Acting by Ciro Santilli 35 Updated +Created
OurBigBook Library by Ciro Santilli 35 Updated +Created
Integer by Ciro Santilli 35 Updated +Created
Penalty kick left right Nash equilibrium by Ciro Santilli 35 Updated +Created
When taking a penalty kick in soccer, the kicker must chose left or right.
And before he kicks, the goalkeeper must also decide left or right, because there is no time to see where the ball is going.
Because the kicker is right footed however, he kicker kicks better to one side than the other. So we have four probabilities:
  • goal kick left keeper jumps left
  • goal kick right keeper jumps right
  • goal kick left keeper jumps right. Note that it is possible that this won't be a goal, even though the keeper is nowhere near the ball, as the ball might just miss the goal by a bit.
  • kick right and keeper jumps left. Analogous to above
Molecular machine by Ciro Santilli 35 Updated +Created
The most beautiful ones:
see also Section "Animations of molecular biology processes"
Sphere by Ciro Santilli 35 Updated +Created
Guitar by Ciro Santilli 35 Updated +Created
The guitar is a highly imperfect instrument if compared to something like a piano, which is much more mathematically elegant.
However, Ciro Santilli just loves this imperfection for some reason, especially in the case of the electric guitar.
Bending, sliding and strumming just feel to good to not have.
And Ciro sucks are doing things in parallel, so the more single threaded approach of the guitar fits his brain/abilities better.
For those reasons, the electric guitar is Ciro's favorite musical instrument.
Pop music by Ciro Santilli 35 Updated +Created
Pop music cannot be good by definition: any art that appeals to the masses (Popular!) has to be a boring watered down version of everything, and therefore boring shit. Just like the movies: high budget movies are shit.
Until maybe one day we can actually get a decent education for everyone.
Musical study by Ciro Santilli 35 Updated +Created
Phase-contrast microscopy by Ciro Santilli 35 Updated +Created
Break the meta by Ciro Santilli 35 Updated +Created
To break the meta means to find a new strategy that offers a significant advantage over the existing meta.
Video 1.
How One Man Changed the High Jump Forever by Olympics (2018)
Source. Dick Fosbury created and implemented the Fosbury Flop jump style in 1968.
Video 2.
Akiyo Noguchi asks the rules while climbing! | Beta Break Ep.1 by Albert Ok (2020)
Source. Happened at the 2015 IFSC Climbing World Cup during the Haiyang, China, bouldering event. The author has a playlist of such climbing meta breaks. In climbing, the meta is called "the beta". Climbing competitions are perhaps the sport in which the meta is broken the most often, since each stage is unique.
Video 3.
Lukas Hofer's Revolutionary Technique by IBU TV (2019)
Source. Lukas created a new technique to pack up his rifle during biathlon competitions.
MathDoctorBob by Ciro Santilli 35 Updated +Created
He got so old from 2012 to 2021 :-)
This dude did well. If only he had written a hyperlinked wiki rather than making videos! It would allow people to jump in at any point and just click back. It would be Godlike.
mathdoctorbob.org/About.html says:
Robert Donley received his doctorate in Mathematics from Stony Brook University and has over two decades of teaching experience at the high school, undergraduate, and graduate levels.
First-order logic by Ciro Santilli 35 Updated +Created
Hilbert's problems by Ciro Santilli 35 Updated +Created
He's a bit overly obsessed with polynomials for the taste of modern maths, but it's still fun.
Cycling by Ciro Santilli 35 Updated +Created
Blaise Pascal by Ciro Santilli 35 Updated +Created
Good quote from his Les Provinciales (1656-57) Letter XII, p. 227:
The war in which violence endeavors to crush truth is a strange and a long one.
All the efforts of violence cannot weaken truth, but only serve to exalt it the more.
The light of truth can do nothing to arrest violence; nay, it serves to provoke it still more.
When force opposes force, the more powerful destroys the less; when words are opposed to words, those which are true and convincing destroy and scatter those which are vain and false; but violence and truth can do nothing against each other.
Yet, let no one imagine that things are equal between them; for there is this final difference, that the course of violence is limited by the ordinance of God, who directs its workings to the glory of the truth, which it attacks; whereas truth subsists eternally, and triumphs finally over its enemies, because it is eternal, and powerful, like God Himself.
French version reproduced at: www.dicocitations.com/citation/auteurajout35106.php.
Japanese (language) by Ciro Santilli 35 Updated +Created
Dot product by Ciro Santilli 35 Updated +Created
The definition of the "dot product" of a general space varies quite a lot with different contexts.
Most definitions tend to be bilinear forms.
We use the unqualified generally refers to the dot product of Real coordinate spaces, which is a positive definite symmetric bilinear form. Other important examples include:
The rest of this section is about the case.
The positive definite part of the definition likely comes in because we are so familiar with metric spaces, which requires a positive norm in the norm induced by an inner product.
The default Euclidean space definition, we use the matrix representation of a symmetric bilinear form as the identity matrix, e.g. in :
so that:
Vector space by Ciro Santilli 35 Updated +Created
Infinity by Ciro Santilli 35 Updated +Created
Chuck Norris counted to infinity. Twice.
There are a few related concepts that are called infinity in mathematics:

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