# Questions tagged [geometry]

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

31,949 questions
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### How to create a 3D graph from two 2D graphs

I have an equation in the x-y plane, and another in the z-x plane. Is it at all possible to combine them into the x-y-z space? I realize that there might not be enough data to fill the gaps, but I ...
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### area of triangle is proportional to scalar product of the normal vector to the chosen edge and radius-vector of third point

How can I proof that: The area of triangle is proportional to scalar product of the normal vector to the chosen edge and radius-vector of third point Thanks for helping.
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### How to compute the parameters of circumscribed hypershpere?

Assume I have an $n$-dimensional simplex on the points $x_0, ..., x_n$, where each $x_i \in \mathbb{R}^n$. I would like to obtain the parameters (center and radius) of it's circumscribed $n$-...
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### Find the side of the square.

The problem I am proposing to solve was posed in a math contest for students of 17-18 years old, this month. With the data in the picture, find the side of the square. I did find the solution but it ...
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### Alternative way to determine whether a point is contained within an arc section of a circle?

The best way contained in answers for this question: https://stackoverflow.com/questions/6270785/how-to-determine-whether-a-point-x-y-is-contained-within-an-arc-section-of-a-c But are there some ...
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### Smallest circumcircle around four non-overlapping unit semicircles

What is the radius of the smallest circle into which will fit four unit half-disks? What arrangement of the half-disks achieves this? How is it proved optimal? The best arrangement I've found fits in ...
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### Projection onto a surface vs projection onto a linearization

Suppose I have a surface $S$ defined by the equation $$h(x)=0.$$ Assume that $h(x)$ is continuously differentiable as many times as we want. Let $P_S(x)$ be the function which maps $x$ onto the ...
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### Congruent triangles in 3 tangent circle configuration

Two circles $\mathcal{C}_1$ and $\mathcal{C}_2$ of centers $O_1$ and $O_2$ are externally tangent at $I$ and internally tangent to a third circle $\mathcal{C}$ of center $O$ that is colinear with $O_1$...
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### How to find a hyperplane with maximum number of points on one side

Given a set of points $S$ in a high dimension real space, is there an efficient way to find a hyperplane through the origin such that the number of points on one side of the hyperplane is maximum over ...
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### How to convert intersection of two lines into an arc?

I am struggling with finding coordinates of a point for arc origin. I am programming a tool which converts a corner (intersection of two lines) into an arc of needed radius. SETUP PICTURE I have ...
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### Isn't mass from purely topology in the absence of matter a contradiction? [on hold]

Consider the 3 dimensional projective space which is empty of matter minus the infinity point. We see that it has ADM mass. In other words, a perfectly fine geometry, orientable and asymptomatically ...
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### Angles at centroid of a triangle

If $ABC$ is a triangle with centroid $P$, I got the impression that the angle $\angle BPA$ at the centroid should only depend on the angle $\angle BCA$ (and not on the other angles). Am I right? Is ...
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### Figuring out positions of some points given other known points and angles between the known and unknown points

So the data in question is a set of points p which all have known positions in space, a set of points q which all have unknown ...
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### Covering the 2-sphere with 6 hemispheres

While reading chapter 2 of Wald's General Relativity titled "Manifolds", I stumbled upon the fact that the 2-sphere $S^{2}$ cannot be mapped into $\mathbb{R}^{2}$ in a continuous 1-1 manner. Wald then ...
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### inequality related to square the sum of any two sides of a triangle with respect to square of other side

Consider a,b,c are three side of a triangle. Now we need to find the relation between square the them sum of any two side of triangle with respect to third side. My approach As we know that the sum ...
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### Overlapping circles covering polygon

While working in GeoGebra I noticed something odd. I had a triangle with a point inside and the point was connected to each of the vertices. For each vertice I had drawn the circle passing through the ...
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### Distance between a point and low-dimensional sphere

Is there a way to analytically calculate the distance between an arbitrary point $\mathbf{x}\in\mathbb{R}^n$ and a low-dimensional sphere embedded in $\mathbb{R}^n$, say one aligned with the axis ? ...
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### How would be a formal answer for an automata geometry problem?

Let an automaton $A$ sit on point $O$ $(0,0)$ and turned to the North. That automaton can execute only any combination of three different commands in each step: Move one unit forward Turn 90 degrees ...
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### How many points are needed to define a circumference?

This doubt comes from a combinatorics problem in a textbook, which states: Consider two strictly parallel lines and seven dots, four of which are over one of them, and three over the other. Three ...
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### Plane cutting a pyramid

Pyramid with equilateral triangle as a base, length of side of pyramid is $s=3$(not a base side). Plane goes through pyramid, and contains base edge, and is normal to a side of pyramid. If surface ...
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### How to calculate vertex, focus, axis etc. from such type of ellipse equation 3x²+8y²+12xy-18x-32y+23=0? [on hold]

Is there any way to find vertex , focus, axis, centre etc from this type of non ideal ellipse, hyperbola or parabola?
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### Pair of lines problem

If the pair of straight lines $x^2+2xy+ay^2$ & $ax^2+2xy+y^2$ have exactly one line in common, then the combined equation of the two lines is given by A. $3x^2+8xy-3y^2$ B. $3x^2+10xy+3y^2$ C. ...
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### Geometry, does this shape have a name?

A Sphere with Diameter 1 perfectly inscribed in A cube with sides of 1, Removing the sphere and splitting the cube on the faces we then have 8 identical "Corners" with three sides being a tetrahedron ...
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### A problem on combinatorical geometry . [on hold]

Hey could someone help with this exercice, i have tried everything but nothing seems to suite work. Any help would br appreciated : Let ABCDEF be a convex 6 sided polygon of sides 1, prove that at ...
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### Are there always two circles that together surround or intersect all points in the following scenario?

Consider $N$ points in $\mathbb{R}^2$ and $\binom{N}{2}$ circles, one for each pair of points such that it intersects both. Is it always possible to pick two of these circles that together surround or ...