# Questions tagged [plane-geometry]

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

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### Intersection of two planes is a straight line [closed]

Let $a_1x+b_1y+c_1z+d_1=0$ and $a_2x+b_2y+c_2z+d_2=0$ be the equations that describe two planes. In my lecture notes, it's written that $a_1x+b_1y+c_1z+d_1=0$ and $a_2x+b_2y+c_2z+d_2=0$ have a ...
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### What is the resulting plane of $plane_1 = plane_2$ intuitively

I have been trying to find the equation of the intersection line between two planes, and was trying some things. The first thing I tried was to just put an equal sign between the two plane equation. I ...
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### Calculate segment of 3D line within distance from 3D triangle

Given an arbitrary 3D line (infinite length) and an arbitrary 3D triangle, how can I calculate which segment of the line (if any) is within a given distance d from the triangle? Considerations: Will ...
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### To find the length of the shortest path that begins at $(-1,1)$, touches the x-axis and then ends at a point on the parabola $(x-y)^2 = 2(x + y −4)$:

This is a question of a parabola but to solve it I need the coordinates of the vertex and focus which at present I'm unable to deduce in this form. I have learnt some standard form such as $y^2=4ax$ ...
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### Intuitive explanation of perspective vs. projection in geometry

I was wondering if someone could please explain the intuition of the distinction between perspective and projection in geometry. Chapter 8 of John Stillwell's Mathematics and its History begins by ...
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### Why is family of planes not working here?

Came across a question where it said $L_1$ is the line of intersection of the planes $2x−2y+3z−2=0$, $x−y+z+1=0$ and $L_2$ is the line of intersection of the planes $x+2y−z−3=0$, $3x−y+2z−1=0$. I ...
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### Find the value of the segment parallel to the side of the triangle by an interior point [closed]

Let P be a point inside a triangle of sides a, b, and c through which they are drawn parallel to the sides of the triangle. If the parallel segments between the sides of the triangle have the same ...
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### Angle within a rectangular-based prism

I've tried to find solutions to similar problems to see how this question should be solved but I didn't have much luck. A rectangular-based prism is shown below. I need to determine the size of angle ...
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### By how much would the length of the solar day change if Earth's rotation were suddenly to reverse direction?

The question in the title has to some extent been answered here: https://worldbuilding.stackexchange.com/questions/79619/does-earths-direction-of-rotation-affect-day-length?newreg=...
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### Can a vertex lie on an edge in a planar graph?

I am wondering if a vertex can lie on an edge in a planar graph- I am not sure if an edge of this vertex is regarded as crossing the edge on which the vertex lies. I have two questions here: Is the ...
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### Are the edges of a planar graph part of its faces? (Graph Theory)

The definition of face I have learned for planar graphs is "a region where any 2 points in it not on $G$ can be connected by a line which doesn't intersect any of the edges of $G$". I am ...
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### How is the face for a tree graph bounded by any sides at all? (Graph theory) [closed]

I have learnt that every face in a planar graph has sides, and that sides are edges which bound the face clockwise. I am very confused about a few things regarding sides: I am not seeing how the ...
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### Connected components of image of non-degenerate boundary component

This is a follow up to my previous question, asked and answered here: Connected components of conformal image of boundary I omitted this by accident from the last question, so I have created this ...
Let $f : G \rightarrow \mathbb{D}$ be a biholomorphism (a holomorphic map with holomorphic inverse), and suppose $G$ is a bounded open subset of the plane. Let $C$ be a compact connected subset of the ...