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:

Sept 6 2015 Math Circle 2.0

Homework Review

What is the value of 5 nickels in pennies

Symmetry

Radial Symmetry? Which animals have radial vs bilateral symmetry?

Robots in Urbana

Students can give a lego guy the following instructions: North, West, South, East.
How many ways to get from this corner to that corner?

ref: Math Circle 1.0 Oct 10 2013

Algebra

Gnomes and Elves eat Vegetables. Gnomes eat one corn cob and one tomato. Elves eat two tomatoes. 

Aug 23 Math Circle 2.0

Symmetry

1. Which shapes are symmetric? Which are asymmetric?

Students were asked to fold figures along axis of symmetry

How many ways can the robot get from point A to point B?

2. Fill in the missing half of each shape 

Robots In Urbana

Following Math Circle 1.0 Sept 29 2013

The robot only understands two instructions:

1. "Go North"
2. "Go West"

A robot starts at the corner of Vermont and Race. What instructions can you give it so that it will move from the corner of Race and Vermont to the corner of Carle and Pennsylvania?

How many ways can it get there?

Can you give it instructions to get back?

Algebra

Each kid has one head and two legs. 

• How many heads and how many legs do three kids have?
• If there are two heads and four legs, how many kids are there?
• If there is one head and six legs, how many kids? (no correct answer here, see below)

An ant has one head and six legs.

• If there is one head and six legs, does the head belong to a kid or to an ant?
• If there are two heads and eight legs, how many kids? How many ants?

Experiment

What happens if you put a pack of mentos in a 2 L bottle of diet coke?