0
votes
2answers
35 views

Equation of a curved line that passes through 3 points?

I have a screen wherein the upper-leftmost part is at x,y coordinate (0,0). Then I have a curved line that passes through 3 points: (132, 201), (295, 661) and (644, 1085). Now, say I want to find 7 ...
0
votes
0answers
23 views

Determine sine wave frequency from two arbitrary points

If I have only two arbitrary points on a sine wave, what would be the simplest method for determining the frequency of the sine wave? The frequency is unknown. The bandwidth is restricted, the time ...
-4
votes
0answers
66 views

Geometric Proof for Fermat's Last Theorem - A Question [on hold]

I have been working on a geometric proof for Fermat's last theorem that I just realized has been worked on already in some shape or form (ba-dum-tsh). Before anyone says it, yes, I am aware that this ...
0
votes
0answers
14 views

Find length of the midpoints of the diagonals in a given trapezoid [closed]

For any given trapezoid, where the bottom base, a, is larger than the top base b -- find the length of MN, the line connecting the midpoints of the diagonals, using only vectors.
0
votes
0answers
16 views

Quartic curves with four connected components

A quartic plane curve in $\mathbb{RP}^2$ can be defined by a quartic equation $F(x,y,z)=\sum a_{ijk}x^iy^jz^k$ with 15 coefficients. Now let's focus on smooth quartics that have a maximal number of ...
0
votes
0answers
21 views

Special case of Bernstein theorem

There is a Bernstein theorem which gives an estimate on the number of complex non-zero roots of system of polynomial equations. Bernstein theorem. The number of solutions in $(\mathbb{C} \setminus ...
2
votes
1answer
32 views

Conic through 4 points

Let $p_1,\ p_2,\ p_3,\ p_4$ be any 4 different points on $\mathbb{CP}^1$ and $x_1,\ x_2,\ x_3,\ x_4$ are 4 different points on $\mathbb{CP}^2$. How can I show that there is unique conic $Q$ passing ...
0
votes
0answers
27 views

is there an existing formula in finding the area of a rhombus wherein only the side is given?

is there an existing formula in finding the area of a rhombus wherein only the side is given? No measure of angles, no lengths of diagonals , height, etc. is given.
0
votes
0answers
27 views

When is a pseudomanifold a manifold?

Under what conditions does a pseudomanifold become a manifold? I.e is there a nice conclusion we can make if our pseudomanifold has a certain homotopy type, or is possibly piecewiselinear to some ...
0
votes
0answers
15 views

“Pseudomanifold with no singularities”

An $n$-dimensional (closed) pseudomanifold is a finite simplicial complex $X$ such that (i) every simplex is a face of an $n$-simplex (ii) every $(n-1)$-simplex is a face of exactly two ...
0
votes
0answers
23 views

Generators of a function field and classification

in the book "Introduction to Compact Riemann Surfaces and Dessins d'Enfants" the autor classify all the compact Riemann surface of genus 3 associated to the curves on form $F(X,Y) = 0$ where $F(X,Y) = ...
0
votes
0answers
65 views

Enriques Noether Theorem

I'm reading the proof of the Enriques-Noether theorem (Beauville A. page 25-26-27). here the stament: Let $p:S \rightarrow C $ a surjective morphism between an algebraic surface $S$ and a smooth ...
1
vote
2answers
39 views

How to derive the hyperbola giving the foci and the fixed differene

Given the two foci coordinates $(x_1,y_1)$ and $(x_2,y_2)$ of the hyperbola and the fixed difference distance, how can I derive its function to be able to draw it.
0
votes
1answer
17 views

Plotting Particular Conic Section

How would I plot $-2x^2 -2y^2 = 1$ on the x-y plane ? I believe it is an ellipse, since the coefficients have the same sign, I just don't know what the major and minor axes would be nor how to plot.
0
votes
2answers
30 views

Curve in union of hyperplanes

If a smooth curve $\gamma: [0,T] \to \mathbb R^n$ is contained in the union of hyperplanes $$ \bigcup_{i=1, \dots, N} H_i$$ does it then follow that one can always find time intervals $[t_0, t_1]$ ...
1
vote
3answers
76 views

Examples of smooth curves of genus $0$ and degree $d>2$.

Can we provide a source of explicit examples ? The degree assumption $d>2$ means that I would like to see examples which are not conics.
0
votes
1answer
36 views

What is the Hilbert curve's equation?!

The Hilbert curve has always bugged me because it had no closed equation or function that I could find. What is its equation or function? For example, if I wanted to find the Hilbert's curve point at ...
0
votes
0answers
29 views

Geometrical problem of maximum area of smallest triangle formed by 3 points in a distribution of n points on an R^2 plane

Another way of stating the gist of the question is: find the arrangement of n points such that one obtains the largest ratio between the area of the smallest triangle formed by three points to the ...
2
votes
2answers
55 views

How to determine whether three ellipses have at least one common intersection point or not?

How to establish a criterion described in equation so that it is easy to determine whether three ellipses have common intersection area (point) or not? Update
2
votes
4answers
76 views

Find the center of a circle on the x-axis with only two points, no radius/angle given

Find the center $C$ on the x-axis of the circle containing $(15,-2)$ and $(7,10)$ I can't seem to find a formula to help me solve this problem without needing the radius or the angle between the the ...
0
votes
0answers
24 views

How to find the tangent vector for intersection of two cones?

Let two points $A=(x_{0},y_{0},z_{0})$ and $B=(x_{1},y_{1},z_{1})$ are given vertex of two cones and the generating angle of two cones are $m$. Intersection of two cones could be either an ellipse or ...
0
votes
0answers
41 views

parametrization of a specific algebraic surface

I consider the surface of degree $5$ of equation: $$ 4 x y - 4 x^3 y - 4 x y^3 + z + 2 x^2 z + x^4 z + 2 y^2 z + 2 x^2 y^2 z + y^4 z - 4 x y z^2 - 6 z^3 + 2 x^2 z^3 + 2 y^2 z^3 + z^5=0 $$ Question: ...
1
vote
1answer
37 views

Lines In the Complex Proyective Plane

The question is In how many points a line in CP^n intersects CP^2?. By a line in CP, I mean a copy from CP^1. I have tried with a sytem of equations, (Because a line in CP^n is the zero locus of a ...
-1
votes
1answer
72 views

Blow-Up over a Field

I want to prove that a function $\pi : \mathbb{C}_{*}^{n}\mapsto \mathbb{C}^{n}$ is bijective. Where $\mathbb{C}_{*}^{n}$ is the explosion of $\mathbb{C}^{n}$ and is defined as $\mathbb{C}_{*}^{n}:= ...
1
vote
1answer
153 views

Felix Klein's view on algebraic geometry

I think, as a first approach one would say that a geometry on a set $X$ is given by an inner product on $X$. Klein then links geometry to group theory by identifying a geometry on $X$ with a group of ...
0
votes
1answer
23 views

Find a projectivity to create a graph.

I have the tetrahedron {xyzt=0} in projective space with homogeneous coordinate (x,y,z,t). I need to create a graph but the tetrahedron in affine coordinate is {xyz=0} and I can't visualize the ...
1
vote
0answers
47 views

Hochschild dimension

I'm curious; if $A$ ia a commutative $k$-algebra over a field $k$ of global dimension $n$, then is its $A^e$-projective dimension $2n$ (this is also sometimes called the Hochschild cohomological ...
1
vote
2answers
36 views

Is equation for ellipse in polar coordinates correct?

Wikipedia gives the following equation for the conic sections in the polar coordinate system: $r = \frac{l}{1+e\cos\varphi}$. According to the article on conic sections, in case of an ellipse $e = ...
2
votes
2answers
61 views

Smoothness and field of fractions

If $k$ is an integral domain and $A$ is a Noetherian finitely presented $k$-algebra for which $A \otimes_k Q(k)$ is a smooth $Q(k)$ algebra, then can it be deduced that $A$ was initially smooth over ...
0
votes
0answers
38 views

Finding the point satisfying the condition

Given N interesting points on the plane. Each interesting point has integer coordinates. Also, all the interesting points form a strictly convex polygon. If we select two coordinates from these ...
3
votes
1answer
79 views

Question about Qing Liu's Algebraic Geometry book

I was just wondering what the real prerequisites are for reading Qing Liu's 'Algebraic Geometry and Arithmetic Curves', and if it is a good first book on the subject. In his preface he states that the ...
0
votes
1answer
33 views

What is the intuition behind contours and their geometric properties

What is the the intuition behind contours? Can someone explain whar are contours, their geometric properties in simple manner
0
votes
0answers
57 views

Alternative Proof why algebraic groups are smooth

Definitions: Let $k$ be a field, by an affine algebraic group we will mean an affine group scheme $G$ over $Spec(k)$ with the property that the coordinate ring of the underlying affine scheme ...
1
vote
0answers
45 views

Linear Transformation of points [duplicate]

Could you help me solve this: For projective coordinate system on the line $l$ are given points $A (2,1)$, $B (1,1)$, $C (0,1)$, $A_1 (0,1)$, $B_1 (1,5)$ and $C_1 (2,1 )$. Find a linear transformation ...
0
votes
2answers
33 views

Solving for points in a plane based on line lengths and geometry

I have the following points and lines in a plane: The problem is this: Given that we know the lengths of lines A, B and C, how can we calculate the coordinates of each point a, b and c? The ...
0
votes
1answer
48 views

Formula of signed distance from hyperplane to point

Let $H$ be a hyperplane defined by the points $p_1, p_2, ..., p_n$ and single point $x$ generally out of the hyperplane. Is there any formula to calculate the signed distance between $x$ and $H$? I ...
2
votes
0answers
104 views

Equation for the Maximum-Area Rotor in a Wankel Engine

I am attempting to construct a specialized Wankel Engine in Autodesk Inventor. For my particular project, the rotor must take up the maximum area, in order to separate the air spaces of the top and ...
1
vote
1answer
67 views

An question on effective divisor (Clifford 'S theorem)

For an effective divisor $D\ge 0$ on a curve $Y$, define $$\lvert D\rvert =\{ D' \in \mathrm{Div}(Y) \mid D'\ge 0 \;\text{ and }\; D' \sim D \}$$ where $D\sim D$ means $\exists$ a rational ...
2
votes
1answer
38 views

Question about geometry in a finite projective space

I apologize again for a dumb question! To add some context (though I think it'll largely be unnecessary): suppose $q$ is a prime, $F:= \displaystyle \mathbb{Z}/q\mathbb{Z}$ is a field. I've defined ...
0
votes
0answers
20 views

Which bound on $a,b,c,d$ is correct?

Let $ABCD$ be a unit square. Four points E,F,G, and H are chosen on the sides $AB,BC,CD,$ and $DA$ respectively. Let the length of the quadrilateral be $a,b,c,d$. Then which of these is always true? ...
1
vote
1answer
58 views

multiplicity of intersection of projective curves

This example is taken from Silverman and Tate's Rational Points on Elliptic Curves. Suppose we have the line $C_1: x+y=2$ and the circle $C_2: x^2 + y^2 = 2$. We see that these intersect at the ...
1
vote
0answers
52 views

Lateral area of a cone with oblique base (elliptical base)

Can someone help me find the lateral area of a straight circular cone with oblique base ( inclined elliptical base) as seen at the following link. ...
2
votes
1answer
125 views

Algebra, Geometry and Algebraic Geometry

I want to know, what is the difference between Algebra, Geometry and Algebraic Geometry ? Your reply is highly appreciated.
1
vote
1answer
37 views

Order of $A/2A$ for $A$ an Abelian variety

Let $A$ be an Abelian variety over $\mathbb R$ of dimension $g$. Then the size of $A(\mathbb R)/2A(\mathbb R)$ is $(\# A(\mathbb R)[2])/2^g$. I'm wondering how one might go about proving such a ...
1
vote
1answer
52 views

What is the nature of this surface?

What is the nature of the surface whose equation is (it depends on $m$) $$x^2+2y^2+(m+1)z^2+2xy-2yz-2x+2y-4z+m^2+4=0$$
1
vote
0answers
39 views

Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
2
votes
1answer
96 views

Chern class of line bundle and vector bundle

Let $L$ is a Line bundle and $E$ a vector bundle of rank $r$ then how can we prove that $$c_1(L\otimes E)=rc_1(L)+c_1(E)$$ where here $c_1$ means first chern class
0
votes
2answers
35 views

How do we define touching lines?

If two curves are touching at one point and intersect one another, how do we define it? If two lines are touching at a point then $L\cap K=\{q\}$ for two lines L and K and q is the touching point. ...
1
vote
0answers
72 views

Algorithm for finding nearest distance from a point to a curved surface in space

I need to write an algorithm which can find the nearest distance from a point in space to a 3D curved surface which is straight in vertical direction but its projection is an arc of a circle (Similar ...
3
votes
1answer
187 views

Finding the shortest path length on a curved surface(hyperboloid)

I wish to find the minimum path length between two points $P_1(\sqrt2,0,-1)$ and $P_2(0,\sqrt2,1)$ on a hyperbolic surface $S =\{(x,y,z)\in R^3\ |\ x^2+y^2-z^2=1\}$ I faintly recall studying ...