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

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5
votes
2answers
1k views

Evenly distribute points along a path

I have a user defined path which a user has hand drawn - the distance between the points which make up the path is likely to be variant. I would like to find a set of points along this path which are ...
4
votes
2answers
2k views

Why can't we construct a square with area equal to a given equilateral triangle?

In modern geometry, given an equilateral triangle, one can't construct a square with the same area with the use of Hilbert tools. Why is this? The claim seems untrue to me, so there must be something ...
1
vote
1answer
274 views

Shapes on a sphere's surface

Since the surface of a sphere is different from a(n Eucleadian) plane, are there shapes similar/analogous to Eucledian plane shapes? Are there analogues of a square, a circle, a star polygon, etc? If ...
3
votes
2answers
1k views

Point closest to a set four of lines in 3D

Given four lines in $3D$ (represented as a couple of points), I want to find the point in space which minimizes the sum of distances between this point and every line. I'm trying to find a way to ...
2
votes
2answers
3k views

Area of a circle externally tangent to three mutually tangent circles

Given three identical circles, with three points of intersection. The line between two of these intersecting points is $3$ feet. They are inside a $4$th circle. All circles are tangent to each other. ...
1
vote
1answer
636 views

How can I calculate the transformation of two 3D triangles?

Given two triangle I have the transformation (three rotation followed by three translation)of both the triangles. How can I calculate the transformation between two triangles? A numerical example will ...
3
votes
1answer
1k views

Algorithm for joining two polygons based on set of 2D points

[Thanks for votes, I fixed the images now] I am working on system, that does some fuzzy logic. I don't have any special types, everything is done with simple math. The last problem I am facing is ...
6
votes
2answers
328 views

What is the probability that a quadrilateral is convex?

Given $4$ distinct randomly chosen points $x_1$, $x_2$, $x_3$, and $x_4$ in the plane such that the polygonal path from $x_1$ to $x_2$ to $x_3$ to $x_4$ to $x_1$ describes a non-self-intersecting ...
8
votes
2answers
727 views

Trace of a bilinear form?

I'm just a beginner of differential geometry, so please forgive me if this is nothing but a silly question or I'm making a critical conceptual mistake. Let $\mathrm{I\!I}(X, Y)$ be the second ...
13
votes
3answers
681 views

Covering the plane with disks

How to prove that it is impossible to cover the plane with disks? /The disks are closed disks and two disks can meet (at most) at only one point (obviously on the border)./ Thank you very much in ...
1
vote
1answer
296 views

How do I restore implied on-curve points in TTF Fonts?

I'm trying to find the coordinates of the implied point p2 using the control points p1 and p3. See here: In the TTF spec they say: Connected quadratic curves have first degree continuity and ...
2
votes
1answer
120 views

Stitching together piece of flat space

If I start with an infinite flat sheet of graph paper, and in polar coordinates cut out a piece according to: $r>0, \ \ -f(r) < \theta < f(r)$ Now I want to stitch the remaining graph paper ...
1
vote
0answers
151 views

Formula for finding the distance between two lat/long coordinates? [duplicate]

Possible Duplicate: How do I measure distance on a globe? Say I have the coordinates of two locations. What formula could tell me the distance between the two? I'm not a math person at all, ...
10
votes
5answers
7k views

Calculate the area of the crescent

I found this problem on a thread on Stack overflow where it was posted as "job interview question". Unfortunately I cannot find the question. But I saved the picture and just cannot figure it out. ...
3
votes
2answers
2k views

two point line form in 3d

the two-point form for a line in 2d is $$y-y_1 = \left(\frac{y_2-y_1}{x_2-x_1}\right)(x-x_1);$$ what is it for 3d lines/planes?
2
votes
2answers
278 views

How to solve this basic math problem?

I'm having this problem on some game I'm coding which I think it's just math and has nothing to do with coding, that's why I'm posting it here and I'm going to simplify the problem without describing ...
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 ...
1
vote
1answer
348 views

correct rotation and translation matrices

I wrote a C++ program that can calculate the magnetic field $\bar{B}$ generated by a circular coil that is placed in the origin, for a given point $\bar{P}$ in 3D ...
0
votes
1answer
64 views

Repositioning for minimap display

I'm doing some game development and have the following problem: I've got a mini map that I draw on, the image is $300\times 300$ in size and I'm displaying the player and enemies that are within a ...
1
vote
1answer
5k views

Parameterizing the upper hemisphere of a sphere with an upward pointing normal

Can someone explain how to do this? area we're dealing with: $x^2 + y^2 + z^2 = a^2, z \geq 0$ I'm aware that the answer is: $x = a \sin(\phi) \cos(\theta)$ $y = a \sin(\phi) \sin(\theta)$ $z = ...
0
votes
1answer
2k views

maths - find vertices when 1 vertex and center point is given in polygon

I want to know if there is any general formula to find out vertices (co-ordinates) of a polygon (3 or more equal sides) when following is given: ...
6
votes
2answers
689 views

Constructing the circle inversion inverse of a point with ruler only

I've been reading a bit about inversive geometry, particularly circle inversion. The following is a problem from Hartshorne's classical geometry, which I've been struggling with on and off for a few ...
3
votes
1answer
809 views

Determining which side of a 3D cube is facing the viewer

Me and a friend are trying to render a rotating cube on a 2D plane(the screen) using java. Here's the problem The cube has 6 sides, each with a specific normal vector of the form $(0, 0, 1)$, $(0, ...
3
votes
1answer
62 views

Curves simplify to lines?

I have what is supposed to be a curve: $$25x^2 - 4y^2 = 100$$ When simplify this to be: $$y = 2.5x - 5$$ it is a line. But isn't it supposed to be the same?
1
vote
1answer
106 views

A simple function to draw an arc (I guess?)

sx = x starting point ex = x end point sy = y starting point ey = y max having all the above, plus the current x, how do I calculate with a formula an y which isn't linear but that goes faster at ...
2
votes
1answer
418 views

3d axis rotation

I have a vector V= and several line segments Seg1, Seg2, Seg3, Seg4. I want to know how to rotate each of the line segments so that the X axis is parallel to my given vector. How can I do this? ...
1
vote
1answer
902 views

Get vector components from from magnitude and angle

I am given the length and the direction of a vector, and I need to get the the X,Y components. I can go one way, but going the other has me a little lost. Example: A man walks 3.50 m south, then ...
0
votes
1answer
418 views

the maximum number of blocks that will fit inside the box?

What is the maximum number of rectangular blocks, each with dimensions 12 centimeters by 6 centimeters by 4 centimeters, that will fi t inside rectangular Box X ? The inside dimensions of ...
12
votes
1answer
676 views

How to divide a pizza into $n$ parts?

Let's say you have invited $(n-1)$ people for dinner. You decide that the main course consists of one pizza for each guest, so you order $n$ pizzas. Unfortunately, the pizza guy on the scooter trips ...
24
votes
1answer
497 views

Rolling a Sphere on the Plane

Suppose one starts with a sphere $S$ resting on a ($2$-dimensional) plane $H$ at the origin. A "move" consists of the following: Let $P$ and $Q$ be two points in $H$. Roll the sphere $S$ along a ...
5
votes
2answers
89 views

Simple question on grid

I should be able to figure this out, but my brain isn't cooperating with me. Say I have a grid of 5x5, with each cell in the grid numbered from 0-24, going from left to right. Given a cell number such ...
3
votes
1answer
337 views

How to compute Hyper-area?

The function $A=(\sin(y)\sin(z)+\cos(y)\cos(z))\sin(w)\sin(x)+\cos(w)\cos(x)$, given $w\in[0,\pi], x\in[0,\pi], y\in[0,2\pi], z\in[0,2\pi]$, defines a three-dimensional "surface" in 4D. ($A = ...
2
votes
1answer
207 views

How to prove these?

This is rather a continuation for this,but this is much precise.After proving and understanding the basic formulas for pair of straight lines I am having some troubles with these: If the equation ...
1
vote
1answer
900 views

Confusion with the various forms of the equation of second degree

I am confused with the second degree equation,an equation of second degree $ax^2+by^2+2hxy+2gx+2fy+c=0$ represents a conic,and nature of the conic depends on the various other conditions,like if ...
6
votes
2answers
1k views

How do I draw an elliptic curve?

I can draw a circle using a compass. I can draw an ellipse using two focal points and a loop of string. I think that you can draw an arbitrary conic with a "generalized" compass for which the pencil ...
4
votes
2answers
295 views

Help finding solution for trigonometric equation

I have a flat mirror and a target. Given the sun's light angle of incidence, I must calculate how much to spin my mirror to hit the target with the light. The problem is shown in the following figure. ...
3
votes
3answers
605 views

How to find the length of this geometry figure

I have a small square inscribed by an outer square, where the degree of tilt is given by theta. The length of the outer square is also given by L. If I were to rotate the inner square by the red ...
3
votes
1answer
244 views

Geometrical interpretation of trigonometric antiderivative

I know about geometrical explanation of [definite] integral as an area under the curve, and I wonder if there are some ideas, which may give similar insight in taking antiderivatives [indefinite ...
2
votes
2answers
132 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 ...
3
votes
3answers
7k views

Foot of perpendicular to line

If $M(x_2,y_2)$ is the foot of a perpendicular drawn from $P(x_1,y_1)$ on the line $ax+by+c=0$, then $$\frac{x_2-x_1}{a}=\frac{y_2-y_1}{b}=\frac{-(ax_1+by_1+c)}{a^2+b^2}.$$ This is given as a formula ...
5
votes
2answers
2k views

Are there any practical applications of the directrix of a parabola?

I know of many applications for the focus of a parabola (satellite dish, whispering gallery, etc.), but haven't been able to find any for the directrix. An internet search has come up empty. I have ...
12
votes
2answers
1k views

Do infinitely many points in a plane with integer distances lie on a line?

Someone posted a question on the notice board at my University's library. I've been thinking about it for a while, but fail to see how it is possible. Could someone verify that this is a valid ...
5
votes
1answer
528 views

In neutral geometry, the line connecting midpoints in a triangle is orthogonal to the perpendicular bisector?

This is a curious problem that is relatively easy to prove in Euclidean geometry, but has stumped me a good while in neutral geometry. For a given triangle, how can one show that the line joining ...
0
votes
2answers
789 views

Calculating the distance from top left corner to bottom right corner on a rectangle

Say I've got a rectangle measuring $140$ cm (height) x $300$ cm (width). What is the distance from the top left corner, to the bottom right corner? And whats the formula for calculating the distance? ...
18
votes
4answers
4k views

The locus of two perpendicular tangents to a given ellipse

For a given ellipse, find the locus of all points P for which the two tangents are perpendicular. I have a trigonometric proof that the locus is a circle, but I'd like a pure (synthetic) geometry ...
4
votes
0answers
104 views

how understand if a segment is inside a lissajous curve

i am a programmer and not a math guru, but i like geometry. so if i'm not accurate in math terminology or i have folly question please sorry me. i'm drawing with a programming language the lissajous ...
0
votes
1answer
191 views

Can we draw the characteristic function of the rationals?

Can we draw this function? $f\colon\mathbb{R}\to\mathbb{R}$, given by $$f(x) = \left\{\begin{array}{ll} 1 &\mbox{if $x\in\mathbb{Q}$;}\\ 0 &\mbox{if $x\notin\mathbb{Q}$.} \end{array}\right.$$ ...
5
votes
1answer
524 views

Doubling the cube with the help of a parabola

Looking into the intersection of abstract algebra and geometry, it's well known that it is impossible to double the cube with ruler and compass, since $\sqrt[3]{2}$ is not constructible. However, I ...
4
votes
2answers
440 views

Rotate a 2D subspace in 4 or more dimensions

Two non-co-linear vectors define a 2D subspace that passes through the origin. In 3D, you can represent a 2D subspace by its Normal. It's very easy to define the angle between the two planes: $\theta ...
1
vote
2answers
679 views

Find out which faces of a 3D polygon cause it to be concave

I have a 3D polygon based on a set of faces. Each face lies in a single plane, and I know the normal for each face (as well as the points that create the face). I also know that each normal points ...