# Questions tagged [projective-geometry]

Projective geometry is closely related to perspective geometry. These types of geometry originated with artists around the 14th century.

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### Parameterisatio of Curve in projective space

Background: I've started reading Miles' "Undergraduate Algebraic Geometry" (Link) recently though struggling a lot. I'm stuck at processing the following paragraph... Sec. 1.7 ...
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### Example of Line at infinity in Miles' Book

Background: I've started reading Miles' "Undergraduate Algebraic Geometry" (Link) recently though struggling a lot. \ Please allow me to just paste the example on Page 23 as follows; I ...
1 vote
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### Tools to investigate unusual algebraic structure

I will begin with a mostly motivational thought about the projective plane. In this plane, every two lines intersect at a singular point. Let's mark the lines set as $\mathcal{L}$ and the points set ...
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### Maximal number of multiple points for an irreducible quartic

I was working on this problem, but I don't see how I can solve it. I was given a hint, but I don't know how to use it. Can anyone help me? Thanks in advance! Let $f \in \Bbb C[x_0, x_1, x_2]$ be an ...
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### 2D different integer valued vertices coordinates of cube projection

On paper we, orthogonal, project a cube as in provided image. But is it always really a cube? And, in this particular example, the 8 different 2D coordinates of the vertices have integer values. But ...
1 vote
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### On Marsden's 'Introduction to Mechanics and Symmetry' Exercise 5.3-4. (fubini study form is closed)

In exercise 5.3-4. in Marsden's book I'm asked to prove that $\mathbf d \Omega^{fs} = 0$ on $\mathbb P \mathcal H$ directly, where $\mathbb P \mathcal H$ is an arbitrary projective Hilbert space (...
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### Projective Geometry Interpretation In combinatorics

Find the maximum number of subsets that satisfy this trait ~ Each Subset has 4 element ~ Each two subset share 2 elements in common ~ There can't be more than 1 number that are included in all subsets ...
1 vote
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### Orthogonal Projection Area of a 3D Cuboid

This problem is asking the same as this problem, but is a cuboid instead of a cube and the independant variables are the roll, pitch, and yaw. I wrote some Mathematica code that finds the area ...
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### Determine and classify the projective conics

Determine and classify the projective conic that contain the points: $\langle 0,0,1\rangle,\langle 0,1,1\rangle,\langle 1,0,1\rangle,\langle 1,1,1\rangle,\langle 1 / 2,2,1 \rangle$. I used this ...
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### Homogeneous coordinates in projective geometry

I am studying Projective Geometry in 3D for Computer Vision. I am confused on the high-level rationale behind our need to map from heterogeneous to homogeneous coordinates, and I would like to confirm ...
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### Is $K_F\cdot C\leq K_X\cdot C$ for a fibre $F\subseteq X$ containing the curve $C$?

I have put this question on Math Overflow Let $X$ be a projective $\mathbb{Q}$-factorial variety ("variety" is irreducible and reduced over a field of characteristic zero; not necessarily ...
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### Perspective sequence that maps collinear points A,B,C,D to D,C,B,A

Find the perspective sequence that maps collinear points A,B,C,D to D,C,B,A. Attempt: If we need to find a sequence of three perspectives that (A,B,C)->(A,C,B), where A, B, C are collinear, then ...
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### Inverse of Zenithal projection

Zenithal perspective projections are generated from a point P and carried through the sphere to the plane of projection as illustrated in the figure below. By a simple geometric relationship, we can ...
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### Euler's line : a projective geometry proof

In a given triangle $ABC$, let $G$ be the common point to the three medians, $H$ be the common point to the three altitudes, and $M$ be the common point to the perpendicular bissectors of the three ...