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La vie Math

La pensée en mouvement

Alain Connes

Les Mathématiques et la pensée en mouvement : une belle conférence d’Alain Connes.

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Coding La vie Math

Robust super-resolution depth imaging

Representation of the super-resolution depth HistNet

Robust super-resolution depth imaging via a multi-feature fusion deep network — arxiv.org/abs/2011.11444.

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Friandises Geek Math

Many lifes

Life in life by Phillip Bradbury

Conway’s Game of Life, emulated in Conway’s Game of Life. The Life pattern is the OTCA Metapixel. The life simulator used is Golly.

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Draft Friandises Math

Infinitely Many Hats (3/3)

Countably infinitely many hats
Countably infinitely many hats

This is the last in a series of three exercices de style to show some interesting aspects of the game of hats: a puzzle which was initially proposed by Lionel Levine.

Here we look at case where each player has a tower of countably infinitely many hats on their head and try constructing efficient strategies from the results of the first exercice.

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Friandises Math

0! = 1

La fonction factorielle est souvent définie comme le produit : $$n!=\prod_{k=1}^n k\text{,}$$ ou bien par récurrence : $$n!=n\cdot(n-1)!\text{,}$$ en prenant par convention : $0!=1$. Mais pourquoi cette convention ?

Zero
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Friandises Math

Classic 15 Puzzle

15-puzzle by Mark Rohlich

Genesis

The Fifteen Puzzle consists of fifteen numbered square tiles in a 4×4 square grid, with one position empty or blank. Any tile horizontally or vertically adjacent to the blank can be moved into the blank position. The task is to rearrange the tiles from some random initial configuration into a desired goal configuration, ideally or optimally using the fewest moves possible.

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Friandises Math

Towers of hats (1/3)

A towering pillar of hats (number $4$)

This is the first in a series of three exercices de style to show some interesting aspects of the game of hats: a puzzle which was initially proposed by Lionel Levine, and arose from his work with Tobias Friedrich on

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Friandises Math Tips

Schizo: a different sudoku solving technique

Over the years, several tips and techniques have been developed to help solve sudoku puzzles with logic rather than brute force. To name a few, sudoku9x9 mentions (among others) hidden single, naked single, x-wing.

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Math

IMO 2019 Problem 1

An exercice with MathJax

Problem 1: Let $\mathbb{Z}$ be the set of integers. Determine all functions $f : \mathbb{Z} \rightarrow \mathbb{Z}$ such that

\begin{equation}
\forall (a, b) \in \mathbb{Z} \times \mathbb{Z}, \quad f(2a) + 2 f(b) = f(f(a + b))
\label{eq1}
\end{equation}

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La vie Math

11n34 – not slice

Inspiring young mathematician Lisa Piccirillo

Lisa Piccirillo from University of Texas, Austin, recently published a paper in the annals of mathematics solving a long-unsolved topology problem : the Conway knot (11n34 in the Rolfsen tables) is not slice.