# Questions tagged [geometry]

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

31,139 questions
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### 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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### 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 ...
1answer
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### 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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### 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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### 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?
1answer
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### 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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### 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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### 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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### 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 ...
1answer
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### 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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### 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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### 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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### 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, ...
0answers
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### 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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### 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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### 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 ...
1answer
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### 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,...
1answer
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### 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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### 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 ...
0answers
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### 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 ...
2answers
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### 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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### 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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### 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 ...
1answer
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### 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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### 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 ...