Intereting Posts

Does the Riemann zeta function converge in higher dimensions?
$13\mid4^{2n+1}+3^{n+2}$
The Instant Tangent
Golden Number Theory
Computing kernel
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Naive set theory question on “=”
Strange Recurrence: What is it asymptotic to?
Find the almost sure limit of $X_n/n$, where each random variable $X_n$ has a Poisson distribution with parameter $n$
Linear independence question from Axler
Closure of image by polynomial of irreducible algebraic variety is also irreducible algebraic variety
Simple related rates derivative question
Estimate the size of a set from which a sample has been equiprobably drawn?
Isomorphic subfields of $\mathbb C$
Lie algebra 3 Dimensional with 2 Dimensional derived lie algebra #2

What is the minimal number of points $N$ to uniquely define the semi-major axis $a$, the semi-minor axis $b$ and the rotation angle $\omega$ of an ellipse whose the center is known/fixed (this is related to ellipse fitting procedures).

In other words, if we consider that the center is known/fixed, on this image what is the minimal number of blue points I need to compute $a$, $b$ and $\omega$ in a unique way ?

EDIT: and what is the number of points needed when the center of the ellipse is not known ?

- How to create circles and or sections of a circle when the centre is inaccessible
- area of figure in sector of intersecting circles
- Rotation $x \to x+a \pmod 1$ of the circle is Ergodic if and only if $a$ is irrational
- Area of intersection between 4 circles centered at the vertices of a square
- Determine Circle of Intersection of Plane and Sphere
- Calculate $\pi$ precisely using integrals?

- How to equally divide a circle with parallel lines?
- Proof of Angle in a Semi-Circle is of $90$ degrees
- How do you find the distance between two points on a parabola
- Proving a property of an ellipse and a tangent line of the ellipse
- A circle with infinite radius is a line
- How can we factorise a general second degree expression?
- Possibly rotated parabola from three points
- Finding the largest triangle inscribed in the unit circle
- Relationship between the sides of inscribed polygons
- Bounds for the size of a circle with a fixed number of integer points

The equation of an ellipse is given by

$$ ax^2+by^2+cxy+dx+ey+f = 0 $$

where $(a,b,c,d,e,f)\in\mathbb{P}^5(\mathbb{R})$, hence you need $5$ points to recover the coefficients, if you do not know where the center is. Otherwise, $3$ points (such that no two of them are symmetric with respect to the center) are enough, since their mirror images with respect to the center of the ellipse still lie on the ellipse, so having $3$ points and the center is like having $6$ points on the ellipse. Obviously, having two points and the center is not enough, since there are many concentric ellipses that pass through the same two points.

- Proving Cartan's magic formula using homotopy
- Does a proof by contradiction always exist?
- Are there infinitely many rational pairs $(a,b)$ which satisfy given equation?
- Finding sum of a series: difference of cubes
- Solve $x = \frac{1}{2}\tan(x)$
- Show that $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $
- $\text{Evaluate:} \lim_{b \to 1^+} \int_1^b \frac{dx}{\sqrt{x(x-1)(b-x)}}$
- Is a decimal with a predictable pattern a rational number?
- Example of a ring with $x^3=x$ for all $x$
- How to prove $\int_0^1\tan^{-1}\left\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$
- Is there a standard way to compute $\lim\limits_{n\to\infty}(\frac{n!}{n^n})^{1/n}$?
- invertible if and only if bijective
- Analytic $F(z)$ has $f(z)$ as derivative $\implies$ $\int_\gamma f(z)\ dz = 0$ for $\gamma$ a closed curve
- Is always $\small {rq-1 \over 2^B} +1 \le \min(q,r) $ with equality iff $\small q$ or $\small r$ is a divisor…
- $\sqrt{13a^2+b^2}$ and $\sqrt{a^2+13b^2}$ cannot be simultaneously rational