# The euclidean space $\mathbb E^3$

## What is $\mathbb E^3$?

The euclidean space corresponds to the “usual” 3D geometry we learn at school. It is the geometry of the flat real 3-dimensional vector space $\mathbb R ^3$.

Click on the button below to reveal a concrete model of $\mathbb E^3$.

## Some views of $\mathbb{E}^3$

**Warning:**
Some of the real-time simulations below requires a powerful graphic card.
If your computer is not fast enough, you can reduce the size of your browser window.
Click on the button below to reveal the fly commands.

The default controls to fly in the scene are the following.
If you have a different keyboard, the keys should be the ones having the same **location** as the given ones on a QWERTY keyboard.

Command | QWERTY keyboard | AZERTY keyboard |
---|---|---|

Yaw left | a | q |

Yaw right | d | d |

Pitch up | w | z |

Pitch down | s | s |

Roll left | q | a |

Roll right | e | e |

Move forward | arrow up | arrow up |

Move backward | arrow down | arrow down |

Move to the left | arrow left | arrow left |

Move the the right | arrow right | arrow right |

Move upwards | ' | ù |

Move downwards | / | = |

HD pictures of $\mathbb{E}^3$ can be found in the gallery

## Features of $\mathbb{E}^3$

Euclidean space is very familiar to us from everyday life, and so we have little to learn of its features from computer simulation. Nonetheless, a select few simulations below are included to allow comparison with other geometries.