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0
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1answer
19 views

Name for shape defined by volume between two concentric spheres

Is there a proper name for a shape defined by the volume between two concentric spheres? My understanding is that, formally, a "sphere" is strictly a 2D surface and there's a formal term for volume ...
-1
votes
1answer
12 views

What's the relation between the number of sites and the number of links for a 2d square lattice? [closed]

How about the case of 3d and 4d... Is there some general relation of the number of links and number of sites?
0
votes
0answers
24 views

Estimating the mean internal distance between borders of an irregular shape

I have two overlapping (not matching) irregular shapes ($X$ and $Y$), and I would like to estimate the mean distance between their limits. What I've been trying so far is obtaining the irregular ...
3
votes
0answers
157 views

Can we rotate a 3D lattice of deformed spheres?

EDIT by EricStucky: The full text of original post below for reference, but I have talked with the OP in chat and believe that this is the mathematical core of the question. Suppose that we have ...
3
votes
1answer
101 views

Prove that there is only one way to make a square using all six tangram pieces

I am pretty sure there is only one way to make a square from the six tangram pieces: How can I prove this is the only way respecting all symmetries?
6
votes
1answer
67 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: ...
1
vote
0answers
16 views

Geometric figures inside a bounding box

Let us suppose that we have a bounding box of length $l$, width $w$, and breadth $b$. I wish to know the dimensions / characteristics of a tetrahedron cylinder cube pyramid inside this bounding ...
0
votes
1answer
23 views

Inverting complicated function (possibly using secant root finder)

So I have the following equation from the 2002 paper "A Rapid Hierarchical Rendering Technique for Translucent Materials" http://graphics.ucsd.edu/~henrik/papers/fast_bssrdf/fast_bssrdf.pdf Here is ...
-1
votes
2answers
77 views

Cut A Shape Into Two Triangles

I have this shape: , and I want to put a straight line somewhere through the shape to cut it into two triangles. I know that this is possible, but I don't know how. Any help is appreciated!
0
votes
3answers
59 views

$x^2 + y^2 - y = 0$ is… a cylinder?

I've this question: Find the area of the intersection between the sphere $x^2 + y^2 + z^2 = 1$ and the cylinder $x^2 + y^2 - y = 0$. Is this second equation even a closed shape? If one were to ...
0
votes
1answer
64 views

Points $S$ and $T$ are on side $\overline{CD}$ of rectangle $ABCD$ such $ \overline{AS}$ and $\overline{AT}$

Points $S$ and $T$ are on side $\overline{CD}$ of rectangle $ABCD$ such $\overline{AS}$ and $\overline{AT}$ trisects $\angle DAB$. If $CT = 3$ and $DS = 6$, then what is the area of $ABCD$? I have ...
0
votes
0answers
11 views

Does the dimension of R have anything to do with proportion of inscribed triangles to their paralellepipeds?

I had a hard time deciding on how to title this question. I hope it gives people some idea so they can give me their two cents. We all know that the formula for a triangle is $$ (1/2)b*h$$ In ...
1
vote
0answers
21 views

Retanguloids and volumes

I am currently going back through all the "Challenge" questions in preparation for exams, and have come across this, any hints on how to approach?
0
votes
1answer
72 views

How do one calculate the area (m^2) of freeform shapes?

Ok, ill be honest, i'm building a patio, and for that i'd like to estimate the cost using sqm. However the shape of the patio is what you might call non-standard. So far i've been able to use ...
1
vote
2answers
46 views

Comparing the shape of two probability distributions

How do we compare the two probability distributions based on their means and standard deviations ? suppose we have the following. 1st probability distribution mean = 0.6645 SD = 0.02345 2nd ...
0
votes
1answer
37 views

How to decide on the shape of the Beta distribution?

Suppose we toss a coin which is not fair. and the probability of success is 0.7. Is that enough to decide on the shape of it beta distribution ? what would be its shape then ? As far as I know, it's ...
0
votes
1answer
35 views

Interpolating Z-Values when given complete and incomplete XYZ pairs

I am building an application that works with PolyLineZ (ESRI Shapefile) data and rewrites outlying Z values. The minimum and maximum Z-values are defined by the user through the interface Let's take ...
0
votes
1answer
92 views

How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
0
votes
0answers
74 views

Estimating the geometric shape of a point cloud without using the vertex information

Consider a point cloud format that describes 3D point clouds by vertices, triangle labels and normal vectors. If we miss the vertex information, is it possible to retrieve the lost data by triangle ...
2
votes
2answers
218 views

fill a rectangle with hexagons

Suppose I have a rectangle and I want to fill it with hexagons without having any white space. The hexagon doesn't need to be in the regular hexagon shape so the only thing that matters is that it ...
3
votes
1answer
96 views

How can I understand is the picture $2D$ or $3D$

I can not understand is this picture 2D or 3D .what is the rule or condition to be a 2D or 3D picture.How can I understand that?please help me?
0
votes
1answer
131 views

How to get perpendicular line to an edge of a polygon.

This is a pretty basic geometry question, but I couldn't find an answer clear enough for me on Google (I don't know much about math). Let's say I have a rectangle. I have the coordinates for the four ...
1
vote
4answers
1k views

What's the difference between width and height?

I've never been to good with Mathematics... I'm wanting to change that as game development has always been a passion of mine. I started studying math on Khan Academy about a month ago and everything ...
2
votes
4answers
59 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 ...
0
votes
1answer
66 views

If you draw a line from the corner of this triangle to the middle of the opposite side, why do the lines intersect at the middle?

This is the triangle (excuse my crude finger painting). I've drawn this for an equilateral triangle, but it holds for other triangles too it seems. This is from Paul Lockhart's book "Measurement", and ...
0
votes
2answers
50 views

Determining the rotation shape

Consider a large number of points distributed on the circumference of a circle with radius r. If I rotate each point with a randomly chosen Euler angle around a randomly chosen coordinate inside this ...
8
votes
1answer
159 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 ...
3
votes
0answers
49 views

Selecting k vectors with maximum spread out of a set of n vectors

Given a set $\mathcal{V}$ of $n$ vectors, find a subset $\mathcal{V}_k = \mathcal{V} - \mathcal{V}_{n-k}$ containing $k$ maximally spread vectors. Intuitively, these $k$ vectors should be spread as ...
7
votes
3answers
380 views

If a point has no dimension and no area how can there be space?

Everyone knows that a point on any plane has zero magnitude, height, width, or volume. A line is a collection of points, and a plane is a collection of lines, while a cube is a collection of planes ...
2
votes
0answers
156 views

Dome with a parabolic shape?

Here is the question: The dome over a town hall has a parabolic shape. The dome measures 48 m across and rises 12 m at its centre. a) Determine the quadratic equation that models the shape of the ...
0
votes
1answer
576 views

fabric design using trigonometric functions

is there any trigonometric function or any others that involve trigonometric function, that draw cool fabric shapes or patterns? I have seen some pictures like but with trigonometric functions... ...
1
vote
2answers
58 views

Rotate shape on a graph

I have some shape built out of points. The coordinates given for each point . (see pic below) I need to rotate this shape by a particular angle (for example 60° see pic below) Is there some formula ...
3
votes
2answers
87 views

What's the symbol m in this sum?

I'm supposed to write some code to calculate the inertia moments of a shape, but I am afraid I have been given too little information. The matrix that I must obtain is this one: $$ \begin{vmatrix} ...
0
votes
3answers
54 views

Volume of Shapes

I'm doing some maths revision at home from a GSCE book and I'm a bit stuck. I'm not sure how to start off. (I know the formulae for a volume of cone and a formulae for a volume of a sphere but I don't ...
0
votes
0answers
61 views

Spherical object with n vertices and no coordinate singularities

I'm programming a tool where I want to track the directions of a unit vector. I want to store the position to which the vector is pointing on a unit ball. Each time the vector points to a position $x$ ...
0
votes
0answers
52 views

Locating a shape defined by five points within a cloud of points

What is the most efficient way to find a shape that is defined by 5 rigid, coplanar, non-collinear points within a 3D point cloud?
0
votes
1answer
122 views

Number of sides a regular polygon has.

The question is "Both tile A and B are regular polygons. Work out the number of sides A has." For this I put B is equilateral ∴ all angles are 60. However, I have no idea where to go from ...
1
vote
2answers
74 views

How to find length when viewing at some angle?

I have a question on angles. I have a rectangular tile. when looking straight I can find the width of the tile, but how do I find the apparent width when I see the same rectangular tile at some ...
1
vote
0answers
30 views

What's the most optimal container consisting of two spacial figures?

I asked myself this question as I was answering an optimization question where I had to figure out what three dimensional shape had the best volume-surface area ratio. Which I find to be a sqhere. It ...
3
votes
0answers
121 views

How can I find a maximal inscribed ellipsoid to a *concave* set of points, in 3D?

I have a set of points which describe the surface of an irregular, natural (i.e., occurs in nature) object. This point set is not necessarily convex, and contains occasional indentations so parts of ...
2
votes
1answer
69 views

I need to trace the edge of a hexagon point by point

To create an animation in code I first need to be able to describe a point by point path around a hexagonal shape. I already have the $\displaystyle \frac{x}{y}$ coordinate of each vertex. I don't ...
1
vote
2answers
81 views

Geometry involving a diagram and inequalities

The answer to the following problem is A by the way. Morever how does that come to be?
2
votes
0answers
24 views

Characterize a large class of shapes using a finite number of parameters

I am doing some numerical computations searching for an optimal shape for a certain functional. In my particular case, the shape $\Omega$ is a 2 dimensional star shaped domain by the origin, which ...
1
vote
0answers
158 views

8 x 8 = 13 x 5 ???

I'm sure some (if not most) have seen this by now and since I'm fairly new to real deep mathematical explorations I'm stumped as to why this would be true. For class I was asked to cut out an 8" x ...
3
votes
1answer
181 views

Can you calculate an area of a curve using a string?

Take a look at this curve. Imagine that I have drawn this on a paper, and that I want to find the area of it. (The thickness of the line is assumed to be constant). Assume that I use a string to ...
4
votes
2answers
598 views

Combinatorics. Inscribed Triangle in a decagon. No shared sides.

How many different triangles can be inscribed inside a regular decagon such that the triangle shares its vertices with the vertices of the decagon, but the triangle shares none of its sides? Here is ...
2
votes
0answers
74 views

How do you call a 3d convex shape made of 8 arbitrary points?

Is there a name for a 3d convex shape made of 8 arbitrary points ? That would be like a cube or a box, except that the distances would not necessarily be equals, neither the angles necessarily be ...
0
votes
2answers
465 views

calculate the volume of water in a portion of a cone

Imagine we have a cone filled with water, if we were to take the upper portion of that cone how would we calculate the volume of water present. For example: So, in this example we have a surface ...
4
votes
1answer
620 views

What kind of quadrilateral is determined by four sides and a diagonal?

Wikipedia says that The shape of a simple quadrilateral is fully determined by the lengths of its sides and one diagonal. but I have my doubts. For example, the two quadrilaterals in this ...
3
votes
1answer
203 views

Fitting Shape in Circle for Shape Classification

I need to classify arbitrary 2D shapes. The classification should be invariant to at least affine transform. To achieve this invariance, I decided to "normalize" each shape by fitting it to a unit ...