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Questions tagged [geometry]

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.

2
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2answers
576 views

Convex polyhedron with open faces

Convex polyhedron $P$ is a subset of $\mathbb{R}^n$ that satisfies system of linear inequalities \begin{align} a_{11}x_1 + \cdots + a_{1n}x_n & \sim_1\, c_1 \\ & \vdots \\ a_{p1}x_1 + \cdots + ...
0
votes
3answers
4k views

how to find point lie on the arc [closed]

i have arc A ,i know startangle,endangle,startPoint,Endpoint,centre,radius of arc and i have point B, i like to find point B lies or not in arc A , i need formula or algorithum for this
2
votes
1answer
192 views

What is the name of this lattice?

Suppose we have an atom at every point with integer coordinates in $\mathbb{R}^d$. Take a ($d-1$)-dimensional hyperplane going through $\mathbf{0}$ and orthogonal to $(1,1,1,\ldots)$. What is the name ...
2
votes
4answers
166 views

how do find the line lies on another line

I have Line $A$ with points $(1,1)$ and $(8,8)$ and another Line $B$ with points $(2,2)$ and $(4,4)$. I would like to prove Line $B$ lies on Line $A$. How can I do this?
11
votes
4answers
1k views

Orientability of $\mathbb{RP}^3$

I was wondering if there is a nice way to see that $\mathbb{RP}^{3}$ is orientable without using tools of algebraic topology, like homology. The only think I could think of was to argue that $\...
9
votes
2answers
917 views

Vortex Voronoi diagram?

Suppose there are a finite number of disjoint unit-radii disks in the plane, each spinning clockwise or counterclockwise at the same angular velocity. The plane is filled with a thin fluid layer, and ...
0
votes
3answers
590 views

Graphing a Parametric Polynomial based on a given set of points

I have been tasked with creating a C++ program (with GDI+ for graphics) that takes a set of user defined points and creates polynomial curve through them. For extra credit, I have to support a ...
13
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3answers
5k views

geometry and topology

I was wondering what are the differences and relations: between geometry and topology; between differential geometry and differential topology; between algebraic geometry and algebraic topology? ...
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4answers
167 views

Finding a line that satisfies three conditions

Given lines $\mathbb{L}_1 : \lambda(1,3,2)+(-1,3,1)$, $\mathbb{L}_2 : \lambda(-1,2,3)+(0,0,-1)$ and $\mathbb{L}_3 : \lambda(1,1,-2)+(2,0,1)$, find a line $\mathbb{L}$ such that $\mathbb{L}$ is ...
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3answers
3k views

Intersection of Cubic curves

This is the question which i am attempting to solve and it seems to be difficult to get rid of the exponents. Show that a the two cubic curves $Y^3 = X^2 + X^3$ and $X^3 = Y^2 + Y^3$ intersect each ...
4
votes
3answers
10k views

Finding point coordinates of a perpendicular bisector

Given that I know the point coordinates of A and B on segment AB and the expected length of a perpendicular segment CD crossing the middle of AB, how do I calculate the point coordinates of segment CD?...
2
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2answers
643 views

a basic question about connect sum of two manifolds

How to prove connect sum of two manifolds doesn't depend on the choices of balls(which would be cutted) and different gluing of boundary spheres? Is it still true in differential category? Thanks!
5
votes
2answers
7k views

Scaling at an arbitrary point and figuring out the distance from origin

Suppose I have a $8 \times 6$ rectangle, with its lower left corner at the origin $\left(0, 0\right)$. I want to scale this rectangle by $\frac{1}{2}$ at an anchor point $\left(3, 3\right)$. So the ...
3
votes
1answer
2k views

How do I determine if a point is interior to an elliptical cone?

Consider a canonical elliptical cone $C$ with its vertex at the origin, with height $h,$ and with a base given by: \begin{equation*} \left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2=1;~z=h \end{...
14
votes
4answers
1k views

Coloring the faces of a hypercube

I will restate the 3-D version of the problem. In how many ways can you color a regular cube with 2 colors up to a rotational isometry. The answer is of course a special case of Burnsides Lemma which ...
4
votes
2answers
5k views

Napier's Rules applied to spherical distance calculations

I was in the middle of writing the same old geographic distance calculation using the Haversine formula when it occurred to me: shouldn't there be simpler way to do this? Haversine is of course ...
5
votes
1answer
298 views

Extension of previous problem, involving $\ell^p$ norm circles

If you look at this previous problem, I asked how to find the sum of all the areas between two taxicab geometry circles. However, upon learning about $\ell^p$ norms, I thought it would be pretty ...
2
votes
2answers
979 views

What is the difference in radii of two concentric circles given an angle and length of a triangle that is inscribed in the annulus?

In relation to this geometric construction: where D is the center of both circles, if the inner radius (x = length of line segments DA and DE), the angle φ = ∠CAB, and the length Δg of line segment ...
11
votes
5answers
7k views

What is the proper geometrical name for a a rectangle with a semi-circle at each end?

I'm talking about the shape made up of a rectangle with a semi-circle at each end. Does it have a particular name? Does it begin with e?
2
votes
2answers
693 views

Some basic questions about the Selberg zeta function

I'm trying to learn about the Selberg zeta function, but it seems like introductory texts assume more knowledge of Riemannian geometry than I'm comfortable with. I have some basic questions that ...
4
votes
1answer
2k views

Do two equal lines also count as intersecting?

So, I asked a question about how to find if three lines are concurrent. I built the algorithm I needed, and it was working well, until I started doubting my power of judgement. So my question: Are ...
4
votes
3answers
6k views

How to find where $3$ lines intersect.

I've got a programming exercise I need to do, but I just can't figure out the math part. I need to check if $3$ of $6$ lines intersect in the same point. I am given the equation $ax+by=c$, and I ...
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vote
3answers
506 views

How can I remove rotations from points defining a plane?

I have coordinates for 4 vertices/points that define a plane and the normal/perpendicular. The plane has an arbitrary rotation applied to it. How can I 'un-rotate'/translate the points so that the ...
3
votes
1answer
622 views

How to formulate such problem mathematicaly? (line continuation search)

I have an array of "lines" each defined by 2 points. I am working with only the line segments lying between those points. I need to search lines that could continue one another (relative to some angle)...
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4answers
13k 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 ...
6
votes
1answer
2k views

Find the radius of a circle based off of its intersection with another

So I have some circles that look kind of like this: I'm given the radius of the circle with center point $A$ which is also the distance $AB$, the distance $AB$ between the two center points on the x ...
6
votes
2answers
4k views

algorithm to calculate the control points of a cubic Bezier curve

I have all points where my curve pass through, but I need to get the coordinates of the control points to be able to draw the curve. How can I do to calculate this points?
3
votes
3answers
6k views

Given coordinates of hypotenuse, how can I calculate coordinates of other vertex?

I have the Cartesian coordinates of the hypotenuse 'corners' in a right angle triangle. I also have the length of the sides of the triangle. What is the method of determining the coordinates of the ...
1
vote
2answers
100 views

Relation of different edges in rectangles

Is there any rectangle, that if you divide it into another rectangle (or any other quadrilateral), the relation between the two different edges is the same in both rectangles? For example - Orginal ...
8
votes
3answers
562 views

Does a continuous scalar field on a sphere have continuous loop of “isothermic antipodes”

For a continuous scalar field on a circle, there is a diameter of the circle such that the endpoints of the diameter have the same value. If you think of the scalar field as "temperature", then what ...
2
votes
2answers
155 views

Calulating length of cable running along exterior of an axle

This question may seem simple, but I have no idea where to start. I'm in design phase of a hobby electronics project and need your help. Basically, I'm going to have two platforms with electronics ...
4
votes
2answers
623 views

Calculating Intersections of Lines and Algebraic Surfaces

For context I am developing a ray-tracer for a computer science class, and want to implement some more advanced shapes than just spheres. So while this is related to schoolwork, I'm not asking you to ...
2
votes
4answers
501 views

Lines parallel to a given line

I have to show that any line parallel to $Ax+ By + c =0$ is of the form $Ax + By + k =0$ How do I show this? Thank you!
1
vote
5answers
404 views

Area of a quadrilateral

The perpendicular bisector of the line joining $A(0,1)$ and $C(-4,7)$ intersects the $x$-axis at $B$ and the $y$-axis at $D$. Find the area of the quadrilateral. Thank you in advance!
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7answers
1k views

Perpendicular bisector

Show that BE is the perpendicular bisector to AC. I tried to prove this through Pythagoras, but the answer I got did not prove it was at a right angle, and therefore said it was not the perpendicular ...
2
votes
6answers
2k views

Cartesian Equation for the perpendicular bisector of a line

Find the Cartesian equation for the perpendicular bisector of the line joining A(2,3) and B(0,6) How do I do this? Thank you!
5
votes
4answers
2k views

Why does symplectic geometry have many applications in mathematics

It is not quite intuitive , at least from its origin. Could any one can give me an intuitive explanation?Thank you!
25
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5answers
3k views

Proof that every polygon with an inscribed circle is convex?

In many elementary (and not-so-elementary) Euclidean geometry texts, a (simple) polygon is said to be tangential  if it is convex and has an inscribed circle (i.e., a circle that intersects and ...
5
votes
3answers
2k views

Is a ball a polyhedron?

In the book Introduction to Linear Optimization by Bertsimas Dimitri, a polyhedron is defined as a set $ \lbrace x \in \mathbb{R^n} | Ax \geq b \rbrace $, where A is an m x n matrix and b is a vector ...
10
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3answers
581 views

Does the nine point circle generalise to some theorem about n-spheres and n-simplices?

I am obsessed with the nine point circle. I was thinking, is there a generalisation to aribtrary tetrahedra and spheres? What about higher dimensions? For each face of the tetrahedron, there is a nine ...
7
votes
1answer
288 views

Find the Volume Enclosed by Terrain and a Certain Sea Level

I have a terrain, which is represented by one mesh with a lot of polygons as shown below: This terrain will be cut by a plane at a certain level. So there are volumes of the terrains that are ...
20
votes
9answers
22k views

Why does a circle enclose the largest area?

In this wikipedia, article http://en.wikipedia.org/wiki/Circle#Area_enclosed its stated that the circle is the closed curve which has the maximum area for a given arc length. First, of all, I would ...
2
votes
1answer
415 views

Choosing solutions for the intersections of n number of circles

Suppose I have an number of distances from an unknown location to a known location. I can use these distances and the known locations to draw a number of circles. The point where all the circles ...
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vote
2answers
1k views

Grid of overlapping squares

I have a grid made up of overlapping 3x3 squares like so: The numbers on the grid indicate the number of overlapping squares. Given that we know the maximum number of overlapping squares (9 at the ...
13
votes
2answers
504 views

Packing disjoint family of discs with radii $\tfrac{1}{2}, \tfrac{1}{3}, \tfrac{1}{4},\ldots$ inside the unit disc

Does there exist a family of discs $\lbrace D_{n}\rbrace_{n=1}^{\infty}$ in the Euclidean plane such that the radius of $D_{n}$ is $\frac{1}{n+1}$, each $D_{n}$ is contained in the unit disc, and $...
5
votes
1answer
703 views

How can I pack $45-45-90$ triangles inside an arbitrary shape ?

If I have an arbitrary shape, I would like to fill it only with $45-45-90$ triangles. The aim is to get a Tangram look, so it's related to this question. Starting with $45-45-90$ triangles would be ...
12
votes
2answers
883 views

Comprehensive compilation of conic section formulae

My frustration started after hours of searching failed to turn up a formula for the vertex of a parabola in the general form $$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$$ As is already well known, the discriminant $\...
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vote
2answers
1k views

Find the coordinates in an isosceles triangle if the triangle it self is in positive axis

A at $(45,10)$, B at $(10,20)$, $AB=AC$ and angle $C=20$ degree find the coordinates of $C$.suggest the formula so i can write code in Perl.
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6answers
5k views

sangaku - a geometrical puzzle

Find the radius of the circles if the size of the larger square is 1x1. Enjoy! (read about the origin of sangaku)
3
votes
2answers
2k views

Deriving volume of parallelepiped as a function of edge lengths and angles between the edges

In Wikipedia it is stated that the volume of the parallelepiped given its edge lengths $a,b,c$, and the internal angles between the edges $\alpha ,\beta ,\gamma $ is: \begin{equation*} V=abc\sqrt{1+...