Math Circle 2.0 Sept 13 2015: Symmetry, Graphs, Algebra, (Robots if time) and Cells

Symmetry, Graphs, Algebra, (Robots if time) and Cells 

Symmetry

Which letters are symmetric?
Draw a line through the axis of symmetry for each letter

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Which letters have

• vertical
• horizontal
• radial symmetry?

How to draw a line of symmetry for B? F? O?

An "O" has radial symmetry ... infinite lines of symmetry

 

 

 

 

 

 

 

 

 

 

 

Graphs

Start with two locations, the castle where the king lives and Philo, where the guitarist lives.

How many straight paths can Gary the guitarist take to the castle?

Bob the Banjo player lives in another town called Memphis (Memphis, TN, only about 3 km from the castle).

How many lines can you make among Philo, the Castle, and Memphis?

Ichabod the Instrument repairman lives in the center. How many straight paths among all four locations?

How many lines can you make b/w n dots

(Next time)

How many 

* Vertices?

* Edges?

* Triangles?

E=V+T-1 (Eulers Formula)

How many V+T?

Algebra

Gnomes each eat 1 apple. Dwarves each eat 2 cabbages.

A Gnome arrives at your tavern. If you are the inkeeper, how many apples do you need to provide? How many cabbages?

A Dwarf arrives. How many apples will you need total? How many cabbages?

Another Dwarf arrives.

...

Experiment

What is a house made up of (bricks). They all look the same but make something bigger.
What are plants made of (cells)? How can we see them? Where can we find them?

Roots?
  * Lets get some roots.
  * Cant see them. Lets look at a radish
  * Cant see the cells.
Lets try to stain them (vodka to clear, dry, rub permanent marker, vodka to rinse)

Which cells are bigger than others?

 Preview: