Concept history

Status changed from reviewed to usable: manque une intuition

Updated browser visibility

Concept reviewed

Concept marked usable

Concept created

Une homotopie de chemins entre deux [[Path in a space|chemins]] $\gamma_{0},\gamma_{1}:[0,1]\rightarrow X$ avec les mêmes extrémités est une [[Homotopy|homotopie]]
$$H:[0,1]\times[0,1]\rightarrow X$$
telle que les extrémités restent fixées :
$$H(0,s)=\gamma_{0}(0)=\gamma_{1}(0),\;\; H(1,s)=\gamma_{0}(1)=\gamma_{1}(1).$$

```jsxgraph
{
  "boundingBox": [-3.2, 2.2, 3.2, -2.0],
  "axis": false,
  "height": 400,
  "elements": [
    {
      "id": "t",
      "type": "slider",
      "parents": [[-2.8, -1.7], [0.2, -1.7], [0, 0.5, 1]],
      "attributes": {
        "name": "t"
      }
    },

    {
      "type": "functiongraph",
      "parents": ["0.425*x + 0.05 + 0.9*(1 - x^2/4)", -2, 2],
      "attributes": {
        "strokeColor": "#2f6f4e",
        "strokeWidth": 3
      }
    },

    {
      "type": "functiongraph",
      "parents": ["0.425*x + 0.05 - 0.75*(1 - x^2/4) + 0.35*x*(1 - x^2/4)", -2, 2],
      "attributes": {
        "strokeColor": "#e34a4a",
        "strokeWidth": 3
      }
    },

    {
      "type": "functiongraph",
      "parents": [
        "(1-t.Value())*(0.425*x + 0.05 + 0.9*(1 - x^2/4)) + t.Value()*(0.425*x + 0.05 - 0.75*(1 - x^2/4) + 0.35*x*(1 - x^2/4))",
        -2,
        2
      ],
      "attributes": {
        "strokeColor": "#3366cc",
        "strokeWidth": 4
      }
    },

    {
      "type": "point",
      "parents": [-2, -0.8],
      "attributes": {
        "size": 3,
        "fixed": true,
        "withLabel": false
      }
    },

    {
      "type": "point",
      "parents": [2, 0.9],
      "attributes": {
        "size": 3,
        "fixed": true,
        "withLabel": false
      }
    }
  ]
}
```