Mathematics of soccer: Shot angles

Consider a situation in which a soccer player runs straight, with tha ball, towards the bottom line of the field. Intuitively, it is clear that there is an optimal point maximizing the shot angle, providing the best place to kick in order to improve the chances to score a goal. If the player chooses the bottom line, the angle is zero and his chances are just horrible; if the player kicking far way, tha angle is also too small!

Locus of the optimal points

Two different types of kicks: Diego Armando Maradona in Napoli-Cesena 2-0, Serie A 1987/88, an amazing example of the "Maradona feeling" about the optimal place to kick

and the "impossible" goal by Marco Van Basten during the final of Euro '88

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from "Mathematics of Soccer" by Alda Carvalho, Carlos Pereira dos Santos, Jorge Nuno Silva. "Recreational Mathematics Magazine" (2014)

The Infinite Improbability Drive

#towelday #InfiniteImprobabilityDrive #DouglasAdams

The Infinite Improbability Drive is a faster-than-light drive. The most prominent usage of the drive is in the starship Heart of Gold. It is based on a particular perception of quantum theory: a subatomic particle is most likely to be in a particular place, such as near the nucleus of an atom, but there is also an infinitesimally small probability of it being found very far from its point of origin (for example close to a distant star). Thus, a body could travel from place to place without passing through the intervening space (or hyperspace, for that matter), if you had sufficient control of probability. According to the Guide, the drive "passes through every conceivable point in every conceivable universe almost simultaneously," meaning that you are "never sure where you'll end up or even what species you'll be when they get there" and "it's therefore important to dress accordingly".
The Guide's entry on the drive also states that it was invented "following research into finite improbability, which was often used to break the ice at parties by making all the molecules in the hostess' undergarments leap one foot simultaneously to the left, in accordance with the theory of indeterminacy". It further explains that many respectable physicists wouldn't stand for that sort of thing, "partly because it was a debasement of science, but mostly because they didn't get invited to those sort of parties."

(source: Wikipedia)

The first application of the concept behind the infinite improbability drive comes from an old experiment from the 20th century:

Well, some researchers were once conducting such an experiment, but when they opened up the box, the cat was neither alive nor dead but was in fact completely missing, and they called me in to investigate. I was able to deduce that nothing very dramatic had happened. The cat had merely got fed up with being repeatedly locked up in a box and occasionally gassed and had taken the first opportunity to hoof it through the window. It was for me the work of a moment to set a saucer of milk by the window and call "Bernice" in an enticing voice -- the cat's name was Bernice, you understand -- and the cat was soon restored.

(from Dirk Gently's Holistic Detective Agency by Douglas Adams)

Some facts about Rubik's cube

posted by @ulaulaman about #RubikCube

Rubik's cube is a 3d puzzle game crated by Ernő Rubik.

In a classic Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement.

On of the first optimal solution is dued to Richard Korf

As far as we have been able to determine, we have found the first optimal solutions to random instances of Rubik's Cube, one of the most famous combinatorial puzzles of its time. The median optimal solution length appears to be 18 moves. The key idea, due to (Culberson and Schaeffer 1996), is to take a subset of the goals of the original problem, and precompute and store the exact number of moves needed to solve these subgoals from all possible initial states. Then the exact solution to the subgoals is used as a lower bound heuristic for an IDA* search of the original problem.⁽¹⁾

Some years before this paper, Korf proposed a self-learning software in order to solve the cube:

This paper describes a program which learns efficient strategies for solving problems such as Rubik’s cube and the eight puzzle. It uses a new general problem solving method based on macro-operators. The strategies learned by the program are equal to or superior to strategies used by humans on these problems, in terms of number of moves required for solution.⁽²⁾

Searching about Rubik's cube, I found a couple of curious papers in which the puzzle is applied to study some deseases:

Like Rubik's Cube, the pancreatic islet is a dynamic puzzle comprised of many interrelated components requiring proper alignment and integration. Phospholipid turnover is one “panel” in the islet; however, an obligate role for phospholipase activation in glucose-induced insulin secretion is not yet rigorously established, despite tantalizing, inferential evidence. It may be that glucose serves principally to potentiate the phospholipase and secretory responses to other signals that act by initiating phospholipid hydrolysis.⁽³⁾

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God's Number is 20
David Joyner. Adventures in Group Theory: Rubik's Cube, Merlin’s Machine, and Other Mathematical Toys (pdf)

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(1) Richard E. Korf (1997). Finding optimal solutions to Rubik's Cube using pattern databases. Proceedings of the fourteenth national conference on artificial intelligence (pdf)
(2) Richard E. Korf (1982). A Program That Learns to Solve Rubik's Cube. Proceedings of the fourteenth national conference on artificial intelligence (pdf)
(3) Metz S.A. (1991). The Pancreatic Islet as Rubik's Cube: Is Phospholipid Hydrolysis a piece of the Puzzle?, Diabetes, 40 (12) 1565-1573. DOI: 10.2337/diab.40.12.1565

From space with love

One year later, Chris Hadfield uploaded a video of his version of Space Oddity performed on the International Space Station. David Bowie had him a permission of one year and so, a couple of days ago, Chris Hadfield deleted the video, but you can see it on the YouTube channel of Sky News:

The most incredible thing is that, following Bowie's request, Hadfield's video is removed from his youtube channel, but it is reuploaded by other users and not only by Sky News...

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via space.com

Analytical Institutions in Four Books

about #MariaGaetanaAgnesi

According to Dirk Jan Struik, Agnesi is "the first important woman mathematician since Hypatia (fifth century A.D.)". The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventù italiana, (Analytical Institutions for the Use of Italian Youth) which was published in Milan in 1748 and "was regarded as the best introduction extant to the works of Euler." In the work, she worked on integrating mathematical analysis with algebra. The first volume treats of the analysis of finite quantities and the second of the analysis of infinitesimals. A French translation of the second volume by P. T. d'Antelmy, with additions by Charles Bossut (1730–1814), was published in Paris in 1775; and Analytical Institutions, an English translation of the whole work by John Colson (1680–1760), the Lucasian Professor of Mathematics at Cambridge, "inspected" by John Hellins, was published in 1801 at the expense of Baron Maseres. The work was dedicated to Empress Maria Theresa, who thanked Agnesi with the gift of a diamond ring, a personal letter, and a diamond and crystal case. Many others praised her work, including Pope Benedict XIV, who wrote her a complimentary letter and sent her a gold wreath and a gold medal.