. In three dimensions, it projects the vector onto the unit sphere.
Is there a term associated with projecting it onto the ...
2
votes
1answer
314 views
Embedding, immersion
Could someone please explain what "embedding" means? (Maybe a more intuitive definition) I read that the Klein bottle and real projective plane cannot be embedded in ${\mathbb R}^3$ but is embedded in ...
2
votes
2answers
2k views
Which way is length and which way is width?
I hear people refer to the dimensions of things as "$2$ by $4$" etc. and I know its length by width, but I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). ...
3
votes
1answer
79 views
Name for this triangle centre
Given a triangle I draw circles around each vertex. I chose the radii of these circles so that they are all mutually tangent. There is only one way to do this. I extend these tangents. They concur at ...
1
vote
1answer
152 views
Name of the intersections of a ball with the octants?
The eight regions of space defined by the eight possible combinations of signs for (+/- , +/-, +/-) for x,y,z are called octants.
Given a ball of radius 1 centered in the origin (0,0,0). How are the ...
1
vote
0answers
208 views
What is an isosurface?
I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it?
Thanks.
2
votes
1answer
256 views
Does anyone know the name of this curve?
I have come upon
the curve with the following parametric equations:
$$x(t)=\log(2+2\cos(t))/2$$
$$y(t)=t/2$$
for $-\pi<t<\pi$. It gives the image in the complex plane under $\log(1+z)$ of the ...
4
votes
2answers
169 views
Is there such a thing as the “edge-face dual” of a polyhedron, and is the “edge-face dual” of a cube a rhombic dodecahedron?
The dual of a polyhedron is a polyhedron where the vertices of one correspond to the faces of the other, and vice versa. Is there always a similar correspondence between a pair of polyhedra where the ...
2
votes
4answers
195 views
Term for Tetrahedron with Three Right Angles at a Point
Is there a name for the tetrahedron/pyramid (four vertices, four triangular faces, six edges) where three edges meet orthogonally at a point? Three of the faces are right triangles.
Another ...
5
votes
2answers
480 views
What is the name of the quadrilateral shape described by two radii and two arcs?
What is the name of the four sided shape described by two radii and two concentric arcs?
Like each black and white section taken individually on this image
Or the double score / triple score areas ...
1
vote
1answer
57 views
How is set of points distanced $\leq r$ from set $S$ is called
What is name of the notion described below.
Let S be any body (set of points) in Euclidian n-dimensional space.
Let H(S,r) be set of all points x that distance between x and y is <= r for some ...
2
votes
2answers
94 views
optimize cuts from sheet of metal - what type of math is that?
A person has a sheets of metal of a fixed size.
They are required to cut parts from the sheets of metal.
It's desireable to waste as little metal as possible.
Assume they have sufficient ...
4
votes
2answers
275 views
name of a shape
Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape ...
3
votes
3answers
85 views
Term for Voronoi diagrams with non-point sites
I am looking for a term used to describe an analog to Voronoi diagrams where instead of a single point defining a cell, a continuous set of points is used. For example, starting with five triangles ...
2
votes
2answers
226 views
Broken glass geometry
If topology is called rubber-sheet geometry, would it be accurate to describe the "cut and shuffle" topic of "piecewise isometries" as broken glass geometry ?
Isometry sounds more geometrical than ...
4
votes
1answer
413 views
what size is a “unit torus”?
Wikipedia articles on "unit sphere" and "unit circle" say the radius is 1. Articles on the "unit square" and "unit cube" say the length of the side is 1. Would you expect a unit torus to have major ...
2
votes
1answer
244 views
“circumference” of a sphere
What is the name for I can only describe as the circumference of a sphere. I mean like the equator on a planet. What is the line called which goes around the entire sphere, it can be anywhere (so not ...
7
votes
4answers
2k views
What Are 4 Sided Shapes Called Again?
I apologise for the really basic question. This didn't really fit on any other StackExchange website so the Maths one was the closest one where I could ask.
Really Basic Question- What are 4 sided ...
2
votes
1answer
315 views
Collective Term for XY, YZ and ZX planes
Is there a collective term for the XY, YZ and ZX planes in 3D co-ordinate geometry? I was thinking "principal planes" but I'm not sure where I heard that.
