Intereting Posts

Question regarding an inequality
How can one find Jordan forms, given the characteristic and minimal polynomials?
Kolmogorov's paper defining Bayesian sufficiency
Zero-dimensional ideals and finite-dimensional algebras
A pair of continued fractions that are algebraic numbers and related to $a^2+b^2=c^m$
What is the meaning of normalization of varieties in complex geometry?
Properties of compact set: non-empty intersection of any system of closed subsets with finite intersection property
Properties of squares in $\mathbb Q_p$
Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$
Gaussian Kernels, Why are they full rank?
Definite integral using the method of residues
Proving a triangle with different edge colors exists in a graph.
Proof that $n^3+2n$ is divisible by $3$
What is a Real Number?
Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$

This may be an obvious question, but I can’t seem to figure it out.

I found an algorithm that receives an equation, and in order to plot its graph, for each pixel in the screen, it will replace the variables for the coordinates of the pixel and evaluate both sides of the equation keeping track of which side is greater. Then, when a point makes the formerly greater side become smaller it will know that this point needs to be painted. I have tested it and does a decent job plotting, giving its simplicity. What I don’t have clear is why this works.

This is where I found the algorithm.

- Fermats Little Theorem
- How can I find the square root using pen and paper?
- Count arrays with each array elements pairwise coprime
- Do dynamic programming and greedy algorithms solve the same type of problems?
- Detecting perfect squares faster than by extracting square root
- Graph Run Time, Nodes and edges.

- Lottery odds calculated in your head, or pen and paper.
- FFT with powers of 3
- Why does the graph of $e^{1/z}$ look like a dipole?
- Calculation of Bessel Functions
- Point inside the area of two overlapped triangles
- Finding the asymptotic behavior of the recurrence $T(n)=4T(\frac{n}{2})+n^2$ by using substitution method
- A problem on Number theory
- Is Dijkstra's algorithm optimal for unweighted graphs?
- Showing that $T(n)=2T(+17)+n$ has a solution in $O(n \log n)$
- How does Mathematica solve $f(x)\equiv 0\pmod p$?

Because an equation with two unknown

$$

f(x,y)=0

$$

can be considered as the intersection of the graph of the function $f$ with the plane $z=0$, so the set of the solution of the equation is the same as the zeros of $f$.

When the difference of the two sides change sign, assuming the function is continuous, then there is a zero, so a point to plot.

- Translating sentences into propositional logic formulas.
- What is contour integration
- Compute integral closure of $F/(x^2-y^2z)$.
- Intersection of Altitudes in Hexagon
- Show structure of a commutative ring in a tensor product
- expect number of multipe draws
- Complete first order theory with finite model is categorical
- Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
- What is the correct answer to this answered combinatorics problem?
- Determine a holomorphic function by means of its values on $ \mathbb{N} $
- Show that the function $g(x) = x^2 \sin(\frac{1}{x}) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$
- How to deduce the Weyl group of type D?
- If $f(0)=f(1)=f(2)=0$, $\forall x, \exists c, f(x)=\frac{1}{6}x(x-1)(x-2)f'''(c)$
- Existence of the limit of a sequence
- Limit of $S(n) = \sum_{k=1}^{\infty} \left(1 – \prod_{j=1}^{n-1}\left(1-\frac{j}{2^k}\right)\right)$ – Part II