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Questions tagged [geometry]

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

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Prove that triangle $XYZ$ is equilateral

Let $ABC$ be an acute angled triangle whose inscribed circle touches $AB$ and $AC$ at $D$ and $E$ respectively. Let $X$ and $Y$ be the points of intersection of the bisectors of the angles $ACB$ and $...
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1answer
24 views

What does the reparameterization mean in Fréchet distances?

I am trying to understand the definition of frechet distance but I am struggling to understand the reparameterization part in the definition. I got the following definition from wikipedia Let A and ...
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3answers
53 views

How to find a tangent to a circle from an external point using calculus?

So I know how to find the tangent from an external point using algebra but that involves many equations making the entire process tedious. Anyways I have a calculus exam coming up and I think I should ...
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1answer
36 views

Find a point that is perpendicular to line and write it in javascript [closed]

Hi and sorry if my post is not the best but is my first time in something like this I have seen this post, I have two directional points. Point A going to point B. Each point has an X and Y ...
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1answer
23 views

Linear combination of two vectors in complex space

Let $\mathbf{x},\mathbf{y} \in \mathbb{C}^2$ be two linearly independent vectors in two dimensional complex space. Assume that $\|\mathbf{x}\|\leq \|\mathbf{x} \pm \mathbf{y}\|$. I want to show (or ...
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2answers
88 views

How can I find the slope of a line tangent to a small circle on a sphere? [closed]

I draw a circle on the earth, so that it passes through the north pole. I then begin walking around the circle, keeping track of my latitude. How do I tell what direction that I'm facing by knowing ...
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0answers
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How to rotate only one axis, being both on logarithmic scale

I have the following chart: And I want to overlay an Excel graph over it. However, between the absice (Frequency, cps) and ordinate (Peak Displacement, in) there is an angle of 135 degrees. The ...
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5answers
45 views

Finding the diagonals of a rhombus with side length $13$, where the sum of the diagonals is $34$ [closed]

How can we find diagonals of the rhombus with side length $a=13$ cm and sum of diagonals $d_1+d_2=34$ cm? Anything doesn't seem to work... I would really appreciate it, if anyone could help me / ...
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37 views

Determining the matrix of a projection

I have a question about the correctness of my ideas regarding the following exercise. Define $A_0=[(1,0,0,0)]$ $B_0=[(0,1,0,0)]$ $A_1=[(0,0,1,0)]$ $B_1=[(0,0,0,1)] \in \...
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3answers
29 views

SAT Math Problem - Corresponding Angles in Similar Triangles

In the following problem, why must ∠BAE ≅ ∠CED? Can't ∠BAE ≅ ∠BDE as well if you simply flip the triangle on top around? For instance: enter image description here
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2answers
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Formula for Arclength of Geodesic Connecting Two Points in the Surface of a Cylinder

Given two points laying on the surface of a cylinder, is there a simple equation for the arclength of the geodesic that connects those two points? In my use case, the cylinder is oriented axially ...
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1answer
24 views

2 points coordinates such that two lines to be medians in a triangle

I have the point and the equations of two lines: and .Also, I know that and . I have to find the coordinates of B and C such that d1 and d2 to be medians in ABC triangle. I found the ...
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0answers
15 views

Get intersection point on 2d plane of two Beams by coordinates and rotation in degrees

I have 2 Beams on a 2d plane of wich i have the starting position and the rotation in degrees from 0-359°. I'm gonna use x and z for the coordinates, where 0° is +z, 90° is +x, 180° is -z and 270° is -...
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2answers
44 views

Determine angles of a triangle given lengths of its sides

If I remember correctly this is high school material; I feel ashamed that I can't solve this now. Lengths of a triangle's sides determine its angles; but how to compute these angles?
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1answer
63 views

clarification about use of immersion in defining embedded submanifolds

the definition of embedded submanifolds as given in the text of boothby is: image of a topological embedding+immersion is an embedded submanifold Suppose we have a smooth manifold $M$ and $N$ ...
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0answers
24 views

Find vertices of a Voronoi diagram of convex polygons

From a set of polygons guaranteed to be : Convex Full (no holes) Non-intersecting (polygons may share edges/points, but not penetrate each other) How do I find the vertices of the Voronoi diagram ...
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0answers
19 views

Convert velocity vector to yaw roll pitch Tait Bryan

I have a cartesian position and velocity vector describing the flight path of an object in the format "time posX posY posZ velX velY velZ" and want to convert it to a "time posX posY posZ ang1 ang2 ...
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2answers
463 views

Where does this property involving quadrilaterals come from?

$ABCD$ is a square. $|AF|=6$, $|FK|=2$, and $DE \parallel AB$. What is $|EK|=?$ My geometry book has a property for this: $$|AF|^2=|FK|\cdot|FE|$$ Can you show me where does this property come from ...
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1answer
55 views

Show that if $AR$ intersects midperpendicular of $MN$ at $X$, then $X\in(I)$

Triangle ABC has an incircle $(I)$ which contacts $BC,CA,AB$ at $D,E,F$. Let $BP,CQ$ be bisectors of $\angle ABC,\angle ACB$ ($P \in AC,Q\in AB$). Line $AI$ intersects circle $(I)$ at $J$ (point $J$ ...
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0answers
59 views

Non-congruent angle of an isosceles triangle

Imagine I have two rays R1 and R2 emerging from point A0. Suppose I have N points (X1, X2, X3, . . . , XN) on ray R1, and (Y1, Y2, Y3, . . . , YN) on ray R2 such that X1 and Y1 are the closest to A0 ...
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1answer
37 views

Calculate Overlapping Area of $2$-Dimensional Shapes

I am running a Computer Simulation where 2 Shapes are moving towards each other and will eventually overlap. I want to calculate the overlapping Area of the shapes - in this example a Circle and a ...
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1answer
29 views

A book for questions on coordinate geometry

Can someone recommend me a book on coordinate geometry which focuses mainly on question solving and consists of ample amount of tough hybrid problems on 2 or more conics, topics like common tangents, ...
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0answers
23 views

Moser circle problem: maximum case for N?

Moser's circle problem sets the upper bound of regions the chords connecting n points can divide a circle into at ${n \choose 4} + {n \choose 2} + 1$. But how can we construct a set of points that ...
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0answers
31 views

Can you construct a hyperbola with only the eccentricity, two axes of symmetry and semimajor axis length given?

I am trying to construct a hyperbola for a project I'm doing and I have the two axes of symmetry, the length of the semimajor axis and the eccentricity. Is it possible? If so, how?
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2answers
47 views

Functions that map a quadrilateral to the unit square?

Given some quadrilateral $Q \subset \mathbb R^2$ defined by the vertices $P_i = (x_i,y_i), i=1,2,3,4$ (you can assume they are in positive orientation), is there a function $f: \mathbb R^2 \to \mathbb ...
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0answers
19 views

Mathematical description of moving sofa problem [duplicate]

Moving sofa problem asks what is the biggest area of a sofa that can be moved through L-shaped corridor. Now how can this problem be described in mathematical terms? So the sofa is basically any ...
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3answers
83 views

Show that $MNPQ$ is a square

Let $ ABCD $ a quadrilateral s.t. $AC=BD $ and $m (\angle AOD)=30°$ where $O=AC\cap BD $. Let $\triangle ABM, \triangle DCN, \triangle ADN, \triangle CBQ $ equilateral triangles with $Int (\triangle ...
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0answers
46 views

Constant scalar curvature with positive Ricci curvature

Let $M$ be a compact smooth manifold and $g$ a Riemannian metric on $M$. By the solution of the Yamabe problem, there exists a metric $\tilde{g}$ of constant scalar curvature on $M$ which is ...
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1answer
44 views

General way of modeling Bézier curves and circles

So it turns out that you can't totally model circles with Bézier curves: How to create circle with Bézier curves? I'm wondering if there is a mathematical system or construction that unifies circles,...
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1answer
44 views

Equivalent Definitions of Lines in Projective Space

I’ve been working with two definitions of lines in $\mathbb{P}_\mathbb{R}^2$, and tried to show their equivalence. The first is that, given two points $a=(a_0:a_1:a_2)$ and $b=(b_0:b_1:b_2)$, the ...
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2answers
41 views

Is there a name for the general class of triangles for dimensions other than two?

Triangles differ from all other two-dimensional polygons in that their angles are rigidly fixed when the side lengths are known. It occurs to me that a triangular pyramid has the same property in ...
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0answers
10 views

mobius transformation given points

Let P,Q,R ∈ ˆ C be the points P = − √2 + i√2 , Q = 2i , R = √2 + i√2 . Let M : ˆ C→ ˆ C be the Mobius transformation with M(P) = Q , M(Q) = R The points P,Q,R lie on a common hyperbolic line (you do ...
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2answers
32 views

What is the travelled distance of the red mark on the upper surface of the rotating cube?

Each side of a cube is 2 unit in length. This cube is kept on a table such a way that one surface (i.e., 4 vertices) of it completely touches the table. At this position, a red point is drawn on ...
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1answer
21 views

Trigonometric solution for finding the lengths of an obtuse triangle given the base, angle, & area

Given a triangle ABC where $\measuredangle BAC = 120^\circ$, $BC = \sqrt{37}$, and area $3\sqrt{3}$, find the lengths AB and AC. Here is my attempt: At first I thought of doing it by getting BA by $...
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1answer
26 views

circle inside an ellipse with fixed width but variable length

Inside an ellipse with width 'a' and length 'b', there is a circle. The circle touches the point (-a,0), which means circle touches the edge of the ellipse but ellipse doesn't cut through the circle. ...
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1answer
27 views

incenter point coordinates given the coordinates of the three vertices of a triangle ABC

I have the following equations: , , .These equations determine a triangle.I have to find the incenter coordinates. I found the coordinates of the triangle vertices and all I know is that I take the ...
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2answers
32 views

How to find largest square from given sticks of n length?

We have n number of sticks and each stick of length 2cm , how to form the largest possible square from the sticks without breaking sticks, find area of largest square? Please give me some clue For ...
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1answer
42 views

Expanding on the intuitive meaning of singular matrices

My question is based on "What is the geometric meaning of singular matrix" posted here some years ago. To make this a bit more intuitive I would like to add an example. A three-dimensional force ...
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2answers
66 views

Prove that radius of circle $r$ exceeds $3/2$

Let $T$ be a circle with diameter $AB$. Let $P$ be a point inside the circle such that P lies on the line $AB$. Consider the circles wit diameters $PA=6$ and $PB=4$. A fourth circle $r$ is drawn such ...
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0answers
27 views

Uniqueness of a vector given two rotations

My question concerns whether it is possible to determine a unique vector given two of the vectors rotations. Assuming we have three known vectors in 3D; $a$, $b$ and $c$, and two angles $\phi$ and $\...
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0answers
21 views

Randy plots a point A. What is the largest number of rays he can draw from A so that all angles are multiples of 10 and unequal?

Randy plots a point A. Then he starts drawing some rays starting at A, so that all the angles he gets are integral multiples of 10◦. What is the largest number of rays he can draw so that all the ...
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1answer
37 views

Scalar multiplication and vector addition with hyperbolic vectors

I'm representing hyperbolic vectors using the Minowski hyperboloid: $x_0^2 - x_1^2 - x_2^2 = 1$. I understand that the distance between two hyperbolic vectors of this form is $acosh(B(u, v))$ where $...
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0answers
23 views

Solid angle definition from an ellipsoid surface

Let assume there is a unit sphere inside a oblate spheroid with minor axis 1 and major axis b. What is the surface area in the oblate spheroid surface produced from extending the subtended solid ...
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1answer
19 views

Vertex Coordinates of Regular Hexadecachoron/16-cell/4-orthoplex?

What are the vertex coordinates of a regular Hexadecachoron? I suspect it's just all 8 combinations of $(0,0,0, \pm\frac{1}{\sqrt{2}})$ but I'm not sure how to be sure for sure.
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0answers
31 views

Relation between 2 different homology and cohomology pairings

Consider $X$ $n-$dimensional smooth compact oriented manifold. Denote $H^i(X,\Omega)$ as the cohomology of smooth differential form, $H_i(X)$ as the $i-$th cycles and $C_i(X)$ as the singular chains ...
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1answer
69 views

What is the value of AD+CD where ABC is an isosceles triangle, D bisects angle ACB, BC = 2017 unit?

$ABC$ is an isosceles ($AB = AC$) and $\angle A = 100^{\circ}$. An point $D$ is on $AB$ so that $CD$ angle bisector $\angle ACB$. If $BC= 2017$ then calculate $AD+CD$. Source: Bangladesh Math ...
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Hyperbolic Geometry (circle)

Consider in $H^2$ the hyperbolic circle centered at $a + ib$ with radius $r$; i.e., the set $C = \left\{z\in H^2\mid dH^2 (z, a + ib) = r\right\}$ Show that $C$ is the Euclidean circle with center $a ...
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1answer
43 views

Are regular graphs always regular in a topological sense in a particular dimension?

Consider a large cloud of points (sites) in arbitrary dimensions. Now I introduce links between the sites, such that any site is connected to exactly two other sites (and there is no self-connections ...
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1answer
28 views

Clarification about a given axiom system.

I am now currently studying Combinatorics of Finite Geometries. One problem asks if the given axiom system below is consistent or inconsistent. There are five points and six lines. Each point is in ...
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0answers
25 views

How to prove surface S is part of a sphere?

Prove that a surface S is part of a sphere if and only if its second fundamental form is a nonzero-constant multiple of its first fundamental form. (Both of them are not zero) I know for a sphere ...