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

learn more… | top users | synonyms

-4
votes
0answers
11 views

In a trapezium $PQRS$, $QP=a,RQ=b,RS=3a$ and the diagonals intersect at $X$. Express $RP$ and $QS$ in terms of a and show

In a trapezium $PQRS$, $QP=a,RQ=b,RS=3a$ and the diagonals intersect at $X$. Express $RP$ and $QS$ in terms of $a$ and $b$. Show that $PX:PR=QX:QS=1:4$
1
vote
3answers
27 views

Peripendicular distance from a line segment

I have a line given by $Ax + By + C= 0$, and a point $x0,y0$. From that point $x0,y0$ in the direction of the line up to distance $d$, I want to find the perpendicular distance of the points from this ...
1
vote
1answer
36 views

How to find m by given information.

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of measure $45^o$ at the major segment of the circle then m= . How to find m.
1
vote
3answers
32 views

Convert the equation to rectangular form $r = \frac {6}{1-\sinθ}$

Convert the equation to rectangular form $r = \frac {6}{1-\sinθ}$ The answer should be: $y = \frac{1}{12} x^2 -3$ But how to arrive at the answer? I tried replacing r with $\sqrt{x^2 + y^2}$, then ...
1
vote
1answer
23 views

What is the probability of two random lines crossing in a unit square?

For the purposes of this question a random line is defined as the line connecting two random points inside the unit square, where a random point is found by generating two random numbers between 0 and ...
1
vote
0answers
37 views

How to give a rigorous proof of a fact about convex polygon?

I claim that there exists universal constants $0<\delta_1(m), \delta_2(m)<1$ such that for any convex polygon $P$ in $\mathbb{R}^n$ with $m$ faces, \begin{equation} \frac{\mathcal{H}^{n-1}(\{x ...
0
votes
0answers
9 views

What does 3D gaze direction contains? And how to convert it to yaw and pitch?

I am trying to use a dataset. But I am facing two problems or confusions in understanding it. Can anbody guide me what 3D gaze direction stands for or means (angles, (x, y, z) coordinates or what)? ...
0
votes
0answers
14 views

What degree do I point a 1m horizontal stick to an evelation of 1140 meters.

I have a 1 meter horizontal yagi antenna at an evelation of 685 meters. How many degrees would I need to tilt it up so it points to the mobile tower at an evelation of 1140 meters 21.5 km away. ...
14
votes
3answers
892 views

The position of a ladder leaning against a wall and touching a box under it

I was reading a newspaper and there was a little math riddle, I thought "how funny, that's gonna be easy, let's do it" and here am I... The problem goes as follow : in a barn, there is a 1 meter ...
0
votes
0answers
10 views

Find angles between sides of triangle and coordinate planes (xy,yz,zx planes) using three 3d vectors .

Given the following, three vectors: a⃗ =3i−2j+5kb⃗ =i−6j+6kc⃗ =2i+3j−k, find the angles between sides of triangle and coordinate planes. I calculated the sides to be 4.58 , 11.45 and 7.87. I also ...
-3
votes
1answer
20 views

Two full-length [on hold]

A high school basketball player is $75$ inches tall. The basketball hoop is $10$ feet above the court. Find the distance in feet between the top of the players head and the basketball hoop.
1
vote
3answers
43 views

Is it possible to find the vertices of an equilateral triangle given its center point?

I was wondering how to find the vertices of an equilateral triangle given its center point? Such as: ...
0
votes
0answers
16 views

Find base coordinates for oblique pyramid with rectangular base with known apex coordinates, unit direction vectors and base side lengths

Given an oblique pyramid with a rectangular base and the following known parameters: apex coordinates $X$ the unit direction vectors $\hat{XA},\hat{XB},\hat{XC},\hat{XD}$, which go from $X$ in the ...
-1
votes
1answer
24 views

Find the equation of the ellipse [on hold]

This question is hard I really appreciate if anyone can solve it. Find the equation of the ellipse that has $e=1/2$, center in (0,0) and passes through $P(9/2,3)$.
2
votes
1answer
18 views

Number of components needed for 3D rotation

Using Euler angles, a 3D rotation can be expressed using 3 real numbers. Using quaternions, 4 are needed and using rotation matrices 9. Is it possible to express a 3D rotation using less than 3 real ...
0
votes
2answers
34 views

Determine the locus of a equation Quickly[Mental Math]

if $Z=X+iy$ then determine the locus of the equation $\left | 2Z-1 \right | = \left | Z-2 \right |$.I can tell that it a circle equation and it is $x^2 + y^2 = 1$.There are a lot of equation in my ...
1
vote
0answers
16 views

Camera calibration: how does checkerboard size/numbers/placement affect accuracy

I am trying to calibrate a camera using a checkerboard by the well known Zhang's method followed by bundle adjustment, which is available in both Matlab and OpenCV. There are a lot of empirical ...
0
votes
0answers
23 views

Uniform Sampling on Intersection of Simplices

I'm trying to sample uniformly on the intersections of several simplicies, with all coordinates being non-negative. That is, given $$A\vec{x}=\vec{b} \ \ and \ \ \vec{x} \geq \vec{0},$$ I want to ...
0
votes
1answer
12 views

Determine Orthogonal and non orthogonal using Coordinates

Can we identify using coordinates that if Polygon is orthogonal or non orthogonal. data = [(100, 100), (100, 200), (300, 200), (600, 400), (1150, 400), (1150,300), (600,300), (300,100)](These ...
1
vote
1answer
27 views

Why does this hyperboloid change into a surface? [duplicate]

Given this equation $x^2+y^2+z^2+2xy+2xz+2yz-x-y-z=6$ and the corresponding quadric: If I rearrange the equation to $(x+y+z-3)(x+y+z+2)=0$ (which is equivalent), I get: So, which is the right ...
0
votes
1answer
21 views

Proper definition of concyclic?

Let $z_1,z_2...,z_n$ be points in the complex plane, then if there exists $Z$ such that $$\vert Z-z_k\vert=a\in\{\text{Real Numbers}\}$$for all $k\in \{1, 2, 3...,n\}$, then $z_1,z_2...,z_n$ are ...
-5
votes
0answers
24 views

tessellation of an arbitrary shape [on hold]

Are there any shapes that we can tessellate any plane shapes (with arbitrary shapes) by them? i.e. if I generate a random shape, how can I tessellate it by some shapes?
3
votes
0answers
36 views

How to transform (rotate) this hyperbola?

Given this hyperbola $x_1^2-x_2^2=1$, how do I transform it into $y_1y_2=1$? When I factor the first equation I get $(x_1+x_2)(x_1-x_2)=1$, so I thought $y_1=(x_1+x_2)$ and $y_2=(x_1-x_2)$. ...
2
votes
2answers
25 views

Find the equation of base of Isosceles Traingle

Given the two Legs $AB$ and $AC$ of an Isosceles Traingle as $7x-y=3$ and $x-y+3=0$ Respectively. if area of $\Delta ABC$ is $5$ Square units, Find the Equation of the base $BC$ My Try: The ...
0
votes
2answers
41 views

Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
1
vote
1answer
18 views

Finding point where angular bisector meets circumcircle in complex plane

If $A(z_1)$,$b(z_2)$ and $C(z_3)$ are vertices of a triangle. It is inscribed in circle |z|=2. If internal angular bisector of A meets the circumcircle at $D(z_4)$. Find $z_4$ interms of $z_1$,$z_2$ ...
0
votes
2answers
28 views

Co-ordinate geometry and area of triangle

When a straight line $ax+by+c=0$ forms a triangle with the axes $x$ and $y$, what is the general formula for the area of the triangle?
10
votes
4answers
1k views

N gunmen in a field

Let n be an odd integer. In some field, n gunmen are placed such that all pairwise distances between them are different. At a signal, every gunman takes out his gun and shoots the closest gunman. ...
-1
votes
1answer
23 views

The limit incentral triangle is equilateral [on hold]

I found a nice problem of geometry but I don't know how to prove it. Given a triangle $T_0$, we build $T_1$ by considering the projections of the incenter of $T_0$ on the sides of $T_0$. In the ...
2
votes
0answers
24 views

What shapes fit evenly inside a Hexagon

So I'm designing a board game that uses a number of adjacent hexagonal boards. These boards need to be divided up into spaces (tiles) that players move through. I've been playing with using Hexagons ...
2
votes
1answer
53 views

What geometric object is given by this equation?

What geometric object is given by this equation? $x^2+y^2+z^2+2xy+2xz+2yz-x-y-z-6=0$ Maple says it's a hyperboloid of one sheet, but is there a way to show it without going the long way by using the ...
0
votes
1answer
17 views

Delaunay Triangulation on Convex Polytopes — Uniform Sampling

My goal is to uniformly sample from a convex polytope. I know that for the simpler case, where I have to uniformly sample from a simplex, I can use Bayesian Bootstrap, discussed in these posts: ...
0
votes
1answer
53 views

Which slope is greater: one going very slightly downward, or one going quite steeply downward? [on hold]

I've been arguing back and forth with someone about this for a while now. It seems to me like a number closer to positive infinity is considered greater, no matter if you are talking about slopes or ...
3
votes
1answer
29 views

spirals around cone

I have multiple spirals running around a cone. The spirals are $$r_\Delta = r_b - r_t$$ $$x(z) = r_b \cos(z) - r_\Delta z \cos(z)$$ $$y(z) = r_b \sin(z) - r_\Delta z \sin(z)$$ $$d(z) = ...
0
votes
0answers
17 views

To circumscribe a square about a given circle.

http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV7.html I was just wondering something . We know that if a line touches a circle at one point, then this means that this line is forming a ...
-1
votes
0answers
27 views

Area of a circle using Area =(D x 0.8862268332656149)Squared

I started off for fun to work out the area of a circle by using a percentage of its diameter and converting this into a decimal. Area =(D x 0.8862268332656149)Squared. then I found that if I squared ...
0
votes
3answers
70 views

Prove sum of $\sin$ of angles is greater than $\sin$ of sum of angles

It seems that $\displaystyle \sum_{x_i \in X} \sin\left(x_i\right) \geq \sin\left(\sum_{x_i \in X} x_i\right)$ where $X$ is a set of angles where $\displaystyle \sum_{x_i \in X} x_i \leq \pi$ radians ...
-3
votes
0answers
34 views

what is the distance [on hold]

I have a hill, I want to build a three piece retaining wall. One wall at the bottom, one wall half way up and one wall cresting the top. The hill is 10 foot high and 10 foot wide. What is the distance ...
1
vote
5answers
49 views

How to determine if 2 line segments cross?

Give two line segments, each defined by $2$ points in $x,y$ space, such as $L_1 = (x_1,y_1)-(x_2,y_2)$ and $L_2 = (x_3-y_3)-(x_4,y_4)$, and that these points are the result of sampled data (they are ...
1
vote
3answers
200 views

Is a ball noncompact?

A compact manifold usually refers to "a manifold without a boundary", for example the usual 2-sphere $S^2$. What about a manifold with a boundary? Intuitively, I think such an example, e.g. a ball ...
0
votes
1answer
17 views

Intersection of a cone and a plane

In $\mathbb{R}^3$, given the cone $K$ and the plane $E_c$ with the equations $4x^2=y^2+z^2$ and $z=c(1-x)$. How do I find out which different geometric objects I get for all $c\geq 0$ if I intersect ...
0
votes
1answer
47 views

Minimal area of triangle

We have the points $A(2, 3-m), B(m+2, -1)$ and $C(m, 2-m)$. Where $m$ is a real number. Find $m$ for which the area of triangle $ABC$ is minimal. So I've tried to find the equation of line $BC$(the ...
-1
votes
0answers
32 views

Point in the circle [on hold]

I have a circle with center $(x, y, z)$. Circle lies in plane which normal also known $(n_1, n_2, n_3)$. How calculate points on circle for given angle?
0
votes
2answers
22 views

Intersection of perpendicular and plane

I have a point $(x,y,z)$ and normal to plane with normal vector $(n_1, n_2, n_3)$. How can I calculate the intersection point of perpendicular from point to that plane? Thank You!
0
votes
1answer
30 views

Determine the lines of curvature of $z=xy$

I have to find the lines of curvature of $z=xy$ I calculate Weingarten Matrix as described below $p_u = (1, 0, v),p_v=(0,1,u),\nu =\frac{1}{\sqrt{1+u^2+v^2}}(-v,-u,1)$ so, $E=1+v^2,F=uv,G=1+u^2$ ...
0
votes
2answers
40 views

How do I solve using the line equation through (2,3) and (4,1)?

My teacher just taught me Coordinate Geometry and she is very fast :3 I cant really cope with the phase and i got loads of homework now. One of the question is "Find the equation of the straight ...
2
votes
0answers
30 views

how to find the edges emanating from a given vertex in a polyhedron

Suppose my polyhedron $P$ is defined as $P={ x\in \mathbb{R}^n \mid Ax=b, x\geq0 }$ I have $x_0$, which is a vertex of $P$. How to find the edges emanating from $x_0$? In other words, I want to find ...
0
votes
1answer
22 views

Prove that the median of this isosceles trapezoid is tangent to both circles.

What the problem really asks me to prove is that a circle can be inscribed in $ABCD$, or that $AB + CD = AC + BD$ or $2AB = AC + BD$ or $AB = \frac{AC+BD}{2} = PK$. I can do that assuming that $PK$ ...
0
votes
0answers
24 views

initial height = 60“. There is 5 degree decline over 163.5”. What is ending height?

I'm building a roof for a structure and need to get the ending height correct. The initial height is 60". The adjacent length (the ground) is 163.5". The decline is 5 degrees. I have gotten the ...
0
votes
1answer
109 views

Angles in triangle proof

Let $ABC$ be an acute triangle. The lines $\iota_{1}$ and $\iota_{2}$ are perpendicular to $AB$ at the points $A$ and $B$, respectively. The perpendicular lines from the midpoint $M$ of $AB$ to the ...