October 15, 2017 - Math Circle 2.0

Warm Up

Find the solutions to the following algebraic equations.

5 + x = 8

8 - y = 1

4 + 5 = z + 6

Game Theory

Play the nickel and penny game that we introduced last session with a partner.  Does any player have an advantage?

Remember the game:
A penny is worth one cent and a nickel is worth 5 cents.

There are two players to the game, player one and player two.  Both players will pick a coin in secret to play.  If both coins that are played match, player one wins both coins.  If both coins that are played do not match, player two wins both coins.  

Create payoff matrix for the nickel and penny game that we discussed in the previous math circle.  

What would happen if we added a dime to the mix to create a dime, nickel and penny game?  Let's answer next class.

October 8. 2017 - Math Circle 2.0

Warm Up

Perimeters of squares and circumferences of circles.  

Game Theory

Last class, we learned how to express a the game paper, rock, scissors in a pay-off matrix.  We found that the game was very balanced in which no player really had an advantage over another player.  Let's try another game....  Pennies and nickels.

A penny is worth one cent and a nickel is worth 5 cents.

There are two players to the game, player one and player two.  Both players will pick a coin in secret to play.  If both coins that are played match, player one wins both coins.  If both coins that are played do not match, player two wins both coins.  Play the game at home and see if you can find a winning strategy to win the most money.

Counting

There are three dogs:  Charlotte, Ozzy, and Rosie.  Each dog has a choice of one of four types of snacks:  Bone, Cupcake, Food, and Treats.  There is only one of each snack so two of the dogs cannot receive cupcake, for example.  Using your counting skills, map out the possible combinations of dogs and snacks.  There are 4 x 3 x 2, or 24 combinations.

Here are some combinations to get started:

               Ozzy        Rosie        Charlotte

1.            Bone        Cupcake   Food

2.            Bone        Cupcake   Treats

3.            Bone        Food         Cupcake

4.            Bone        Food         Treats

 

Map the rest of the combinations for homework.

October 1, 2017 - Math Circle 2.0

Homework Review

Using the supplied cup, measure the circumference of the cup.  Next, draw a square that inscribes the circle.  Is the perimeter of the square greater than the circumference of the circle?

Circumference of the circle

Use a string to mesasure the circumference of a set of circles.  Compare the diameter of the circles to the circumference.  In all cases, the circumference of the circle is a little over 3 times the diameter of the circle.  The number that expresses the ratio of diameter to circumference is represented by the greek letter pi.


Rock Paper Scissors

Learn how to play Rock, Paper, Scissors.  

Can you win at Rock Paper Scissors with a strategy?  Create a payoff matrix.

From:  http://shack.typepad.com/shack_in_japan/2012/05/game-theory-for-middle-school-day-1-payoff-matrices-and-rock-paper-scissors.html

September 3, 2017 - Math Circle 2.0

Warm up

Homework review.  
You need to capture precisely 4 gallons of water for some unknown experiment that requires precisely 4 gallons of water.  The tools available to you are a 3 gallon container, a 5 gallon container and an unlimited water source that allows you to fill the 5 and 3 gallon containers.  How would you fill the containers to get precisely 4 gallons of water?  

Make a scale model of classroom

What does scale mean?  Also is the classroom a rectangle or a square?  Draw a scale model of the classroom.  Can we calculate the size of the classroom to the size of the paper?

Number Puzzle

For the puzzle below, use the numbers 1 through 6 only once per position.  Try to have all the sides of the triangle add up to the same number.

For homework, use only the numbers 1, 3, and 5 once to complete the puzzle.  The sides must add to 11.

August 27, 2017 - Math Circle 2.0

Warm Up

Scale of the solar system.  Watch movie:

https://www.youtube.com/watch?v=Kj4524AAZdE

Perimeter

Introduce perimeter of a square and a rectangle.  How do we define a rectangle and a square?  How many side lengths of a rectangle do you need to know to calculate the perimeter?


Puzzle

Cows in a field game


Homework puzzle

You need to capture precisely 4 gallons of water for some unknown experiment that requires precisely 4 gallons of water.  The tools available to you are a 3 gallon container, a 5 gallon container and an unlimited water source that allows you to fill the 5 and 3 gallon containers.  How would you fill the containers to get precisely 4 gallons of water?  

August 20, 2017 - Math Circle 2.0

Warm Up

Welcome back to Math Circle.   Let's discuss the solar eclipse that will happen Monday, August 21, 2017 in the USA.


Pinhole Camera

Safety first!  Never look at the sun directly without ISO 12312-2 compliant solar glasses.  You may look at the sun indirectly by making a pinhole camera.

Follow the link below to get the directions.

https://eclipse2017.nasa.gov/sites/default/files/EclipseCerealBoxViewer.pdf


Size of Sun, Earth, and Moon

The following link has a summary of the sizes and distances of the sun, earth, and moon.

http://blair.pha.jhu.edu/scale.html

Almost four diameters of the moon span the earth.
109 diameters of the earth span the sun.

The distance from the earth to the moon is 110 moon diameters
The distance from the earth to the sun is 11759 earth diameters

What does that look like?
How can we create a model of this?
What is a diameter anyway?

Scale - 1 earth diameter = 1 inch
distance from earth to moon is 30 inches
distance from earth to sun is 11759 inches, or 980 feet, or distance to the top of right of the rectangle formed by the sidewalks north of Foellinger auditorium.

aug 20

...2857142857142857143x7=?

---

Quadrangles - what is the taxonomy:

Kites (pairs of neighboring sides equal) - Parallelograms (opposite sides <=> opposite angles are equal)-Trapezoids (pairs of neighboring angles are equal)

Rhombi (=diamonds)   Rectangles

Squares

Midsides operations: take midpoint of all 4 sides of a quadrangle Q, get another quadrangle M(Q).

Turns out, - M(Q) is always a parallelogram!

Q-rhombus <=> M(Q) - rectangle, and vice versa.

---

Logics:

Two villages (Knights and Knaves), a person at the fork - which road goes to Knights village?

Larry, Leon, Tom, L's are liars, Tom tells truth. How to find if you speak to Larry?

---

When the angle between the hands is wider: 5 past 11, or 10 past noon?
$x^2 $