I got through the first unit this week, Similarity, and started working through the next unit Right Triangles and Trigonometry but unfortunately didn’t get too deep into it. Similarity was more difficult than I anticipated. Some of the questions forced me to “think outside the box” so to speak which I found fairly tough. Although I had to work through the questions quite slowly, I got through the unit test with a 100% score on the first try which I thought was a good indication that, though I found the unit difficult, I had a strong understanding of the concepts taught by the end of it.

The first thing I learned this week was what’s known as the Angle Bisector Theorem. This theorem states that by bisecting any angle of a triangle (i.e. splitting one angle of the triangle into exactly two even angles), the sides of the two new triangles created will have the same ratio of lengths. Working through these questions, I used a lot of cross multiplying which was good practice and which I found to be fairly simple. The concept that the ratio of lengths are equal in the two created triangles when using the ABT was the difficult part for me to fully comprehend.

One of the most interesting things I learned this week, a concept which I’ve heard about and always thought was an interesting idea but never knew much about, is what’s known as the Golden Ratio. Sal spent a video going over a painting (I forget the artists name) and explained how the image used of the Golden Ratio and how it affected the look of the painting. The course didn’t get too deep into the G.R. and stated that I’ll learn more about it in future videos, but the few things I learned about it are:

• It’s denoted with the Greek Letter Phi which looks a bit like a circle with a vertical line through it.
• It’s an irrational number
• The G.R. = 1.6180339887…

I began working on the following unit Right Triangles and Trigonometry on Thursday and got through a good chunk of material on right angle triangles. I was reminded that the hypotenuse is the longest side of a right triangle and opposite the 90-degree angle. I then went through 4 videos on different “proofs” as to why the Pythagorean Theorem works. One of the videos went over a proof which was named after a 12^th century Indian mathematician named Bhaskara. Although I wouldn’t be able to reiterate his proof here, I specifically made a note to mention that his proof blew my mind. It was a video that made me think that math is cool. (Ya, you heard me.)

The unit then got into what are known as 45-45-90 triangles and 30-60-90 triangles (the numbers refer to the interior angles of the triangles) and the formulas to help find their side lengths. It turns out if you’re dealing with either of these two triangles, the lengths of the sides will always follow specific ratios. Those ratios are:

• 45 : 45 : 90
  • 1 : 1 : {2} (square root of two)
• 30 : 60 : 90
  • 1 : {3} : 2
  • x/2 : x{3}/2 : x

Using these ratios, I worked through questions that gave me the length of one side of one of these types of triangles and, through cross multiplication using the length of one of the sides and these ratios, I was able to find the length of the other two sides.

Finally, I ended the week by starting to work on trigonometry. As I mentioned at the end of my last post, I was excited to start trigonometry mainly because I think it sounds like a bad-ass subject and that I think it would be cool to be able to say “I understand trigonometry”. In the less-than 1 hour I’ve spent working on it, the few things I’ve learned are:

• Trigonometry
  • Stands for:
    • “Trig” = Triangle
    • “Metry” = Measure
  • Three parts to remember:
    • Sine (a.k.a. “Sin”)
    • Cosine (a.k.a. “Cos”)
    • Tangent (a.k.a. “Tan”)
  • How they’re applied – “Soh Cah Toa”:
    • Soh – Sin = Opposite/Hypotenuse
    • Cah – Cos = Adjacent/Hypotenuse
    • Toa – Tan = Opposite/Adjacent

At this point, I don’t understand the point of trig but find the formulas easy to remember and use. I’m interested to find out where all of this is headed and how it will apply to more difficult questions. As far as I know, Sin, Cos, and Tan all apply to the angles inside a right triangle. I believe trig will help me to find the angles inside of right triangles and the lengths of the sides but, as I said, at this point I’m not sure.

Yesterday, Jan. 26^th, 2020, basketball legend Kobe Bryant died. When I think about Kobe Bryant I immediately think about his completely unrelenting, insane work ethic. It’s easy to go online and find stories/examples of him working harder than anyone else to be the best. Recently I’ve been feeling that, though I’ve been working relatively hard to be productive and improve myself, I need to push myself harder to do more and become more self-disciplined. As I write this, thinking about Kobe Bryant, I’m feeling incredibly inspired to be like him and to push myself to work harder to become the best I can be. Whatever my equivalent to staying up all night taking jump shots is, that’s what I need to do.