# 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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### Can adjacent points exist in geometric space?

My question is going to focus on quite a counterintuitive thing. A couple of preliminaries. I understand geometric space as a set of points. A point, in turn, is an abstract idealization of an exact ...
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### i want a general equation to calculate the change in slope angle of tangent lines between two points on an arc [closed]

I have an arc in the xy coordinates, I can calculate everything regarding the second point using this post, but I want the simplest general equation to give me the slope angle of the tangent line at ...
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### What shape a point with a constant distance along a parabola will trace?

Define a parabola where it's directrix will be a line over the Y axis and the focus point will be a point in the X axis. Example parabola Define a distance n and grab a point D in the parabola where ...
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### Proof of Triangle Inequality for $d(g; x, y) = \left(|x-y|^4 + g\,| x \times y |^2\right)^{\frac{1}{4}}$

I am seeking assistance in proving that a function, denoted as $d(g; x, y)$, defined on $\mathbb{R}^2 \times \mathbb{R}^2$ and parameterized by the non-negative real number $g$, may satisfy the ...
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### solution-verification | Prove that the triangles $AMD'$ and $ACB'$ have the same center of gravity.

the question Let the cube $ABCDA'B'C'D'$ and $M$ be a point on the semi-right $(AB$ so that $BM=AB$. Prove that the triangles $AMD'$ and $ACB'$ have the same center of gravity. the drawing the idea ...
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### Prove that the distance $d$ from point $A$ to plane $(DNC)$ verifies the relation $d< \frac{AB+3AD}{6\sqrt{2}}$

the question In the triangle $ABC$ we consider $(AM$ the bisector of the angle $\angle A$ so that $MB=3MC, M\in (BC)$ and $N\in (AB)$ so that $BN=2NA$. On the plane of the triangle $ABC$, the ...
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### What is happening in this 'multi'-sinusoidal function?

Edit: Thanks to those commenting, I fixed my issue and now have reached the below function, as I had aimed. My remaining question would be how I might describe this function. I have taken the function ...
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### 3d geometry hvvtvgvvkvuv [closed]

Consider the tetrahedron formed by the planes y+z=0,z+x=0,x+y=0, x+y+z=a . The direction cosines of the shortest distance lie between the planes y+z=0 and z + x = 0 is:
I cannot differentiate area formula for semicircle Area = $1/2π r^2$. I cannot use the constraint equation $50=πr+2r$ as the area is already in terms of radius. How can I do this without limits and ...