I’ve already made an article on the 2D version of this problem, if you want to check it out before this one, you can visit https://www.mattiagiuri.com/2020/04/21/a-very-notorious-problem/. Now, the 3D version says: if you have 3 reals x, y, z chosen randomly between 0 and 1, what’s the probability that It’s important to notice that any […]
Month: November 2020
Lorenz Attractor In Python Graphed
In my school course ‘Python For Physics’ we had to choose among some topics to study and implement in Python, and I and my colleague decided to go for the Lorenz Attractor equations. The Lorenz System is a system of differential equations which generates a very chaotic plot, where chaotic means that little variations may […]
Problem For A Particular Occasion
I proposed this problem in a birthday team competition I wrote, but at the time I asked for its equivalent in 18 dimension. Today I’ll explain it in 3 dimensions, and I want to point out that 3 is the perfect number for today’s occurrence. Now, how many parts of space (finite or infinite) can […]
Using Symmetry
I put this problem in an old team competition I organized. It is not simple, and I asked only for the case where n is even, now I’ll show you the complete version. Let be reals in an interval of lenght 1. Find the maximum value of Now, let’s treat as constants and let be […]
A Problem From Three Days Ago’s Simulation
This problem took me a while to solve because of its calculations, but it’s actually very instructive. It makes you see how few conditions can determine a lot. All of the data is in the figure above, we have to find the area of the rectangle. Now let where alpha is the biggest of the […]
Hearts Equations In Math
In this article, I’ll show you five different equations you can use to plot your own heart. Let’s start with the simplest: I think this is the most classic of the five I’m going to show you. If you prefer one which is a little bit thinner, there is this one: On the other hand, […]
Algebra Problem From Yesterday’s Simulation
Given two polynomials and , let a, b, c, d be the roots of , find First, notice that We know that plugging a, b, c, or d into gives 0, so we have to find the sum of squares of the roots minus the sum of the roots plus 4. By Vieta’s Theorem, the […]
Geometry Problem From Today’s Simulation
Today there was a national maths team competition simulation on phiquadro.it and, although I was really on fire, I was really upset I had no time to solve this geometry problem, so I decided to publish it here. In the figure above, the equilateral triangle ABC has circumradius = 10. An isosceles trapezoid is drawn […]
A Strange Recursion
This is a really nice recursion I wanted to share. We have to find the general formula for the nth term of the succession. We have: Also: By subtracting the two expressions and simplifying we get: Now, since we can further simplify to get the final form: By solving the recursion’s equation we can find […]
Plotting Waves In Python
I really like plotting waves in Python: there are many ways you can show interesting patterns both in 2D and 3D. I’m obviously using the numpy and matplotlib libraries to create and plot the functions. 2D Wave Plot I really wanted to try to reproduce Arctic Monkeys’ AM cover image, and that’s what I was […]