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

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1answer
21 views

Jordan curve of infinite length

I was thinking about Jordan curve with infinite length and Koch snowflake seems to be a valid answer intutively. Can anyone give mathematical proof for this?
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2answers
24 views

Find the projection of the line $x+y+z-3=0=2x+3y+4z-6$ on the plane $z=0$

Find the projection of the line $x+y+z-3=0=2x+3y+4z-6$ on the plane $z=0$ The equation represents the line of intersection of two planes. Using augmented matrix $$ \begin{bmatrix} 1 & 1 ...
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3answers
34 views

How to prove that $x^2 + 3y^2 = 1$ is contained inside of the unit ball?

What is the best way to show that $S = \{(x,y) | x^2 + 3y^2 = 1\}$ is contained in the unit ball without graphing the set?
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1answer
22 views

How many points among them should we take to ensure that some two of them are less than the distance $1/5$ apart?

We are given a fixed point on a circle of radius $1$, and going from this point along the circumference in the positive direction on curved distances $0,1,2,\ldots$ from it we obtain points with ...
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0answers
12 views

Hyperplane of an mn-dimensional space [on hold]

Can someone explain to me why the hyperplane of a $mn$-dimensional space would have dimension $(m-1)n$?
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0answers
20 views

Given $5$ points on a sphere, divide the surface into $5$ congruent connected regions containing one point.

There are $5$ points on the surface of a sphere. Is it always possible to divide the surface into $5$ connected congruent regions such that each region contains one of the $5$ points?
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1answer
8 views

Computation of minimal axis-aligned bounding box of an arc segment.

I'm trying to compute the minimal bounding box of an arc segment so when it's time to render it, I only have to examine pixel coordinates within a minimal rectangular region. The code below covers ...
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1answer
22 views

Constructible numbers defined over the rationals

If $z$ is constructible, then its minimal irreducible polynomial has a degree a power of $2$. Does the polynomial have to be defined over the rationals? I am asking this because we can ...
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0answers
33 views

Having trouble interpreting the geometry of this setup.

A circular conductor, with cross section given by $(x-d)^2+y^2=b^2$, i.e. radius $b$ and centered on $x=d$, has a circular core, made up of the interior of the circle $x^2+y^2=a^2$, with ...
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1answer
19 views

What does equally oriented mean

What does it mean for two triangles to be equally oriented? I have heard this term a lot but I haven't seen a definition of it. I know that in $3$-space two triangles are considered to be equally ...
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1answer
10 views

Modulo angle (rotation) in $2D$ space

Input parameters: space dividor (number), vector (vec2) Desired result: Divide space in $X$ sectors, then move all vectors to one sector. (Angle of any vector wont be larger then $360/X$.) Example ...
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3answers
28 views

calculate radius of circle that by given length of square that is inside it

in this picture a length of square edge is 8 cm. I want to calculate the radius of circle. i try to calculate it, but i don't know how. I calculate this:
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1answer
31 views

Showing that $\alpha$ satisfies the equation $\sin 2x=x$

This is an A level question. For better understanding, I will attach a screenshot of the question and the mark scheme. Question: Here's what I have done: $$A(OBA) = \frac 12r^2α$$ [basic ...
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1answer
42 views

Quarter Circle packing

Just today, I was making tortilla chips, and I began to wonder, what is the most efficient way to pack circular quarters onto the plane? This sort of circle packing is most efficient for circles, ...
-4
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2answers
62 views

The area of square [on hold]

What is the area of the square versus a,b and c ? Thanks Edit to clarify the question, based on the OP's response to comments. The segments with lengths $a$ and $c$ are parallel, joined by $b$ ...
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1answer
23 views

How do you calculate the change in thickness of a cylinder, if you shave off a flat section?

I have a piece of steel, cylindrical (hollow), 200mm outside diameter with 160mm inside diameter (...
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2answers
33 views

How to determine that the 3 points given in homogeneous coordinates are collinear? [on hold]

How do I prove that the 3 points given in homogeneous coordinates are collinear? $$A=(1,3,2)^T, B=(0,6,8)^T, C=(3,3,-2)^T$$
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1answer
26 views

length of radius of circles between their tangents

In this question, we have five circle that touch each other. we draw their tangents. If we know that smallest circle radius is 8 and biggest circle radius is 18, then what is the length of PF? Note: ...
0
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1answer
18 views

Translate a Rectangle Position from 1 Image to another [on hold]

I have a Large Size Image.Since its too large for processing within a small time, i need to resize it.I have the coordinates of a rectangle in the resized image.Is there a way i can translate this ...
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3answers
22 views

Area of rectangle and triangle derivation

I was wondering about the derivation for the area of a triangle and the area of a rectangle. Of course, we all know them to be $\dfrac{1}{2}bh$ and $bh$ respectively, but where is the derivation of ...
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0answers
21 views

locus of a variable straight line [on hold]

Geometry: A variable straight line always intersects the lines x=c,y=0; y=c,z=0; z=c,x=0. find the equation to its locus. taking the equation of a line in parametric form and substitute the given ...
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1answer
25 views

Deriving formula for externally tangent circle to internally tangent circle

($x^2+(y+1)^2=R^2$ should say $x^2+(y-1)^2=R^2$) I am trying to derive a formula for the radius of the circle that is externally tangent to the internally tangent circles of the quarter-circle, and ...
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0answers
44 views

Why are carrom boards square? [on hold]

This question may seem a little off-topic for this site.... We have all seen carrom boards.Now,why are carrom boards always square and not rectangular?Is it only because distance to the pockets will ...
0
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1answer
32 views

How many non-congruent triangles with perimeter 11 have integer side lengths? [on hold]

How many non-congruent triangles with perimeter 11 have integer side lengths? I failed to solve it. Can anyone help?
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2answers
35 views

Triangle with a square in it, with the side of $2\sqrt{3}$, what's the altitude of the triangle? [on hold]

We have a triangle and within is a square with the side of $2\sqrt{3}$. What's the altitude of the triangle ABC? All 3 angles in the triangle are same (60). Pic: http://imgur.com/gallery/SAmhU7z/new ...
2
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1answer
58 views

Does a convex hull solution in 3 dimensions result in a minimum-area or maximum-volume solution?

The wikipedia entry for convex hull shows a 2-d example of a random set of points on x-y plane, and the "elastic band" solution that bounds the points with the convex hull solution. The definition of ...
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1answer
19 views

Prove that the sum of the vectors from the centre to the vertices of a regular hexagon is 0

Prove that the sum of the vectors from the centre to the vertices of a regular hexagon is 0 Let's call the centre $O$ and the vertices are $A, B, C, D, E$ and $F$. Therefore, the sum in the ...
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1answer
19 views

Finding $y_{A,i}$ and $y_{B,i}$ in this geometric relationship problem.

Finding $y_{A,i}$ and $y_{B,i}$ in this geometric relationship problem. I'm an high-speed aerodynamics student. I am studying a sweptback wing like in the figure below (in green). Notice that I ...
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1answer
34 views

Find $|CM|$, if $|CA|=a$ and $|CB|=b$. [on hold]

Let $O$ be a center of a circle, circumscribed over $\triangle ABC$. Perpendicular, drown from the point $A$ on the line $CO$, cross the line $CB$ in the point $M$. Find $|CM|$, if $|CA|=a$ and ...
1
vote
1answer
33 views

Prove that $MN = \dfrac{|b − c|}{2}$

In triangle $ABC$, point $M$ is the midpoint of $BC$ and $N$ is on the angle bisector of $\angle A$ such that $MN \parallel AB$. Prove that $MN = \dfrac{|b − c|}{2}$. Attempt: I drew it out and ...
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2answers
35 views

Expand polygon to grid in $x-y$ plane

Given a polygon in the $x-y$ plane, what is the simplest formula for expanding the polygon so that all sides lie on a grid? The image below demonstrates the problem I am trying to solve. The filled ...
0
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1answer
16 views

Conformal curvature line parametrization

While reading a paper I found a definition which is confusing me. Def: A conformal curvature line parametrization $(x,y) \to F(x,y)$ is called isothermic. I know what a conformal ...
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0answers
20 views

Distance function for N-prism

Im looking for distance function that describes N prism. Im looking for pentagon prism, heptagon prism and octagon prism functions. Function accepts vec3 position, which is observer position. ...
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0answers
12 views

How to compute homography matrix H from four corresponding points [duplicate]

I am using 4 point correspondence to compute elements in Homography matrix $H$. \begin{align*} [x']={}& [h_1 h_2 h_3] [x] \\ [y']={}& [h_4 h_5 h_6] [y] \\ [(1)]={}&[h_7 h_8 h_9] [(1)] ...
2
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2answers
27 views

Find Length of line which has rotating object.

I have 3 Images. A, B and C. if I place it on graph, its look something like this. Now main image is A and I place B and C on that image's (A) center point. For easy understanding, let's consider ...
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1answer
25 views

Four Spheres Intersect Along Circles: Prove That Circles' Planes Are Either $\parallel$ to The Same Line, Or Have a Common Point

Problem: Let $\,A,\,B,\,C,\,D\,$ be four distinct spheres in a space. Suppose the spheres $A$ and $B$ intersect along a circle which belongs to some plane $P$, the spheres $B$ and $C$ intersect ...
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1answer
34 views

How many triangles ABC with 𝐴𝐴 angle ABC= 90° and AB= 20 exist such that all sides have integer lengths? [on hold]

How many triangles ABC with angle ABC= 90° and AB= 20 exist such that all sides have integer lengths?Is it somehow related to the Phythagorean Theorem?Here is my attemp to solve it: 400+BC^2 = AC^2 ...
3
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2answers
82 views

How to determine the reflection point on an ellipse

Here is my problem. There are two points P and Q outside an ellipse, where the coordinates of the P and Q are known. The shape of the ellipse is also known. A ray comming from point A is reflected by ...
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0answers
47 views

Interesting cube subdivisions: what is going on here, and what are these polytopes?

I was messing around recently with a unit cube. If you draw vertices on the midpoint of each edge of the cube, then connect those points by new edges, you will form the wireframe of what I figured ...
3
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4answers
51 views

Prove that the altitudes of an acute triangle intersect inside the triangle.

Prove that the altitudes of an acute triangle intersect inside the triangle. I can pretty easily see that this is true by a pythagorean theorem argument. Given any two sides, the smaller length ...
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1answer
18 views

Rotation matrix between two similar cuboids using their upper sides ( and the planes defined by these sides)

I have two different images and with them an estimation of two planes ( defined in the same system). I would like to get the rotation matrix, quaternion or euler angles of a surface within this ...
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1answer
37 views

Center point of 2 tangent circles along 2 tangent lines

Given points P1, P2, and P3, I need to calculate the center point of 2 tangent circles, C1 and C2, with radius R. Line P1P2 is tangent to circle C1 at P2, line P2P3 is tangent to C2, and C1 and C2 are ...
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0answers
35 views

Geometry perpendicular proof

How would I prove that there is a line perpendicular to any given line through a given point not on the line?
3
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2answers
34 views

Is it possible to define the position of a gunshot using and array of microphones?

If I had four microphones, located on poles that were at corners of a square that's 300 feet on a side (or some other specific configuration that would make the math easier), would I be able to use ...
0
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1answer
28 views

Computing the approximate or exact area of an isosurface

The isosurfaces I'm reading about are defined by a constant value v in a scalar field. The scalar field is defined by placing n vectors in k-space such that ...
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0answers
54 views

Perimeter of a teardrop (made by two adjacent circles)

I'm trying to determine the perimeter of a teardrop shape formed by two adjacent circles (non-intersecting) with mutually tangent lines drawn on both sides of the circles. I've attached a sample ...
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0answers
54 views

Find $a$, $b$ and $c$. [on hold]

As title said, How to find angles $a$, $b$ and $c$? Thanks in advance!
4
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1answer
54 views

Number of ways to separate $n$ points in the plane

Say you are given $n$ points such that no three are colinear. Show the number of ways to separate them into two subsets by drawing a straight line depends on $n$ but not the position of the points.
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1answer
29 views

Partitioning a convex object without cutting existing convex subsets

$C$ is a convex object in the plane. $D_1,\dots,D_n$ are pairwise-disjoint convex subsets of $C$ such that $D_1\cup\dots\cup D_n \subsetneq C$, like this: Is it always possible to partition $C$ to ...
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0answers
13 views

Geometry trapezoid angle bisectors

Let $ABCD$ be a trapezoid with $AB||CD, AB=11, BC=5, CD=19,$ and $DA=7$. Bisectors of $\angle A$ and $\angle D$ meet at $P$, and bisectors of $\angle B$ and $\angle C$ meet at $Q$. What is the area ...