Crystallographic restriction theorem lattice basis, the rotation operation must map every lattice point into an integer number of lattice vectors, so the entries of the rotation matrix in the lattice basis — and hence the trace — are necessarily integers. Similar as in other proofs, this implies that the only allowed rotational symmetries correspond to 1,2,3,4 or 6-fold invariance. For example, wallpapers and crystals cannot be rotated by 45° and remain invariant, the only possible angles are: 360°, 180°, 120°, 90° or 60°. Example The general crystallographic restriction on rotations does "not" guarantee that a rotation will be compatible with a specific lattice.
Olympic triangle to re-align the course to the new wind direction. With a 60, 60, 60 triangle, if the wind shifts 15 degrees either way, one of the reaching legs will be a 45-degree broad reach, while the other will be at 75 degrees to the wind and will be a close reach. Many dinghy classes have a target length for a race for the first boat. This time might take into consideration the age of competitors, how physically demanding the class is and how physically demanding the conditions are. 100 minutes is often used by Herons in Australia as an informal