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

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0
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3answers
23 views

What type of angle is $3+ \frac{1}{6}$ of a complete rotation?

Angle less than $90$ deg is acute, angle greater than $90$ and less than $180$ is obtuse and angle greater than $180$ deg is reflex. Now, what if an angle is a $3+\frac{1}{6}$ of a complete rotation? ...
0
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0answers
8 views

Angle for sloped surface intersection

I'm not sure if this is the right SE site for this questions so apologies if it's not. But I've got a question about calculating angles that I can't seem to figure out the maths for. To add a bit of ...
0
votes
1answer
14 views

Which of the following point is outside the triangle?

If $P(6,7),Q(2,3)\ \text{and}\ R(4,-2)$ be the vertices of the triangle , then which of the point is not contained in the triangle? $a.)(4,3)\quad \quad \quad \quad b.)(3,3)\\ c.)(4,2)\quad ...
1
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0answers
21 views

Where can I find a good drawing software?

Maybe this is a little off-topic but often, when writing articles, I find myself in need of a good drawing software (for MAC or Windows) that would allow me to draw figures like the one below: Do ...
0
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0answers
12 views

Two exercises about hypermetric

These two exercises are about hypermetric. For the first one, I believe that induction for k should work. But I don't know what's special about the metric, and cannot prove the inequality for $k=4$. ...
-1
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1answer
29 views

Diagonal of a cube [on hold]

The hyperdiagonal of a cube extends from the upper back left to the lower front right. If all the side lengths of the cube are $6$ inches, what is the length of the hyperdiagonal of the cube?
4
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2answers
57 views

The lines $x+2y+3=0$ , $x+2y-7=0$ and $2x-y+4=0$ are sides of a square. Equation of the remaining side is?

I found out the area between parallel lines as $ \frac{10}{\sqrt{5}} $ and then I used $ \frac{|\lambda - 4|}{\sqrt{5}} = \frac{10}{\sqrt{5}} $ to get the values as $-6$ and $14$ . I am getting the ...
2
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1answer
14 views

Prove that AX is symmedian

Let $ABC$ be a triangle and let $M$ be the midpoint of $BC$. Let $O_1$ be the circumcenter of $ABM$ and $O_2$ be the circumcenter of $ACM$. $X$ is the circumcenter of $ABC$. Prove that $AX$ is the ...
1
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2answers
28 views

Circumcenter of Tetrahedron (in 4D)

I am trying to calculate the circumcenter of a tetrahedron in 4 dimensional space. Basically what I am looking for is the center of the smallest sphere which passes through all 4 vertices of the ...
0
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0answers
9 views

Max and Min of number of points that are uniformly distributed on a surface

Can I calculate an upper bound and a lower bound (or max or min) on the number of points that are uniformly distributed on a surface, knowing the area of the surface ? More precisely, I have a sector ...
0
votes
1answer
14 views

Points nearby a line

Suppose we have a number of points in $2d$. I'm looking for a way to determinate a line, which has a maximum number of points in a given range. There is no need that the line intercepts one of the ...
1
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2answers
46 views

Problem on Straight lines

I am working on this question. A light ray coming along the line $3x+4y=5$ , gets reflected from the line $ax+by=1$ and goes along the line $5x-12y =10$. Now, I have to find out the value of $a$ and ...
3
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1answer
19 views

The necessary and sufficient condition for a regular n-gon to be constructible by ruler and compass.

I have a problem concerning the necessary and sufficient condition for a regular n-gon to be constructible by ruler and compass. $\bf My$ $\bf question:$ For a given positive integer $n$, how can we ...
2
votes
2answers
34 views

An equation involving ratios in a triangle.

In triangle $ABC$, if the incenter is $I$ and $AI$ meets $BC$ at $D$, show that $$\frac{AD}{ID}=\frac{AB+BC+CA}{BC}$$ I tried using similar triangles and got nowhere, couldn't find any use for the ...
20
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5answers
1k views

I think I see mysterious lines inside triangles—how to prove their existence?

Lately I've been fooling around with points inside a triangle and the sum of their distances from all sides. This was when I noticed a weird behaviour: For each point I chose there always seemed to ...
1
vote
0answers
16 views

Compute volume of the tetrahedron from circumsphere test

I'm working on a computational geometry algorithm. In every iteration I solve the matrix below, where (a,b,c,d) are the vertices of a tetrahedron, and e is an arbitrary point. Solving the determinant ...
0
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2answers
27 views

Constructions of perpendicular in hyperbolic plane

Consider the disc model of hyperbolic plane $\mathbb{D}^2$ and a line $g$ through the origin $(0,0)\in \mathbb{D}\subset\mathbb{C}$, i.e. a diameter of the circle $\partial \mathbb{D}=S^1$. Let ...
4
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0answers
45 views

Are closed simple curves with that property necessarily circles?

This is a more interesting follow-up to the question Are closed simple curves with this property necessarily circles? Let $\gamma:[0,1]\to \mathbb R^2 $ be a closed simple $C^1$ convex curve and ...
2
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1answer
47 views

Are closed simple curves with this property necessarily circles?

Let $\gamma:[0,1]\to \mathbb R^2 $ be a closed simple curve and $\Gamma$ be the region enclosed by $\gamma$. Let $O$ be the center of mass of $\Gamma$. Suppose that any line that goes through ...
1
vote
1answer
67 views

What is the name of this geometric shape?

#1 I am trying to find the name for this when $d1 = d2$ What is the name of this object? #2 Assume d1 is different than d2. What is the name of this kind of object?
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0answers
42 views

the formula for the volume

If you know that the volume of cube ($a^3$) represents the sum of the surface squares ($a^2$). Following the same logic: If we know the area of the circular segment is equal to the area of the ...
0
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2answers
25 views

The angle between $u$ and $v$ is $30º$, and the vector $w$ of norm $4$ is ortogonal to both $u,v$. Calculate $[u,v,w]$.

The angle between the unit vectors $u$ and $v$ is $30º$, and the vector $w$ of norm $4$ is ortogonal to both $u,v$. The basis $(u,v,w)$ is positive, calculate $[u,v,w]$. I did the following: ...
1
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0answers
28 views

Intersecting lines in sectors of a circle.

Good day everyone, I'm trying to simulate a Laser Range Finder (LRF for short) in a corridor environment. I'm including a small fast sketch I did of this. I can't upload images yet, so I include just ...
0
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1answer
32 views

Dual plot for complex roots of quadratic equation

Real roots of quadratic equation $ x^2 - \sqrt 3 x + 1/2 =0 \tag{1} $ can be plotted on $x$- axis as its parabola intersection at $ (\sqrt 3/2 \pm 1/2,0). $ In an improvization I assign ...
1
vote
2answers
284 views

Average distance between two randomly chosen points in unit square (without calculus)

Imagine that you choose two random points within a 1 by 1 square. What is the average distance between those two points? Using a random number generator, I'm getting a value of ~0.521402... can ...
5
votes
0answers
69 views

What is reflection across parabola?

Reflection across a line is well familiar, reflection across a circle is the inversion, the point at a distance $d$ from the center is reflected into a point on the same ray through the center, but at ...
1
vote
2answers
37 views

Find the length of angle bisector $AD$.

In $\triangle ABC$ , the internal bisector of the angle $\angle A$ meets $BC$ at $D$. If $AB=4$, $AC=3$ and $\angle A=60^{\circ}$, then the length of $AD$ is $a.)\ 2\sqrt3\\ \color{green}{b.)\ ...
2
votes
2answers
37 views

Find the plot of $y=1+\cos t$, $x=\sin^2t$.

I'm trying to find the plot for the following : $$y=1+\cos t, x=\sin^2t$$ I'm trying to get ride off variable $t$. This is what I done for some reason is incorrect : ...
0
votes
2answers
24 views

Find the area of the shaded region under given curcumstances

It is given that $ZV||XY,WZ=ZX,ZV=2a~~\text{and}~~ZX=2b.$ Find the area of the shaded region. $a.)\dfrac{4ab}{2}\\ b.)\dfrac{8ab}{3}\\ \color{green}{c.)6ab}\\ d.)3ab\\$ $\quad$ I found that ...
5
votes
3answers
68 views

Given two points, how to find a circle through them that's also tangent to the $x$-axis?

A seemingly simple geometry problem that is surprisingly difficult. I want to find the radius of a circle that is tangent to the $x$-axis, but also must contain two given points. I understand there ...
0
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0answers
25 views

Vertical/Horizontal stretch ratio. [on hold]

I'm trying to calculate 3 points on a grid by using 3 other points and calculating a ratio. I have the original values of all the points and was using the ratio (x1/x2) (y2/y1) for the points however ...
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votes
0answers
18 views

How to find the image of the line $y=ax$ from upper half plane to poincare disk?

with cayley transformation $m(z)=\frac{z-i}{z+i}$ i cant find a solution for this exercise so if you have any suggestion for the solution will be very helpful ...
0
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0answers
21 views

To a given straight line in a given rectilinear angle, to apply a parallelogram equal to a given triangle.

There's again one small detail on which I'm not sure. (Proposition 44 - book 1) http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI44.html Here's the quote : "Then HLKF is a parallelogram, HK ...
-5
votes
0answers
27 views

Prove that ABCD is cyclic if and only if it is a rectangle [on hold]

Prove that $ABCD$ is cyclic if and only if it is a rectangle, in which case its circumcenter is the point where its diagonals intersects.
1
vote
0answers
18 views

min and max number of hexagons in hexagonal tiling

Is there a way to calculate the maximum and minimum number of hexagons in a hexagonal tiling of a surface with regular identical size hexagons, knowing the area of the surface and the area of the ...
0
votes
1answer
23 views

Speed at which hands of clock approaching one another.

A clock's hour hand's length is $1$, and its minute hand's length is $r$. First I had to find the distance between the tips of the hands at 4:00. I did this using the law of cosines. This gives me ...
0
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4answers
36 views

For every integer vector $\overrightarrow{a}$,there is a integer vector $\overrightarrow{b}$ such that $\overrightarrow{a}\bot\overrightarrow{b}$

In $R^3$,show that for every integer vector $\overrightarrow{a}$,there is a integer vector $\overrightarrow{b}$ such that $\overrightarrow{a}\bot\overrightarrow{b}$ Generally,in $R^n$,for every ...
0
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0answers
14 views

hexagonal tessellation (tiling): uniform distribution of centers of hexagons?

Consider a disk of Radius $R$. We divide the disk into n equal sectors (in the form of pizza slices) . $n= 2^i$ and $i$ is a non-negative integer. Each sector is enclosed with two radii and an arc ...
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votes
1answer
31 views

How do you express the following equations for a circle? [on hold]

A circle of radius a is centered at a point r1. (a) Write out the algebraic equation for the circle. (b) Write out a vector equation for the same circle. (c) How would you modify (a) and (b) above ...
6
votes
4answers
69 views

Prove that for any given $c_1,c_2,c_3\in \mathbb{Z}$,the equations set has integral solution.

$$ \left\{ \begin{aligned} c_1 & = a_2b_3-b_2a_3 \\ c_2 & = a_3b_1-b_3a_1 \\ c_3 & = a_1b_2-b_1a_2 \end{aligned} \right. $$ $c_1,c_2,c_3\in \mathbb{Z}$ is given,prove that $\exists ...
1
vote
4answers
37 views

Find the length of chord $BC$.

On a semicircle with diameter $AD$. Chord $BC$ is parallel to the diameter.Further each of the chords $AB$ and $CD$ has length of $2$ cm while $AD$ has the length $8$ cm.Find the length of $BC$. ...
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1answer
28 views

Geometry volume and surface area [on hold]

How do I get the two sides of the top of the prism ($9$ & $9\sqrt{3}$)
0
votes
1answer
21 views

What is the optimal way to detect a collision between an AABB figure and a non-AABB figure?

Background I'm looking to do this programmatically in Java, but if desired you can post solutions in C/C++ or plain English instructions if you're not a programmer, but I would appreciate an ...
0
votes
3answers
48 views

If the surface area of a box is 32 and its volume is doubled what is the new surface area? [on hold]

Original surface area :32 Original volume: x New volume: 2x What is the new surface area? Please provide an explanation or show work, I don't know how to do it.
0
votes
1answer
24 views

How can I derive the resultant of 2 bearing/elevation pairs

Say, for example I have a gimballed camera mounted on a metal plate, which is itself fixed horizontally to a boat. I can measure the elevation and bearing of both the camera with respect to the plate ...
1
vote
2answers
24 views

What does it mean for a set of closed shapes to intersect?

To my understanding, a "shape" is a set of points in $n$-dimensional space. e.g., rectangles, triangles, lines, spheres, hyperspheres, etc.. For two (or any amount) of shapes to "intersect", the ...
2
votes
1answer
16 views

Find the three closest surrounding neighbors from a data

I have a data of coordinates $x$ and $y$ where we know the range of both variables, e.g. $(x,y)\in[0,1]^2$. So for a given any random point $\theta_0=(x_0~~y_0)^T$ in the range of $x$ and $y$ I would ...
3
votes
4answers
93 views

How to prove that a straight line is an infinite set of points?

From the basic elementary level when we start reading geometry we get this idea developed in us that a straight line is the conjuction of infinite points.but how to prove this? I mean is this an ...
1
vote
2answers
22 views

Find the ratio of curved surface area of frustum to the cone.

In the figure, there is a cone which is being cut and extracted in three segments having heights $h_1,h_2$ and $h_3$ and the radius of their bases $1$ cm, $2$cm and $3cm$, then The ratio of the ...
0
votes
1answer
17 views

Deriving the Geodesic Equation

I found a derivation of the geodesic equation that includes this step as I write it: $$ \frac{d (g_{ab}\dot{x}^b)}{dt}=\frac{1}{2}\partial_ag_{bc}\dot{x}^b\dot{x}^c \Rightarrow \\ \\ ...