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1
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1answer
49 views

How to solve this problem using spherical coordinates system?

The question is very simple: Volume inside the solid limited by:$ (X^2+Y^2+Z^2=16), (X^2+Y^2=4)$ using SPHERICAL coordinates system. The final answer however can be checked making a "cylindrical ...
0
votes
0answers
11 views

Fitting shapes of know sizes on another larger shape in diagonal fashion

How can I place shapes of known dimensions (with variation) on a larger shape, when intersection of these shapes is permitted and I must make the biggest gap between them? Please note that I wish to ...
2
votes
0answers
53 views

3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
0
votes
1answer
30 views

How you could you change the surface area formula for a cylinder to calculate the curved surface area of the half pipe?

Skateboarders use half pipes for doing tricks. A half-pipe is a half cylinder. Explain how you could manipulate the surface area formula for a cylinder to calculate the curved surface area of the ...
1
vote
0answers
35 views

What shapes fit evenly inside a Hexagon

So I'm designing a board game that uses a number of adjacent hexagonal boards. These boards need to be divided up into spaces (tiles) that players move through. I've been playing with using Hexagons ...
4
votes
1answer
38 views

Divide a square into different parts

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with geometry, which perhaps yields the shortest, simplest proofs, but other ...
3
votes
1answer
53 views

How to find the center of a log spiral?

Given just a few points on a log spiral, how to find the center? Considering that the circle is a degenerate case of the log spiral, is there a way to generalize the method for finding circle centers ...
3
votes
1answer
41 views

Arrange 1-12 around a circle

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with plain old algebra, which yields the shortest, simplest proofs, but other ...
5
votes
2answers
111 views

How to solve this riddle?

How to solve this riddle? All rooms have the same shape and size. Every room has one entrance, and two exits: one on the left, and one on the right (on opposite directions). Both exits lead to a ...
1
vote
0answers
43 views

A quadrilateral drawn in the complex plane, Show that ABCD is a square if and only if $i(a-c) = (b-d)$.

A quadrilateral drawn in the complex plane has vertices $A,B,C,D$, labelled anticlockwise. These vertices are represented, respectively, by the complex numbers a, b, c, and d. Show that ABCD is a ...
0
votes
0answers
22 views

Shape of generalized helix

This is a homework assignment that I fail to understand. The problem is to find the shape of a generalized helix $r=r(s)$ when the fixed vector is $v=(0,0,1)$ and $r(0)=0$. I have found forms that ...
0
votes
0answers
37 views

What do you call a torus with a center?

This may be a dumb question, but what is a torus with a center called? (Imagine a doughnut, without it's center taken out.)
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votes
2answers
57 views

Bisecting line segments in a tetrahedron. [closed]

Suppose that $OABC$ is a regular tetrahedron with base $ABC$. Suppose further that $T$ is the mid-edge of $AC$, $Q$ is the mid-edge of $OB$, $P$ is the mid-edge of $OA$, and $U$ is the mid-edge of ...
1
vote
2answers
51 views

Relationship between the side lengths of a tetrahedron and an inscribed tetrahedron with vertices at the centroids

Suppose that $OABC$ is a regular tetrahedron with sides having centroids $\lbrace E,F,G,H\rbrace$ also forming a regular tetrahedron. What is the relationship between the side lengths of $OABC$ and ...
2
votes
4answers
117 views

I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
2
votes
0answers
49 views

whether any shape can be placed on a tiled surface?

After read "Prove that any shape 1 unit area can be placed on a tiled surface",I think on a surface of equal square tiles where each tile side is 1 unit long,the shape ,less than some constant C>1 ...
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votes
2answers
66 views

What is the name of this strange shape? [closed]

Firstly i don't care about the stuff on the shape or the triangle in it i just want to know the name of the overall shape http://en.wikipedia.org/wiki/File:Pythagorean.svg Also is there a way to ...
1
vote
2answers
44 views

Finding the missing length

How do i find the ST?? What more information do I need? I used Pythagorean theorem, but I still can't find the answer.
0
votes
1answer
16 views

Find correleation between values and degrees

I have an arc that starts at $252$ degrees and ends at $288$ degrees, I would like to assign non - linear values on it with this ratio: $1 - 180$ degrees. $5 - 135$ degrees. $10 - 90$ degrees. $30 - ...
4
votes
1answer
25 views

Find the “surface vertices” of a collection of points.

I am currently doing some experiments in order to simulate liquids. I have a collection of 3D points that interact with each other to form a body of water. I would like to form a mesh from these ...
0
votes
0answers
30 views

Possible areas within an integer grid

Given a 1x1 grid with 4 lattice points $[(0,0),(0,1),(1,0),(1,1)]$ (equivalent to a $2 \times 2$ grid of vertices), there are 2 shapes and areas that can be formed: a triangle and a square. There are ...
16
votes
8answers
1k views

Can someone explain 4th dimensional objects?

I'm not sure if I should ask this in mathematics or in physics. From what I can tell, there are only 3 dimensions: X, Y, and Z. However, I have seen a lot of things about fourth and even fifth ...
3
votes
1answer
49 views

Name for “3-dimensional figure-8” shape

Take a sphere or ellipsoid or similar (hereafter just called sphere) ... and imagine pinching it in the middle, deforming it by moving two points that were on opposite sides of the sphere inward until ...
18
votes
5answers
2k views

How to prove that it is possible to make rhombuses with any number of interior points?

I was given some square dot paper which can be found on this link: http://lrt.ednet.ns.ca/PD/BLM/pdf_files/dot_paper/sq_dot_1cm.pdf and was told to draw a few rhombuses with the vertices on the dots ...
2
votes
1answer
30 views

A “house” (pentagon) with square height $x$ and triangle height $\frac12x$…

Imagine a simple drawing of a "house," a triangle with half of the height of a square that it's laying on, to form a pentagon. If the square's height is $x$ and the triangle's height is $\frac12x$ ...
0
votes
1answer
42 views

Definition of the golden rectangle? [duplicate]

Is this true: The golden rectangle is defined as: X=A+B Y=A Y:X is as B:Y For bonus points: what other shapes with defined orientation but undefined size can be defined in an XY grid by using ...
0
votes
0answers
36 views

Does this construction method produce all possible convex pentagons (up to similarity)?

I read a question somewhere here about convex pentagons. I began to wonder if there was a way to list all possible convex pentagons and came up with the following method: 1) Draw a base line AB of ...
0
votes
0answers
41 views

Constructing a pentagon from a circle

To my understanding you can create any regular N sided shape by using a circle. I decided to give this an attempt from the equations/ formulas given from the internet. Just a side note - is it ...
0
votes
0answers
24 views

What width of material will give the least waste when cutting 3 different sized shapes from it?

I have a finished product that is made from 3 parts. The size of each of the 3 parts that make the finished product are as follows: Ellipse 83cm x 67cm Rectangle 235cm x 5cm Rectangle 130cm x 5cm ...
0
votes
0answers
26 views

Finding the vertices of a square giving the mid point and radius

I'm a programmer with terrible mathematics skills, but I'm getting by with studies. I'm trying to find out the vertices (x,y) of a square, giving the ...
0
votes
0answers
31 views

Non-existent polygon.

Every website I go to which lists all 2-Dimensional polygons begins from the three-sided triangle and works up from there. Given that the area of any regular polygon can be calculated (in degrees) ...
0
votes
0answers
31 views

Can this set of points be called a geometric shape?

If I have a graph $G = (V, E): V \subset R^2, E \subset (R^2, R^2)$, can its visual representation be called a geometric shape if it has edges that are fully enclosed within the minimum area hull of ...
0
votes
1answer
135 views

How's it possible that for two or more shapes given the same area, that each shape can have distinct perimeters?

I've just 'discovered' (of course am not the first though) a very strange property in geometry relating to the the relationship between the Area and the Perimeter of an object. Say you have box A ...
0
votes
1answer
156 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
89 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
40 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 ...
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votes
1answer
87 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
188 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
77 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 ...
61
votes
10answers
12k 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
164 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
147 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
2answers
116 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
34 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
65 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
325 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
14 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
47 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
23 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
52 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 ...