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-6
votes
0answers
38 views

Why are the squares on a chess board congruent figures? [closed]

Two geometrical figures that have exactly same shape and same size are called congruent figures. For example, the squares on a chess board or rings on a target. Why are they congruent ?
0
votes
1answer
46 views

volume of water in the the pool and domain range of function question

im working on advanced problems and the question is following: A swimming pool is 20 ft wide, 40 ft long and 3 ft deep at the shallow end, and 9ft deep at its deepest point. 1) Express the volume of ...
1
vote
1answer
59 views

Super conic sections?

I know graphs of the form $A x^2 + B xy + C y^2 + D x + E y + F = 0$ are conic sections. But what would happen if I changed the highest power to 3? Would this be a new 3D shape, a 4D version of it, or ...
1
vote
1answer
28 views

Can a 1-side, 1-border object exist in 3D?

We are three friends discussing whether a three dimensional object with a single side and a single are can possibly exist. I first came up with a Moebius strip as an affirmative example The second ...
-1
votes
1answer
56 views

Why are circles always 360 degrees? [duplicate]

Please Answer quickly i am really confused Most websites say that people thought a circle is 360 degrees because there are 360 dayes in a year but there are not they also say that the base number is ...
0
votes
1answer
28 views

Area of ellipse formed by slicing a cylinder

What is the equation of the area of the ellipse when a cylinder of radius x is cut by a plane inclined at an angle a. Angle a is the angle between the plane and the axis of the cylinder. If a is 90 ...
1
vote
2answers
69 views

How to get proficient?

I'm currently a 1st year undergrad and I feel like my mathematical ability is very poor. I want to get better at a lot of different areas so I can feel very comfortable with mathematics. I see ...
57
votes
10answers
11k views

Is there a shape with infinite area but finite perimeter?

Is this really possible? Is there any other example of this other than the Koch Snowflake? If so can you prove that example to be true?
0
votes
1answer
69 views

Use of Delaunay Triangulation and Voronoi Diagram to find alpha shape using Edelsbrunner's algorithm

I am learning how to find the shape of a set of points in 2-D. I understand that Alpha Shape method is a good way to find the shape of a set of points. Alpha Shape was originally introduced by H. ...
0
votes
2answers
26 views

Question on volume of swimming pool

Swimming pool is of length 20m, wide 5m and height of the swimming pool increase from the 1.6m to 4.4m. What is the volume of swimming pool? How I approached: Area of swimming pool = Area of cube + ...
1
vote
3answers
80 views

cube / shape question for my daughter (which I can't answer)

5cm sided cube. If a 1cm cube is cut from each corner, how many faces will the new shape have? Thank you
1
vote
0answers
29 views

unique cube arrangments

i have received this math riddle which i cannot solve, the riddle: given a set of cubes, a unique shape is any shape that was created joining cubes sides together and does not match any previously ...
1
vote
2answers
59 views

Oval/quadrupole characterization

Context: Points on a circle satisfy the equation: $$x^2+y^2=r^2$$ where $r$ is the radius. In a similar manner one can show for an ellipse: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ is satisfied($a$ ...
1
vote
1answer
68 views

Finding the radius and height of a cone inside a cone

I need to find the volume of a metal cone that is hollow with a thickness of 2cm. The radius of the big cone is 8cm and the height is 12. The thickness determents the radius, and height of the little ...
1
vote
0answers
11 views

create polygon section with equal sides

I have to create essentially these sections of a polygon. I have width(W) and height (H), and number of sides (3 on left abc and 4 on right image ABCD) I need each side to be equal. How can I ...
0
votes
2answers
29 views

How to define distance between two functions in a non-linear space (example of non-linear space: shape space)?

Suppose I have two parametric circle $f_1=(acost,asint)$ and $f_2=(bcos t,bsint)$, $t\in(0,2\pi),a>0,b>0$, which lies in some non-linear space. Are there any way, how to define the ...
0
votes
2answers
21 views

Rectangular Bisection

This may be a really stupid question but... If I bisect a rectangle twice diagonally. Do all the angles at the corners equal 45°? So, if I drew this diagram accurately, would each red angle equal ...
2
votes
1answer
33 views

Do two lines lay in the same 4-dimensional plane

I don't know how quite to phrase this, but I'll try. Because two point are co-linear and two lines cannot always be used to define a plane and aren't always in the same plane, are two lines always ...
0
votes
0answers
229 views

Why Shape space is manifold?

In Shape analysis, often shape is considered as continuous parametrized closed curve and the shape space as Hilbert Riemannian manifold. Can any one help me to understand, why the shape space is ...
1
vote
2answers
34 views

Isosceles Trapezoid Diagonal Lengths

In isosceles trapezoid $ABCD$, $AB=6$, $BC=9$, $CD=8$, and $AD=9$ find the distance from point $D$ to $BC$ (perpendicular).
0
votes
1answer
36 views

What is “Disjoint line segments”?

I'm unable to find a definition for disjoint line segments. Can someone please define it and if possible show images with examples?
0
votes
0answers
32 views

Recognize a shape with a set of Data points

So I have a number of points on graph. For Ex: (1,1) (2,5) ......... and so on. And I want to recognize which shape is it closest to from circle, triangle and rectangle. -By closest I mean ...
1
vote
2answers
45 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 ...
3
votes
1answer
236 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
146 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
81 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
27 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
29 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
342 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
61 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
91 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
12 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
32 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
129 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
72 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
38 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
57 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
141 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
86 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
294 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 ...
4
votes
1answer
130 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
164 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
2k 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
71 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
78 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
54 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
197 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 ...
4
votes
0answers
55 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 ...
9
votes
4answers
634 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
259 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 ...