Rotation Groups Math
Teacher desk game fast facts.
Rotation groups math. The rotation group is a groupunder function composition or equivalently the product of linear transformations. There are 4 main lie rotation groups i have put the full story on this page. The rotation group and quantum mechanics1 d. Although these groups all represent rotations around the origin they may have different properties for instance each object in the group may correspond exactly to one rotation.
1 the rotation group a rotation can be described by giving a matrix rsuch that a vector vgets transformed to a vector vunder the rotation with v i r ij v j. Sp n a group of rotations in n quaternion dimensions. For math i had 3 small groups and named them different fruits. For reading i had 5 6 small groups and named them different animals.
Sakurai modern quantum mechanics. It is a subgroupof the general linear groupconsisting of all invertiblelinear transformations of the real 3 spacer3 displaystyle mathbb r 3. Your middle groups are easy to plan. This is when the kiddos come to me at the carpet or small group table for the actual lesson that is presented on their level.
So n a group of rotations in n real dimensions. In my experience i believe that including small group maths rotations in your classroom allows you to work with smaller more targeted groups of students. I also kept master rotation charts in my guided math guided reading binders for my reference. These rotation groups are all subsets of the sl n f special linear group.
Su n a group of rotations in n complex dimensions. At the end of the day it depends on your class their capabilities and behaviours. Soper2 university of oregon 30 january 2012 i o er here some background for chapter 3 of j. Providing time for you to provide instruction appropriate to their knowledge.
G2 f4 e6 e7 and e8 a group of rotations in n octonion dimensions. While i don t do a whole group lesson at the beginning we do come back for share time to talk about our new learning.