123 lines
8.5 KiB
Markdown
123 lines
8.5 KiB
Markdown
---
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aliases:
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- principe du parapluie
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- parapluie
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excalidraw-plugin: parsed
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tags:
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- excalidraw
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excalidraw-open-md: true
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---
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up::
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#s/maths #s/philosophie
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> [!definition] parapluie
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> Un parapluie désigne, en matématiques, une combinaison particulière de deux fonctions :
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> $$\boxed{f^{-1}\circ g \circ f}$$
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>
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> En général, cela désigne le fait de réaliser un processus $g$, mais de réaliser d'abord un processus $f$, et ensuite un processus $f^{-1}$ qui est la [[application réciproque|réciproque]] de $f$.
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>
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> L'intérêt est d'exécuter $g$ dans le contexte apporté par $f$, mais sans garder ce contexte.
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> Par exemple :
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> 1. mettre le parapluie ($f$)
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> 2. traverser le pont ($g$)
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> 3. enlever le parapluie ($f^{-1}$)
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> Cela permet de traverser le pont sans être mouillé, mais les autres paramètres sont inchangés (on a pas gardé le parapluie).
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>
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> ![[principe du parapluie.svg|600]]
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^definition
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# Exemples
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- lorsque l'on pose une clef sous le paillasson :
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1. on prends la clef sous le paillasson
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2. on ouvre la porte
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3. on remet la clef sous le paillasson
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- pour changer d'étage si deux bâtiments sont reliés par des passerelles, mais seulement l'autre possède un ascenseur
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- Les bâtiments A et B sont reliés à châque étage par des passerelles
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- Le bâtiment A ne possède pas d'ascenseur, le bâtiment B possède un ascenseur
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- pour changer d'étage si on est dans le bâtiment A :
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1. traverser la passerelle de A vers B
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2. changer d'étage dans B
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3. traverser la passerelle de B vers A
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- arrondir des nombres à $n$ décimales près
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1. multiplier le nombre par $10^n$
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2. arrondir à l'entier le plus proche
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3. diviser le nombre par $10^n$
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- la morue salée
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1. saler le cabillaud
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2. stocker la morue une fois salée
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3. dessaler la morue
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%%
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# Excalidraw Data
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## Text Elements
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Contexte initial ^qyhVpnCu
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Autre contexte ^Rs3HtYNb
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## Embedded Files
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ebd737646a18b1703fdc6d539462dcd83ccbd752: $$f$$
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e6909725163af4b38886b036f3f29fbe8b70d0db: $$f^{-1}$$
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ba26171d9cf41859cb968ee0741dc00618359ed2: $$g$$
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## Drawing
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```compressed-json
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iQej/EEXCUd3t/t01OlxwZgMN35cCYCEVzIF4EG8AQTH1j4cIGRFxKyIAA==
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```
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%% |