# Questions tagged [projective-geometry]

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

1,545 questions
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### Distance between homogeneous transforms

I am working in homogeneous coordinates to represent affine transforms in 3-d. As such, my points in $\mathbb{R^3}$ get a fourth coordinate, and my transforms are 4x4 matrices. To be clear, I ...
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### What knowledge should I have before learning projective geometry? (I'm an 11th grade student)

I wanted to learn projective geometry. I don't know much about it. I came across projective geometry in a book called 'Euclidean geometry in mathematical olympiads' and I was very interested in it. So ...
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### Lines in projective and affine space

I'm trying to understand lines in affine and projective space in order to solve problems 2.15 and 4.13 in Algebraic Curves by William Fulton: https://www.google.com/url?sa=t&source=web&rct=j&...
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### Kernel of ${\rm GL}(n,F)$ on ${\rm PG}(n-1,F)$ over a division ring $F$

I am reading Peter Cameron's note on Classical Groups and I got confused with Proposition 2.1 on page 14. I have no problem in proving that the elements in kernel are scalars. However, I don't ...
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### Explicit formula for the projection from the line to an arbitrary circle

Overview: Given an arbitrary point $t$ on the horizontal axis of a Cartesian plane and a point $\textbf{p}$ on a circle, I would like to find the point $\textbf{t}'$ located at the intersection of the ...
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### Are superelliptic curves singular?

It is an easy corollary of the Riemann-Hurwitz formula that smooth double covers of $\mathbb{P}^1$ can only be branched over an even number of points. Let $F(x,z) \in \mathbb{C}[x,z]$ be a homogeneous ...
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