# Tagged Questions

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

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### Area of piece of paper folded around straight line of orientation $\theta$

Imagine drawing a straight line $l$ through the center of a square piece of paper with area $1$. Now fold the paper along that line. Q: What is the function for the area covered by the folded ...
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### Exact Expression for numerical Solution 0.9595767

I need you to do just what any math genuis in a shallow Hollywood movie does: looking at big tables of numbers and seeing exact structure! These $3 \times 3$ matrices are solutions to a well-posed ...
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### Two new conics associated with two triangles inscribed a conic

1-Let $ABC$ and $A'B'C'$ be two triangle inscribed a conic. Let $P$ be a point on the conic. $PA$ meets $B'C'$ at $A_1$, define $B_1, C_1$ cyclically. $PA'$ meets $BC$ at $A'_1$ define $B'_1, C'_1$ ...
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### The set of polynomials which “cut out” smooth subsets of projective space is open and dense

Let $k[x_0,x_1,...,x_n]_d$ be a space of all forms (in other words, homogenous polynomials) of degree $d$ of variables $x_0, x_1,...,x_n$ over algebraically closed field $k$. Let's think of ...
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### How to determine that the 3 points given in homogeneous coordinates are collinear? [on hold]

How do I prove that the 3 points given in homogeneous coordinates are collinear? $$A=(1,3,2)^T, B=(0,6,8)^T, C=(3,3,-2)^T$$
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### Transform in eigenvetor space

Hello I have a squared matrix C C = 0 2.2361 63.7887 2.2361 0 61.6117 63.7887 61.6117 0 and I calculate its ...
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### Image of a line or conic on Veronese surface.

This is part of Exercise 5.13 from Undergraduate Algebraic Geometry by Reid: Consider the Veronese surface $S$ defined by the map: $$\phi: \mathbb{P}^2\rightarrow \mathbb{P}^5$$ where ...
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### Is the map $\phi: \mathbb{P^2\rightarrow \mathbb{P^1}}$ defined by $\phi(x,y,z)=(x,y)$ birational?

This is Exercise 5.3 (a) in Undergraduate Algebraic Geometry by Reid. Does the map $\phi: \mathbb{P^2\rightarrow \mathbb{P^1}}$ defined by $\phi(x,y,z)=(x,y)$ define a rational map? Determine ...
Proposition 5.5 in Undergraduate Algebraic Geometry by Reid says (I only write down a brief idea since the proposition is long and involves some other notations to define): The affine variety $U$ ...