# Math Worksheet

Scratch pad

To show: $1+8+16+\dots+8(n -1)= (2^n -1)^2$

a. True for $n=1$

b. if true for $n$, then true for $n+1,\ n>1$

# Subgroup of the Triangle Symmetries.

$\color{blue}{f}\color{lime}{\circ}\color{red}g;\quad f, g \in G$

$\circ$ | $id$ | $r1$ | $r2$ |
---|---|---|---|

$id$ | $id$ | $r1$ | $r2$ |

$r1$ | $r1$ | $r2$ | $id$ |

$r2$ | $r2$ | $id$ | $r1$ |

If we look at just the upper left corner of Cayley table for the equilateral triangle symmetries, we discover that the rotations and the id (do nothing) form a group. Satisfy yourself that this meets the requirements of a group.

# Cayley notation

These are the permutations of the equilateral triangle symmetries in Cayley notation. $r2$ is read, for example, "1 goes to 2, 2 goes to 3, and 3 goes 1." Many texts use $i$ or $e$ for $id$, rho ($\rho$) for $r$ and mu ($\mu$) for $f$.

*Sources:*

*Recommended:*

** Categories:** Worksheets

*Tags:*

This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

**Backlinks**

- Miscellenious DE Exercises Answers
- Abstract Algebra: Permutations Groups
- Boole Chapter II Exercises
- Boole Chapter II Worked
- Misc. DE Exercises Worked
- Verify Solutions of DEs Exercises Worked 2
- Verify Solutions of DEs Worked 3
- 2nd Order Homogeneous DE Exercises Answers
- 2nd Order Homogeneous DE Exercises Worked
- Boole Chapter II Answers
- Integration by Parts Exercises
- Integration by Parts Worked Exercises
- Miscellenious DE Exercises
- Trench Introductory DE Exercises
- Trench Introductory DE Exercises Answers
- Trench Introductory DE Exercises Answers p.2
- Trench Introductory DE Exercises Answers p.3
- Verify Solutions of DEs Exercises Worked

This page is MathWorksheet