LL 28

This week I learned about how membranes are formed, certain molecules are hydrophobic on one side while hydrophilic on the other side so the molecule forms into a sphere with hydrophilic parts touching the water on the outside and inside. And hydrophobic molecules touching each other between the two layers.

I also took the test to get into the mega society called the ultra test, which you have to have a one in a milliion iq to pass. I didn't even get close, but I learned a lot.

https://megasociety.org/admission/ultra/

                                                           Mega society logo

LL27

 This week Michael did his Art of Problem Solving class.  There were several problems giving him trouble but he worked through them patiently.  I think he learned more about perseverance and communicating with the team helping him.  He's been writing in his journal consistently, which makes me so happy. He also enjoyed his BYU math club class even though the problems were too difficult for him.  He took a book from my mom's house and reads a concept each night about how to be better.

LL 26

 This week I solved a difficult math problem that I've been working on for a while.

How many sequences of 15 coin flips have 5 HH 4TH 3HT 2TT for example HHTTTTH has 1 HH 1 TH 1HT and 3 TT.

Solution: Imagine we only cared about the 4TH and 3HT, the only sequence of flips that works is THTHTHTH. To build up to the actual problem we need to add the 5HH and 2TT, there are four different places we can put the HH, they are where the H's are. So it's equivalent to putting 5 balls into four buckets which is 5 choose four or 56 possibilities for H, using a similar argument we can show that there are 10 possibilites for T. And 56*10=560 which is our answer.

(this isn't explained super well, here's the official solution.)

LL 25

 This week I learned about differential equations, differential equations are equations that show how a system will change rather then how it is at any given moment. They're usefull for nearly every field of math and science, especially phicics.

I also made a game called light beam frenzy.

https://scratch.mit.edu/projects/955832773/

https://www.3blue1brown.com/lessons/differential-equations