An epicycloid is the figure that a fixed point of a circle draws when the circle rotates on the circumference of another one. How to plot such things in Python? There is a trick: such figures depend on the ratio of the still circle’s and the rotating circle’s radius. Let’s say we have an integer […]
Author: giuricrocodile
Python Basic Stock Predictor
Machine learning in economy is very important, and one of its application is predicting the behavior of the stock market. How can you do that, the idea is creating a model that reads the previous graph of the market and gives the predicted behavior as output. To do so, one cannot use the simple Tensorflow […]
Happy 2021!
Happy 2021 everyone! As a way to start out the new year, what’s better than an article about the mathematical properties of the number 2021 to prepare for the next Mathematical Team Competitions? To start out, 2021 is not a prime number, its factorization is: Hence, be prepared for a lot of chinese remainder theorem […]
A Problem From Stanford Mathematics Tournament 2008 (Team Test)
Daphne is in a maze of tunnels shown below. She enters at A, and at each intersection, chooses a direction randomly (including possibly turning around). Once Daphne reaches an exit, she will not return into the tunnels. What is the probability that she will exit at A? The Idea At first, I will denote by […]
The Meaning Of It All
‘The Meaning Of It All’ is one of my favourite books written by the hero-physicist Richard P. Feynman. This book is a collection of three conferences Feynman held in 1963 at the University of Washington. He’s famous for the intellectual provocation he used to throw at the audience and for his clear way of speaking. […]
Shortlist 2001/G1
Let be the center of the square inscribed in acute triangle ABC with two vertices of the square on side BC. Thus one of the two remaining vertices of the square is on side AB and the other is on side BC. Points and are defined similarly. Prove that lines and are concurrent. The Idea […]
AI Artist
A nice programming challenge is writing a program that modifies an image to give using the style from another image, which in my case is Van Gogh’s Starry Night. Let’s take a look at the input image. A take of the houses of parliament at night. Now let’s see the output image after 7000 iterations. […]
Guthrie Govan
One of my favourite guitarists is Guthrie Govan. He is a jazz fusion guitarist and his signature guitar is Charvel HSH FLAME MAPLE. His peculiarity is that is technique is so perfect he treats the guitar as part of his body: he is able to play with every technique. The very first Guthrie’s piece I […]
The Solitude Of Prime Numbers
A very interesting Novel is ‘The Solitude Of Prime Numbers’, by Paolo Giordano. It talks about the story of Mattia and Alice, who both have some serious personal problems, and about how their relationship grows in time. I really appreciated how the author was able to continuatively switch points of view and put himself into […]
Algebra At Christmas
Why not? I mean, it’s a nice inequality to try out. What if I asked you to find the maximum value of Well, time to apply the AM-GM inequality. First, let’s say that Notice that by the AM-GM inequality applied on the 4 positive real numbers Hence, we get that with equality when