Monday: Today, I coded a machine that generates a list of prime numbers between 1 and input from the user. Unfortunately, that machine broke for some reason so I don’t have a photo, but it was basically printing out a list that looked like this: [2, 3, 5, 7, 11, 13, 17, 19, 23, …] I also started learning about optimization problems. I didn’t really get them so I will be returning to this tomorrow. I also started planning for SelfDesign® because the school year is coming up in a week! I found out that there are a lot of new activities for grades 8-9, including Gr 8-9 Circle, Gr 8-9 Themes, and Genius Hour! Gr. 8-9 Circle is hosted every month where you meet other kids your age and chat about what you are doing. Themes are every week where you do activities with other Gr 8-9 learners. And Genius Hour is also every month where we basically attend a class and learn about cool stuff!
Tuesday: Pretty eventful day! Just kidding. Today, I worked on math (about optimization problems), science (about magnets), writing (about cool collisions), and computer science (about checking if a number is prime). I also did violin class today, and it was pretty fun because we started a new song (about a DOG of all things) and we almost finished the old song (about classical music *grin* called Concerto in A minor, Op. 3, No. 6, 1st mvt. by Antonio Vivaldi).
Wednesday: Today, I learned about the four fundamental forces and what they do. I also learned about the applications of integration in 3D, and I also created a JavaScript program about finding out if a number is prime almost instantly! It does have some flaws though because it’s only about 50% accurate… But, there is a solution!
Thursday: I basically did the same thing as Wednesday… I learned about how to calculate 3D volume with cylinders, and I did some problems with wave interference. I also went to the LAST day of taekwondo today! So we played dodgeball 😉
Friday: I didn’t do too much today… I learned about the Taylor series and how that can be used to approximate a non-quadratic equation as a quadratic equation. I also learned and did problems about electromagnetic waves, such as ultraviolet and visible light. I also got 100% on the quiz and Khan Academy says that I mastered it.
I learned about the Fermat primality test, where you take the number you want to test (P), and then you pick a random number below P (call it A), and to see if a number is prime, all you do is take A to the P-1 power, and then you mod that with P. Then you see if the result is equal to one. Mod is a function that works like division, but it returns the remainder instead of the value, unlike division. For example, if you test 11 and choose an A of 4, you do 4^(11-1) = 1,048,576. Then that modulo 11 (1,048,576 mod 11) = 1! so 11 is prime.I started learning about magnetic forces and the cross product, which is a way of multiplying two vectors together. Basically, to take the cross product of two vectors, you multiply the magnitudes of the two vectors and then multiply by the sine of the angle made between them.I saw a cool article about colliding galaxy clusters and how they interact, so…… I wrote about it! Basically, a galaxy cluster called Abell 1775 collided with a cluster and it was really cool. I learned about how you can optimize functions. For example, let’s say you have a rectangle with an area of 1000, and you want to try and minimize the perimeter.I learned about some applications of integration in three dimensions! So I learned how you can find the volume of a shape that is squeezed between two other 3D shapes, and the equation for that.I learned about vector fields and the different properties that they have. I also learned about the four fundamental forces: gravity, electromagnetism, and strong and weak forces, which are responsible for nuclear decay.I saw this OTHER cool article about what is inside the core of a neutron star, sooooo…… I wrote about how a NASA space telescope (NICER) gave new insight about what’s at the core of a neutron star! (Spoiler: We don’t know.)I made a little machine that checks if a number is prime or not, and it uses a property of prime numbers that is called “Fermat’s Little Theorem.” Look at the photo at the very top of this page for an explanation. Anyway, this machine has a big O notation of 1, or O(1), which means that no matter how much stuff you chuck at it, the runtime remains the same. Cool, right? This is WAAAY more efficient than checking every single number before it, which had a big O of n^2, meaning that the runtime grows with the SQUARE of the number of inputs.But there IS a downside because this machine is only 50% accurate in the worst-case scenario. that means, in the worst-case scenario, it basically flips a coin, and if it’s heads, it says that it’s prime, but if not, it says that it’s not prime. So how do you improve this? well, the easiest way is to run the test AGAIN, which decreases the chance of error by 50%! If you run it enough times, the probability of getting an error will be insignificantly small we can basically ignore it. So if you run it 20 times, the chance of failure is 1/2^20, or 0.0000953674316%.Here is the code.I learned about how you can calculate the area of a 3D shape with disks, where you slice up the shape into disks and calculate the area of all the disks added up. The formula involves integration: Definite integral between 0 and 2 of PI times the function f(x) squared times dx.I did some problems with wave interference. I don’t know why but for some reason, the Khan Academy science course didn’t show me the quizzes and exercises the last time I learned about it… Maybe it’s new.I started doing a computing course on Khan Academy, where I learned about internet security (like HTTPS) and IP addresses (like 213.11.106.161), and a whole bunch of other stuff that I did, such as file compression and logic gates. I also saw how phishing attacks might work, and things like that. I learned about electromagnetic radiation and what it can do to living things. I also did the quizzes and Khan Academy says I mastered the course 😀I started learning about the Taylor series on Khan Academy math. The basic concept is that you take a function (like sin x) that isn’t quadratic, and you approximate it with a quadratic equation by taking its derivative a bunch of times.I watched a video about the Taylor series on one of my favourite channels, 3Blue1Brown.I tried making a Taylor series on a graphing calculator. I tried e^x, only to realize that the series for that is 1+x+x^2+x^3+x^4+… 🙁 -_-
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