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

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4
votes
3answers
57 views

Difficult Coordinate Geometry and Calculus Question

I was given this question by a friend and after tirelessly working on it I have not come up with anything substantial. I was hoping someone in the community could provide a pointer or possibly a ...
-1
votes
0answers
19 views

how t calculate the area of a rectangle intersected by an arc [on hold]

I need to make two calculations: Determine the arc that is needed between the two intersection points of a rectangle. Knows: Size of the rectangle, location of the intersection points. I want to ...
2
votes
0answers
31 views

What's the most general geometry branch?

What is the most general geometry of curves and surfaces? For example, at curves, we define in differential geometry the tangent vector as the derivative of a regular curve, but visually many other ...
2
votes
1answer
25 views

Calculate tangent points of two circles.

I have 2 circles with given center coordinates and radius. And now I need to find the coordinates of all 8 tangent points to those circles? I found this site explaining exactly what I want do to: ...
0
votes
2answers
34 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
votes
0answers
9 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
2answers
18 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
vote
0answers
27 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 ...
-2
votes
0answers
35 views

Square & square root [on hold]

What is the minimum distance a snake which can only crawl has to cover t to reach the diagonally opposite vertex of the cube. IF Side and height is "S".
-1
votes
1answer
33 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
votes
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
votes
1answer
20 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
vote
2answers
30 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
votes
0answers
10 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
vote
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
votes
1answer
20 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 ...
22
votes
5answers
2k 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 ...
2
votes
0answers
18 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
votes
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
votes
0answers
48 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
votes
1answer
48 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
68 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?
-2
votes
0answers
45 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
votes
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
vote
0answers
29 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 ...
1
vote
1answer
33 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
70 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
votes
0answers
26 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 ...
-1
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
votes
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
votes
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
votes
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 ...
-4
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 $BC$. ...
-2
votes
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
49 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 ...