MathO 2.0: March 27, 2020

We are now totally on line using zoom.

Here's what we covered today:

1. Warm up involving Alice and Bob and Bulls and Cows

If Alice guesses 3 4 7, and Bob responds with 1 bull and 2 cows, what are the possible different correct responses?

Answer:

3 7 4
7 4 3
4 3 7

2. St Endle's Inn

3. Circular Addition

4. Introduction to Scratch Programming

Math O 2.0 : March 22, 2020

Warmup problem: 

Grandma Sue has a large pan that she uses to make grilled cheese sandwiches.  She grills each sandwich 30 seconds on each side, and her pan can hold two sandwiches at a time.  How quickly can she make 3 sandwiches?

Wizards and Elves:

St Endle's Inn is a restaurant that caters to Wizards and Elves.  

St Endle decides that there must be a total of 9 Wizards and Elves in the Inn at one time.  Plot some values that work.


St Endle later decides that there must be 6 more Wizards than Elves in the Inn at any time.  Plot some values that work.

St Endle (after a particularly long night at the draught barrel) decides that twice the number of Wizards in the Inn should be 6 more than the number of Elves.  Plot some values that work.

Addition on Circles:

A number line is a great way for us to visualize adding numbers together.  What if the number line was rather a number circle?  We can create different circles with different numbers on them.  

Here is an 8-circle

2 + 3 = 5 on the 8-circle
5 + 3 = 0 on the 8-circle
6 + 7 = 5 on the 8-circle

Here is a 10-circle

4 + 5 = 9 on the 10-circle
6 + 7 = 3 on the 10-circle
8 + 9 = 7 on the 10-circle

(some of us figured out that for any number, the ones-place is its value on the 10-circle)

What is 423 + 295 on the 10 circle?

November 17

• Warmup: 
• what is bigger, $754/344$ or $75/34$? 
• tile the plane with devils
• Binomial coefficients. Pascal triangle.
• Return to counting paths in a graph...
• Sets. Formulae. Subsets: predicates and interpretations.
• Game B&C?

November 10

• Warmup: 
• what is bigger, $354/734$ or $35/73$? 
• what is the last digit of $1\times 2\times \ldots\times 11\times 12$? 
• Induction: cut 2^n x 2^n square - one corner into L-trigons.
• Squares on the surface of $10\times 10\times 10$ cube are painted in white and black.
• How many squares are altogether?
• If 301 square is painted white, is there always a pair of opposite white squares?
• Return to counting paths in a graph...
• Sets. Formulae. Subsets: predicates and interpretations.
• Game B&C?
  

Homework

• Draw the areas described by the formulas

November 3

Past homework:

• prism+tetrahedron
• cutting the cube to get regular 5-gon

New:

• Extending faces of cube, they partition space into how many pieces?
• Same about tetrahedron, prism, octahedron
• x^3=5/4 y^2=9/8. What is greater, x or y?
• Roll coins
• Wire-frame with sides 3,4,12. That is the distance between endpoints?
• Induction: cut 2^n x 2^n square - one corner into L-trigons.

Sets,

October 27

• Warmup:
• $x^5=2; y^8=3$. Which is greater, $x$ or $y$?
• Turning coins around each other
• Ball jumping, first jump 1/2 foot; each next jump 20% shorter. How far will it go?
• Pythagorean theorem. 
• How to find the diagonal of a brick?
• Back to residues: build tables for mod $5,6,7,8$. 
• No zeroes in the tables for what modules?
• What happens if we multiply rows?
• Game - bulls and cows...

October 20

• Homework: pentahedron; origami?
• If $x^3=26$ and $y^2=9$, what is bigger, $x$ or $y$? 
• Two players try to move short hand to 5 o'clock. They start at 1, and can move it ahead 2 or 3 hours. Who wins?
• Geometric progressions - how to find their sums.  When the sum converges. 
• What about other convergences: example of $1+1/2+1/3+\ldots$
• $a^6\mod 7$ for $a=1,2,\ldots,6$.
• The following sets are given:$$A = \{1, 3, 7, 137\}, B = \{3, 7, 100\}, C = \{0, 1, 3, 100\}, D = \{0, 7, 100, 333\}. $$
  Describe the sets:
• \(A \cup B\);
• \(A\cap B\);
• \((A \cap B)\cup D\);
• \(C \cap (D\cap B)\);
• \((A\cup B)\cap (C \cup D)\);
• \((A\cap B)\cup (C \cap D)\);
• \((D\cup A)\cap (C \cup B)\);
• \((A\cap (B\cap C))\cap D\);
• \((A\cup (B\cap C))\cap D\);
• \((C \cap A)\cup ((A\cup (C \cap D))\cap B)\)