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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1answer
12 views

Find the area of the convex quadrilateral

So i have $ABCD$ is a convex quadrlateral and $E$ is the intersection point of diagonals. Given that $AE=2,BE= 5, CE = 6, DE =10$ and side $BC = 5$. I know the formula $A=\frac{1}{2}d_1 d_2 \sin ...
2
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0answers
17 views

Volume of a sphere with two cylindrical holes.

Consider a sphere of radius $a$ with 2 cylindrical holes of radius $b<a$ drilled such that both pass through the center of the sphere and are orthogonal to one another. What is the volume of the ...
0
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0answers
11 views

How many cases can draw diagonals that Applicable 2 above condition?

Imagine A $n$_regular polygon that vertex is named by $1$ to $n$. We know can draw $\frac{(n)(n+3)}{2}$ diagonals in $n$_regular polygon and also know if we want draw Maximum diagonals are not ...
-6
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1answer
58 views

you know root square of -1, what is the larger of the square? [on hold]

there is a square ABDC, $BD = \sqrt{-1}$ what is the value of AB=BC=DC=AD?
1
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1answer
51 views

If the curvature of a curve in a plane is a constant, is the curve contained in a circle?

If the curvature of a curve in a plane is a constant, is the curve contained in a circle?(Suppose curvature is positive.) one of my homework problems needs to use this, but I am not sure whether this ...
0
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0answers
25 views

What is a transformation that can't have shearing called?

What is a transformation called when it can have separate scaling for x and y, rotation, and translation, but it cannot have shearing or scaling AFTER rotation? Basically if this transformation is ...
1
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0answers
42 views

The area visible from two lighthouses with angle of vision 30 degrees, built at distance 10km from each other

The distance between 2 lighthouses is 10 km. What is the maximum area of the ocean in which both can be simultaneously visible if the angle of vision for each lighthouse is 30 degrees?But the minimum? ...
0
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0answers
10 views

find a point $C \in r$ (line) such that $d(C,\pi)=d(A,r)$

I have a line $r:(x,y,z)=(2,1,0)+\lambda(0,4,-3)$, $A=(2,4,4)$, a plane $\pi:4y-3z-4=0$. I have to find a point $C$ such that $d(C,\pi)=d(A,r)$ where $d$ is the distance.
0
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1answer
10 views

Tetrahedron in vector space: Finding a vector connecting two points

Edited to add: The tetrahedron is not necessarily a regular one. First off, the point $M$ is the centre of gravity for this tetrahedron. I have a base $\{e_1,e_2,e_3\} = ...
0
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1answer
32 views

Distance between a point and a line! [duplicate]

I have a big problem with geometry. How I do calculate the distance between the vectorial line $r:(x,y,z)=(2,1,0)+\lambda(0,4,-3)$ and the point $A=(2,4,4)$? I tried to solve the problem but ...
2
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0answers
24 views

Rotating an inscribed square in Geogebra

I am trying to figure out how to rotate the inside square so that the sides lengthen based on the degree of rotation. For example, after rotating 90 degrees in either direction, it should precisely ...
0
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1answer
9 views

Polygonal chain in a rectangular parallelepiped

Given a rectangular parallelepiped ABCDA1B1C1D1 with edges AD = 6, AB = 8, AA1 = 8. Points M and N are the middles of A1B1 and C1D1. Points E and F are chosen on the edges CC1 and DD1 so that C1E = 3, ...
0
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1answer
28 views

prove that $\angle BGC=90^\circ $

In a $\triangle ABC$ the medians $BE$ and $CF$ meet at the centroid G. Given that $AG = BC$, prove that $\angle BGC=90^\circ $
1
vote
0answers
11 views

Polyhedron that is not protected by the vertex set.

Given a polyhedron in the usual three dimensional space you can consider a specific point $y$ and define the points which can be "seen" by that point $y$. A point $x$ is seen by $y$ if the line ...
0
votes
1answer
13 views

Find the area of trapezium given certain angles and length of diagonal

In the trapezium $MNOP$, $MP$ is the major base and $NO$ is the minor base. Knowing that the angle $P$ is $58° 15'$, the angle $OMP$ is $21° 45''$, and the diagonal $OM$ is of $6.5$ cm, calculate the ...
4
votes
1answer
46 views

Where is the “thread” of a river?

Lawyers speak of the "thread" of a river. When the boundary between two counties or states is a river, it is usually the "thread" of the river, a path running along the center of the river. (In ...
1
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1answer
29 views

Find sides and height of isosceles trapezium given information about its diagonals

In an isosceles trapezium the diagonals cut at a point $O$ which divides them in two segments of $3$ cm and $7$ cm. If one of the angles formed between them is of $120°$, find the measures of the ...
0
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1answer
14 views

Find the adjacent sides of the quadrilateral.

The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is $60^0$. If the area of the quadrilateral is $4\sqrt3$, then remaining sides are. a. 2 and 3 b. 3 and 4 c. ...
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0answers
31 views

Identify a geometric theorem with probabilistic proof

Some months ago, I saw a theorem and its proof that was left on the blackboard from a previous computer graphics lecture. As far as I remember, the theorem went something like: It is possible to ...
0
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0answers
40 views

Find the lengths of two segments in a triangle with a line parallel to a side

Take a look at the picture, I am suppose to find the value of x and y. I have already manages to figure it out but here are a few questions that I need to understand. AD/AB = CE/CB = CA/ED x= ...
1
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0answers
39 views

$\text{Ker}A=\text{span}(u) \implies A=mat_C\left( u\wedge . \right)$

i found this equality and i wonder how can i find the right term $$\dfrac{1}{2}\left(\begin{matrix}0&1&1 \\ -1&0&1\\ -1&-1&0 ...
0
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1answer
26 views

Geometry: Circle inscribed in square

A circle is inscribed in a square $ABCD$ of side length $2$. There is a point $P$ on the circle such that $PA=a$. Is it possible to find $PB,PC,PD$ in terms of $a$? I haven't solved a problem like ...
2
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0answers
31 views

Defining a topological relationship between two objects

I am looking for a mathematical definition/description of the following relationship between two objects. It's similar to a knot (as in topology) but between two objects. I've found a similar problem ...
0
votes
1answer
16 views

determine the point of intersection on a facet in n-dimensions

I'm trying to solve a what I think is a classic line/plane intersection problem. However, this type of problem is new to me so please excuse me if I am misusing the terminology. I have two points in ...
2
votes
1answer
64 views

Prove that $\angle DAP=\angle CAB$ in a parallelogram $ABCD$

Let $ABCD$ be a parallelogram, and let $K$ be on $BC$ and $L$ on $CD$ so that $BK\cdot BC=DL\cdot DC$. Let point $P$ be where $DK$ and $BL$ intersect. Prove that $\angle DAP=\angle CAB$ (angles $DAP$ ...
1
vote
1answer
60 views

Pullback of a differential form

My question is in regards to a proof in Lee's 'Introduction to Smooth Manifolds'. He proves a lemma about the pullback of a differential form on a manifold $N$, where $F:M\rightarrow N$ is a smooth ...
0
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1answer
23 views

Book for projective geometry

I am looking for a blue colored book about projective geometry,as I remember, on sheep or goat covers. My friend suggested me two books before. I choose another one but recently I am interested in ...
3
votes
1answer
43 views

Triple Angle Condition

Let $ABC$ be a triangle with integral side lengths such that $\angle A=3\angle B$. Find the minimum value of its perimeter. Essentially we want sinb, sin3b, sin4b to have rational ratios (manipulate ...
0
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0answers
14 views

How can the surface integral (for a surface defined with parameters) be derived without using vectors?

It is possible to derive the arclength analytically by using the Pythagorean theorem: given a curve y(x), infinitestimal length dl along the curve can be given as: $(dl)^2 = (dx)^2 + (dy)^2$ ...
3
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0answers
33 views

Connect two point in page using short ruler [duplicate]

There is problem that my friend and me don't have solution for it. the problem is that can we connect to point in page with straight line using a ruler that it length is too much shorter than distance ...
1
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1answer
26 views

Data transformation of angles such that $90^\circ$ is equal to $-90^\circ$

Is there a transformation I can perform on a dataset of angles (from $-90^\circ$ to $90^\circ$) such that the transformation of $-90^\circ$ is equal to that of $90^\circ$? I am only interested in what ...
-1
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1answer
18 views

What happens to the underlying geometry when a lower dimension matrix is embedded in higher dimension?

For example, we can represent a rotation in the xy plane as $$R=\left\{ R(\theta)=\begin{pmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{pmatrix}, 0 \leq \theta ...
1
vote
0answers
18 views

Using inequalities to find vertices of a polytope

Consider vectors of integers $x\in\mathbb N^d$ satisfying $$ \begin{align} \forall\ i=1..d & \ \ [0 \leq \ell_i \leq x_i \leq u_i]\\ \forall\ i=1..d-1 & \ \ [x_{i+1} \leq x_i] \end{align} ...
2
votes
1answer
48 views

Finding orthogonal matrix that maps one vector to another

Let $w, v \in \mathbb{R}^k$ be two known vectors such that $||w|| = ||v||$ ($|| . ||$ is the usual Euclidean norm). My questions are related with the problem of finding $Q$ orthogonal such that $v = Q ...
2
votes
2answers
73 views

how they deduce that $\det A=1$ just from the first coeffcient and minor

i found solution of exercice that said show that A is rotation to do that we have to compute det A=1 but they found it directly Is there any relationshipe between the first coeffcient and minor ...
1
vote
1answer
27 views

Distance between a point and a parametric form of a line [on hold]

I have a problem with di dastance between a point and a line. There's the point $A=(2,4,4)$ and the line $s:(2,1,0)+\lambda(0,4,-3)$. How do I calculate the distance between A and $s$?
0
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0answers
22 views

Geometric interpretation or solution of an induction problem

Problem: Suppose you begin with a pile of $n$ stones and split this pile into $n$ piles of one stone each by successively splitting a pile of stones into two smaller piles. Each time you split a pile, ...
0
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0answers
28 views

Determine the positions of the point $M$ [on hold]

Given an isosceles right triangle $ABC$ wwith the right angle at $A$, and its circumcircle centered at O. $M$ is a point moving on the minor arc $AB$. Let $D$ be a point on $MC$ such that $AD\perp MC$ ...
-3
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0answers
71 views

Do you have any idea?

Let $M$ be a point moving inside a triangle $ABC$ with all sharp angles, with the property that $$\angle(B) + \angle(AMC) = 180.$$ Knowing that $\{E\}:= AM \cap BC$ and that $\{F\}:=CM \cap BA$, ...
0
votes
1answer
27 views

Isometry of $\mathbb{R}^n$ which is not product of $n$ reflections

I saw that every isometry of $\mathbb{R}^n$ is product of at most $n+1$ reflections. Q. Is there isometry of $\mathbb{R}^n$ which can not be written as product of $n$ reflections? I tried to get an ...
0
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0answers
8 views

The Cusp $w^2 + p(z,w)=0$ is desingularizable in the origin $O \in \mathbb{C}$

I have just studied a method in projective geometry over complex numbers on how to desingularize a curve in a point but i'm a little bit confused. I don't know the name of this classical method in ...
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0answers
25 views

Triangles congruency exercise

This exercise tells that: $$AD = AE, \angle A \cong \angle DEC, \angle ADE \cong \angle BDC$$ Then I have to show that $$\triangle ADB = \triangle EDC$$ The exercise solution highlights that we ...
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0answers
14 views

Finding the height of a tunnel [on hold]

The entrance to a railroad tunnel in the country village is in the shape of a semi circle. 7 feet from the center of the circle, the height of the entrance is 24 feet. How tall is the tunnel at its ...
0
votes
1answer
13 views

Obtain an equation for a parametrized curve segment

I am trying to express the segment of a curve in terms of $t$. For example, for a straight line between $(1,1)$ and $(2,2)$, I can express it like: $$ (x,y) = (1,1) + t (1,1), \space 0\le t \le 1 $$ ...
2
votes
1answer
43 views

Is a connected Reinhardt Domain which containg $0$ necessarely a polydisc?

I'm studying several complex variables basics. Roughly speaking: call $D\subseteq\Bbb C^n$ the set of points in which a given power series $$ \sum_{\alpha\in\Bbb N^n}a_{\alpha}(z-z_0)^{\alpha} $$ ...
0
votes
1answer
22 views

Centroids of Two Triangles Coincide.

Take a 6-gon $A_1A_2A_3A_4A_5A_6$. Let $B_1$, $B_2$, $B_3$, $B_4$, $B_5$, $B_6$ be the middle of the side $A_1A_2$, $A_2A_3$, $A_3A_4$, $A_4A_5$, $A_6A_1$ correspondingly. Let $O_1$ be the point of ...
1
vote
1answer
17 views

External Tangents of Circles.

If we have three circles C1 C2 C3. Consider the intersection between the external tangents of each pair of circles . Show that the three points of the intersections are collinear. Is this a well ...
-3
votes
1answer
25 views

boolean simplification , help please [on hold]

If we begin with $\;\bar A\,\bar C+ \bar B\,\bar C + A\, B\;$ how can we transform to $\;\bar B \, \bar C + B \,\bar C + A\, B\;$. I'm so lost please help.
0
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0answers
16 views

External Angle Bisector

How do you prove that for any triangle three points of intersections of bisectors of its external angles with opposite sides belong to one line. I'm having a hard time with the collinearity part.
0
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0answers
24 views

Endless repeating tiles

Regarding to this question ( "Hall of mirrors" OR "wraped plane" - Problem ) there's still an open point: how can i determine if the sum of all vectors pointing from p1 to p2 is ...