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

1
vote
0answers
21 views

one question about differential geometry,show the curvature k($\phi$)

One often gives a plane curve in polar coordinates by $p=p(\phi)$,$a\le\phi \le b$. (1)Show that the arc length is $$\int_{a}^{b}\sqrt{p^2+\dot p^2}$$,where $\dot p$ means the derivative of p with ...
0
votes
0answers
35 views

Find the angle in a triangle

Find the angle $a$: I came up with 20 degrees but not sure. Can somebody help here.
1
vote
1answer
10 views

Finding the length of $BC$ in a kite

Calculate the length of $BC$. I first started by letting $M$ the point of intersection of $AC$ and $DB$. Now $MB^2+MA^2 = 9$, $MD^2+MA^2 = 16$, $MD^2+MC^2 = 36$. Therefore, $BM^2+MC^2 = BC^2$ Can ...
0
votes
0answers
12 views

Mean width of an ellipsoid

Let $E$ be an ellipsoid in $\mathbb{R}^d$ defined by the equation $\sum \frac{x_i^2}{a_i^2}=1$. Is there a formula to express the mean width (or an approximation of the mean width) of $E$ in term of ...
1
vote
0answers
9 views

Perspective projection of a circle: what is the size of the semi-major axis?

It can be proven that the perspective projection (or camera projection) of a circle is an ellipse. But I also need to prove that the semi-major axis has the same size as the radius of the original ...
2
votes
0answers
10 views

How prove $\left(\frac{D}{\sqrt{3}}+\frac{d}{2}\right)^{2}\geq n\cdot\frac{d^{2}}{4}$ for $D=\max{A_iA_j}, d=\min{A_iA_j} (1\leq i<j\leq n)$?

Let be n points $A_1,A_2,A_3,...,A_n$ on plane $(n\geq 3$). Let $D=\max{A_iA_j}, d=\min{A_iA_j} (1\leq i<j\leq n)$. How prove $\left(\frac{D}{\sqrt{3}}+\frac{d}{2}\right)^{2}\geq ...
1
vote
1answer
20 views

Intersection of Two Planes

I keep hearing different answers for what the intersection of two planes is. I believe it is a line, but it can also be a plane IF the two planes are not distinct. However other sources are saying ...
-7
votes
0answers
24 views

Pyramid inside a rectangular tank [on hold]

a rectangular tank has a base 60cm by 20cm. A solid metal pyramid with a square base of sides 10cm each and height 27cm is placed inside the tank. The tank is then filled with water until it just ...
2
votes
2answers
27 views

How to explain why a curve is on a cylindrical surface?

The question may be a bit general but I'm unsure about how to define it. I have a curve: $\vec r(t) = (2\cos(t),2\sin(t), 2t)$, for $0\le t \le 2\pi$, The problem I'm trying to pose : "Show that ...
1
vote
1answer
17 views

Getting the intersection of a line and a plain

My line (2,1,10) goes through the plain with the normal (-2,3,8). Now I would like to calculate the intersection with following ...
0
votes
0answers
3 views

Decide conditions on smooth function $r$ such that $\nu$ is a regular curve and decide functions $r$ for which $\nu$ has speed $1$

Decide conditions on smooth function $r$ such that $\nu$ is a regular curve and decide functions $r$ for which $\nu$ has speed $1$ Let $r: \mathbb R \rightarrow \mathbb R$ be a smooth function ...
5
votes
7answers
40 views

How does one prove that if $\cos(t) = \cos(t')$ and $\sin(t) = \sin(t')$ then $t = t' + 2k\pi$?

How does one prove that if $\cos(t) = \cos(t')$ and $\sin(t) = \sin(t')$ then $t = t' + 2k\pi$ ? I've tried proving the above statement, which I think is valid. I know $\sin(t)$ is injective on ...
0
votes
3answers
56 views

Parametrization of the ellipse $\frac {x^2} {p^2} + \frac {y^2} {q^2} = 1$.

Consider the ellipse ($p > q > 0$) $$\frac {x^2} {p^2} + \frac {y^2} {q^2} = 1$$. I want to prove that $$\mu(t) = (p \cos(t), q \sin(t))$$ is a parametrization of the ellipse. I see that $(x/p, ...
0
votes
3answers
30 views

How to find the radius [on hold]

I have to find the radius of the circle. AB=1,5 AD=2 AD is a tangent Please help!
-2
votes
0answers
26 views

A 57“ arm has a vertical pin at one end, if the pin angle changes by .020” how much does the other end of the arm move? [on hold]

A 57" arm has a vertical pin at one end, if the pin angle changes by .020" how much does the other end of the arm move? ok, let me try this.
0
votes
1answer
29 views

Angle quadrisection in a triangle

In triangle ABC, AB=84, BC=112, and AC=98. Angle B is bisected by line segment BE, with point E on AC. Angles ABE and CBE are similarly bisected by line segments BD and BF, respectively. What is ...
2
votes
1answer
26 views

Homeomorphisms of different spheres

It is pretty straightforward to show that if $X$ is a Banach space under two equivalent norms, then the respective open unit balls $B_1$ and $B_2$ are homeomorphic only by showing that $B_i$ is ...
3
votes
0answers
30 views

Points Distributed evenly around a circle: how many points are in each region?

A circle of circumference $2$ is split into three arcs of length $\frac{2}{3}$ (so the regions are $[0,\frac{2}{3})$, $[ \frac{2}{3},\frac{4}{3})$, $[\frac{4}{3},2)$, $2$ identifies with $0$) and ...
0
votes
0answers
16 views

midpoint of the diagonal of the quadrilateral and rhombus

$EBA,FCB,GDC,HAD$ is a similar triangle which is drawn externally of quadrilateral $ABCD$, where the sides of quadrilateral $ABCD$ become the base of the similar triangle. Let $M,N,P,Q$ are midpoints ...
3
votes
0answers
19 views

Prove that the circle which contains ATB and incircle of ABC touch in one point(T).

Incircle of $ABC$ touches $AC$ in $D$, $BC$ in $E$ and $AB$ in $K$. $J$ is the center of the excircle which touches the side $AB$. The circumcircle of $ADJ$ and $BEJ$ intersect in point $J$ and $T$. ...
2
votes
1answer
19 views

Stereographic projection of a sphere

What should have been a simple exercise in geometry has morphed into a multi-day affair with me figuratively tearing my hair out. I have no clue what's wrong. This image accompanies the problem: ...
2
votes
1answer
21 views

Seperating points in the complex plane

Given a finite set of points say $p_1,p_2, \ldots, p_n$ in the complex plane, how do I find another point $q$ such that ray $R_i$ joining $q$ to $p_i$ are all distinct. I would be happy with any kind ...
0
votes
0answers
25 views

Linear transformation of vector

I have computer graphics class and i had something like that on lecture: $$ \begin{bmatrix} \overrightarrow{b1} & \overrightarrow{b2} & \overrightarrow{b3} \end{bmatrix} \begin{bmatrix} c1\\ ...
1
vote
1answer
44 views

Centre of symmetry of a triangle

Suppose we have a $\triangle ABC$ wherein points $D,E,F$ are confined to move along the edges of $BC, AC, AB$ respectively such that $\triangle DEF \sim \triangle CAB$. What would be the centre of ...
0
votes
0answers
8 views

Tangent cone to the graph and epigraph

Good morning! I am solving this example: Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a function given by $f(x) = \left\{ \begin{array}{rl} x \cdot sin(\frac{1}{x}) & \text{if } x > 0,\\ 0 ...
2
votes
1answer
19 views

How find $\min_{a\in\mathbb R}f\left(a \right)$ for $f(a )=\max_{1\le k\le n}\left|x_k+ay_k\right|$?

Let them be given points in the plane $P\left(x_k,y_k\right)$, where $k\in \{1,...,n\}$. Let $f(a )=\max_{1\le k\le n}\left|x_k+ay_k\right|$ , where $a\in\mathbb R$ . How find $\min_{a\in\mathbb ...
0
votes
0answers
19 views

What does 'forms a right-handed set' mean?

In a question I am reading, the following question appears. What if $\vec{A},\vec{B}$, and $\vec{C}$ are mutually perpendicular and form a right-handed set? What exactly does "form a ...
0
votes
1answer
19 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 ...
3
votes
1answer
46 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 ...
-6
votes
1answer
65 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
vote
2answers
92 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
votes
1answer
29 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
vote
2answers
70 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
votes
0answers
13 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
votes
1answer
11 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
votes
1answer
34 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
votes
1answer
30 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
votes
1answer
12 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
votes
1answer
33 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
12 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
14 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
63 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
vote
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
votes
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. ...
1
vote
0answers
36 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 ...
-1
votes
0answers
44 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
vote
0answers
42 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
votes
1answer
27 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 ...
3
votes
0answers
32 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
20 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 ...