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
2answers
35 views

about shortest path between points

Let $P=(0,1)$ and $Q=(4,1)$ be points on the plane. let $A$ be a point which moves on the $x$-axis between the point $(0,0)$ and $(4,0)$. let $B$ be a point which moves on the line $y=2$ between the ...
2
votes
2answers
48 views

Labelling the Vertices of Dodecahedron

Dodecahedron has 20 vertices. I want to label them by $1,2,3,4,5$ with the following rule. The five vertices of each face should have different labels. Q. What ...
1
vote
2answers
22 views

how to find spherical coordinates of adjacent vertices surrounding central vertex in A3/D3 lattice

How could you define (using spherical coordinate system) all the adjacent vertices directly connected to a central vertex in a tetrahedral octahedral honeycomb? Alternatively it would be useful to get ...
0
votes
0answers
38 views

Triangle $ABC$ and equilateral triangles $ABC'$, $BCA'$ and $ACB'$.

We consider a triangle $ABC$ whose angles are less then $120°$ and construct the equilateral triangles $ABC'$, $BCA'$ and $ACB'$, exterior to $ABC$. $I$ denotes the intersection of $(AA')$ and ...
0
votes
0answers
19 views

Study the caracteristics of the transformation $f=r\circ t \circ h$.

Let $OABC$ be a square with $(\vec{OA},\vec{OC})=\frac{\pi}{2}$. Let $r$ be the rotation of center $B$ and angle $\alpha=\frac{\pi}{2}$, $t$ the translation of vector $\vec{CA}$, $h$ the homothetic ...
2
votes
3answers
48 views

Given an equilateral triangle, show that $MA + MC = MB$.

I have to solve the following problem: Consider an equilateral triangle $ABC$ and $\mathcal{C}$ its circumscribed circle. Let $M$ be a point located on the arc of the circle defined by $[AC]$ which ...
0
votes
1answer
21 views

Geometry parallel angles

1 picture. Find value of u, v and w 2nd picture. find value of x
-1
votes
1answer
32 views

Angles and Parallel

a and e are both (...), both have arms to the right on n g and b are both (...), both have arms to the left on n I'm not getting this, I am taught in another language so I do not know what it's ...
0
votes
0answers
8 views

Is this a Hamiltonian Directed Cycle? Need help proving.

Say that there is $S$, a finite set of unit squares. So, $S$ is chosen from a larger grid of unit squares. The unit squares of $S$ are tiled with isoceles right triangles. Each of these triangles has ...
0
votes
1answer
27 views

Proving that the dot product is distributive?

I know that one can prove that the dot product, as defined "algebraically", is distributive. However, to show the algebraic formula for the dot product, one needs to use the distributive property in ...
2
votes
1answer
25 views

Similarity of triangles?

The question is: "$ABCD$ is a quadrilateral in which angle $B =$ angle $C$ and $AC$ bisects angle $BAD$. If $BA$ and $CD$, when extended, meet at $E$, prove that $AD/DC = AE/BE$." I'm finding this ...
1
vote
1answer
17 views

Determining direction from three points on a line

I have a small geometry problem that for some reason I just can't get a grasp on. You're given three points on a line in 3D space, p1, p2, p3. (assume for simplicity that they're named ...
0
votes
2answers
43 views

If ABCD is a square and M is any point on CD…

If $ABCD$ is a square and $M$ is any point on $CD$, the angle bisector of angle $BAM$ intersects $BC$ at $K$ then how to prove that $MA=DM + BK$.
-1
votes
1answer
25 views

Getting angle vector makes with the x-axis

If we have the velocity of a particle moving on a path, $\frac{dy}{dx}=0.43$ then why can we say that the angle the velocity vector makes with the x axis is $\arctan(0.43)$? I don't understand why ...
2
votes
2answers
79 views

$\sin \left( {5x} \right) = 2\sin \left( {3x} \right)\sin \left( {4x} \right)$

ask gentlemen to help solve the equation Where the real number $$ x \in \mathbb{R}: \sin \left( {5x} \right) = 2\sin \left( {3x} \right)\sin \left( {4x} \right); $$ I notice that $$x = k\pi \quad ...
1
vote
1answer
14 views

The ratio of the perimeter of rect P to the perimeter of rect Q is 2:5. The area of rectangle P is 12 sq ft. What is the area of rect Q? [closed]

The ratio of the perimeter of rectangle P to the perimeter of rectangle Q is 2:5. The area of rectangle P is 12 square feet. What is the area of rectangle Q?
1
vote
0answers
23 views

Two similar regular polyhedra have given surface areas. What is the ratio of their edge lengths? [closed]

Two similar regular polyhedra have surface areas 16 cm.sq. and 64 cm.sq. What is the ratio of their edge lengths?
1
vote
0answers
20 views

Twisted colouring problem

I had doubts in the following similar looking questions I came across:- $Q1.$ The Cartesian plane is coloured with 2 colours. Prove that there exists 3 points of the same colour, which are the ...
1
vote
1answer
13 views

Given Lines t, m, and n are tangent to the circle at W, Y, and X (respectively). What is the arc of WY [closed]

The tangent lines t and m meet outside the circle at point C, lines m and n meet at point B and t and n meet at point A. Angle XBY is 50 degrees, Angle WAX is 60 degrees. I need to find the arc of ...
0
votes
1answer
42 views

Parametrisation of curves in 3D and using properties of $\mathbf{r}(t)$ to show that the curve is on the surface of a sphere.

A curve $C$ in $\mathbb R^3$ has a parametrisation $\mathbf r(t)$. Suppose $\mathbf r(t)\neq 0 \,\forall t\in \mathbb R$ and $\mathbf r(t)\cdot\mathbf r'(t)=0$ for all points of $C$. Show that $C$ ...
0
votes
2answers
38 views

$ABCD$, $P$ is any interior point, $PA=24, PB=32, PC=28, PD=45$

could anyone tell me how to solve it? I have a convex quadrilateral $ABCD$, $P$ is any interior point, $PA=24, PB=32, PC=28, PD=45$ cm, I need to know the perimeter of $ABCD$. Thanks for helping. ...
0
votes
0answers
30 views

Show that circle generates the surface $(x^2+y^2+z^2)(\frac{x^2}{a^2}+\frac{y^2}{b^2})=x^2+y^2$

$POP'$ is a variable diameter and the ellipse $z=0, \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and a circle is described in the plane $PP'ZZ'$ on $PP'$ as diameter. Prove that as $PP'$ varies, the circle ...
0
votes
2answers
14 views

Using Similar Triangles to solve for the equation of a line

Consider points A=(−10,−4) and C=(8,5). The point B is on the line passing through A and C. The x-coordinate of B is −1. Determine the y-coordinate of the point B. This question has been asked ...
0
votes
0answers
22 views

Are isosceles right triangles the only ones whose circumcenters lie on their incircles? [duplicate]

I recently (stupidly) asked this question, to which user Blue responded quickly with the example of the isosceles right triangle. Which triangles have circumcenters on their incenters? Do they have to ...
0
votes
1answer
48 views

Is there any triangle whose circumcenter lies on its incircle?

Is it possible for a triangle's circumcenter to lie on its incircle? My guess is yes, but I haven't succeeding in explicitly finding one or proving that it exists.
1
vote
1answer
51 views

Prove that four points lie on a circle.

Let $ABC$ be a triangle such that $2AB=AC+BC$. Show that the incentre, the circumcircle, midpoint of $AC$ and midpoint of $BC$ lie on a circle. I reduced the question to prove that both midpoints, ...
3
votes
1answer
53 views

If the red curve is an ellipse, is the green curve also an ellipse? [duplicate]

See the figure below: The red curve is an ellipse; the blue curve is a unit circle. Green curve is the locus of the circle center. Is the green curve an ellipse?
0
votes
2answers
41 views

Quadratic Forms in $n$ dimensions

In my linear algebra high school textbook, there is a 'Project' that extends geometrical ideas to '$n$-dimensional space'. I have no idea what to do or where to begin for this question. Show ...
0
votes
2answers
15 views

Given a line, calculate a perpendicular line to make a T shape

I am working with SVG vector graphics, and I want to make a dynamic T shape by adding a perpendicular line. I have a line with two points (4,17) and (11,3). How can I figure out (x1,y1) and (x2,y2)? ...
0
votes
2answers
47 views

About the sum of sines of two angles

Suppose that $0\le \alpha\le \pi/2$ and $0\le \beta\le \pi/2$ such that $\alpha+\beta\ge \pi/2$. Can we prove that $\sin(\alpha)+\sin(\beta)\ge 1$?
0
votes
1answer
23 views

Find ray between an angle in the same plane as the angle

If I have an angle $\angle{ABC}$, I want to know how to find a ray $\overrightarrow{BD}$ such that $\overrightarrow{BD}$ is in the same plane as $\angle{ABC}$, and the measure of $\angle{ABD}$ is some ...
0
votes
1answer
17 views

Distance of a point from a line specified by coordinates

I'm working on an open source program that involves drawing and it would be helpful to see which line is closest to the user's selection. I have a point specified by coordinates and a line specified ...
1
vote
0answers
42 views

Quadric and tangents planes

Let $Q$ be the quadratic $x^2 + 4xy - 2y^2 + 6z^2 + 2y +2z = 0$ Prove that $Q$ is a cone and find its vertex. Write the tangent plane $A$ to the cone in $(0,0,0)$ and say which kind of conic is the ...
0
votes
1answer
42 views

Weird vector projection form

Let $C^0[1,3]$ be the $\Bbb R$-vector space equipped with the usual scalar product (by the integral ). Calculate the projection of the function $f(x)= 1/x$ onto the subspace $W = L\{x\}$ Well, my ...
2
votes
3answers
52 views

Lazy Caterer's Problem: why a new line can cut all the others

The lazy caterer's problem is to figure out the maximum number of pieces formed by $n$ straight cuts of a pizza. Any time two cuts meet new pieces are generated, so for maximum number of pieces it ...
0
votes
1answer
60 views

Find the area of the shaded region of this trapezium

In the figure, $ABCD$ in a trapezoid. Given that $AD$ is parallel to $EC$ and $EB=2(AE)$ Find the area of $ABCD$ and $AEFD $ I know the area of a trapezoid $A=\frac{(b_1+b_2)}{2}h$ and I think that ...
2
votes
1answer
49 views

Intersecting Circumcircles

I came across this interesting problem which I have tried to solve for many days.Consider a scalene triangle ABC. The Euler Line and circumcircle are drawn. G is a point on the Euler Line and F is a ...
1
vote
1answer
18 views

Quadrilateral into a trapezoid

Consider a quadrilateral with none of its sides equal. Show that it is possible to use the four sides to construct a trapezoid. I'm not sure what to do? Do I have to rearrange the sides or can I do ...
0
votes
2answers
22 views

Trapezium problem

I am trying to solve the following geometry exercise: In an isosceles trapezium the sum of its bases is equal to $6\sqrt{2}$ cm and the minor base is equal to the half of the major base. Suppose the ...
0
votes
1answer
13 views

show if the parametrized curve is regular

I'm trying to show if a curve is regular or not I know at first we have to find its derivative and check if it is equal to zero or not if it is equal to zero then its not regular For example let ...
12
votes
1answer
151 views

Automorphism group of a lattice's Voronoi cell

Let $\Lambda$ denote a lattice of $\mathbb{R}^n$, i.e. $$\Lambda = \left\{\sum_{k=1}^n n_i\mathbf{a}_i\ \bigg|\ n_i\in\mathbb{Z}\right\},$$ for $n$ linearly independent vectors $\{\mathbf{a}_i\}$ in ...
1
vote
1answer
28 views

Geometrical shapes overwiev [closed]

I am looking for huge summary with hierarchical structure of solid geometrical shapes with exact definition, solid properties (e.g. number of edges, faces, corners, regularity, symmetry and many ...
-1
votes
0answers
19 views

Boundary created by two crossing paths

I have a path that starts at the origin and goes in a straight line for some distance d1. At d1, it begins a right-handed turn. The turn has a constant radius R over an angle theta1. After tracing ...
2
votes
1answer
87 views

Geometric meaning of Cauchy functional equation

What is the geometric meaning of Cauchy's functional equation? $$f(x+y) = f(x)+f(y) \quad \forall x,y$$
2
votes
0answers
27 views

Is there an intuitive reason why hippopede, the intersection curve of a sphere and a cylinder, is traced by composing two rotational motions?

The hippopede is historically famous because Eudoxus used its properties in the first mathematical model of planetary motion. He nested concentric spheres rotating at different inclinations to each ...
1
vote
1answer
62 views

Why klein Bottle is 4-D?

I am wondering that Klein Bottle is 4-D. Can any body tell me how it is possible? I can give coordinates for each point of the Klein Bottle with 3 values. Then how it can be 4-D? What is immersion? ...
0
votes
1answer
21 views

About the inversion of hyperbel into lemniscate

I assume you know that a lemniscate $r^2 = \cos{(2\phi)}$ (polar coordinates) transforms during the inversion w.r.t. a unit circle into $r^{-2} = \cos{(2\phi)}$. I wonder what happpens with the two ...
2
votes
1answer
43 views

Why ternary diagrams work

I am trying to understand why ternary diagrams work. In order that the altitude criterion be valid, if I correctly understand, given equilateral triangle $ABC$, whose vertices I name as the three ...
0
votes
1answer
30 views

embedding projective plane in 4-space? [closed]

Is it possible to embed projective plane in 4-space? If not what is the reason and what is the smallest singularity set?
2
votes
1answer
53 views

What is the topology of this quotient of $S^2 \times S^1$?

So suppose you take an $S^2$, then you put an $S^1$ fiber over it which degenerates by smoothly shrinking to a point at its poles. What is the topology of this space in more familiar terms (assuming ...