The Forgotten River

Most people on the east coast of the United States will have a certain perception of a river: wide, flowing, natural, the constant noise of the water flow, the birds chirping, other animals making sounds, those kinds of things. Even on the west coast, there are still rivers such as the Colorado River, and others that fit this description, which just comes to show that there are high standards for a river in the United States. But there is one river which has been forgotten and mostly just covered up from the public outside of the city that it lives in. This is the forgotten river: the Los Angeles River.

I had been passing by the Los Angeles a River every single weekday when I went to CalState LA for my trial semester for qualifying for a program that will get me to college early. But I never noticed that I passed by the river every single time until the last two weeks. It was concrete. Like a drain. Our humanities and ecology class talked about the Los Angeles River and how it had been forgotten and how unnatural it was. It honestly just didn’t look like a river. It just looked dull. Turns out, it had been that way for around 70 years, and before it had been even worse. Before the Army Corps of Engineers decided to turn a natural river into concrete, it was disrespected. The river was polluted beyond means. The river wasn’t even used as the main water source at that point. 

But why was it so disrespected and polluted by the people back in the 20th century and late 19th century? It was because it was not respected by the Americans who came to settle in the Los Angeles area. Before the Americans came to settle, both the natives and the Spanish (later would be Mexicans) respected the river and used it as a water source. The Americans, focused on their Manifest Destiny, decided to go to war with the Mexicans, and were able to win, and they received their land in the west coast and Texas. The Americans, having such high expectations for rivers, were, quite literally, disappointed when they realized the river was more like a stream. They envisioned rivers like the Ohio or the Hudson, and the Mississippi. Instead, they were treated to this stream, and so they polluted the water, due to their lack of empathy for the river. The river was so polluted, that when the Army Corps of Engineers came along, the river was to be only used as a flood drainage system.

The Los Angeles River is forgotten by many people from the east coast and even in California. But the river was a key part in attracting settlers to settle along the river. And now, as awareness of nature seems to grow day by day, the river is more likely to be revitalized to its former state. The river may be forgotten now, but there may be a resurgence coming soon.

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The Forgotten River

Why are people’s opinions so hard to change?

We’ve all experienced this before probably at least once in our lives: you’re having an debate on a topic and you’re trying to convince someone that their side is right and their side is wrong. But it always seems to come up short.Why? Are we just incapable of saying the right words to convince them? Or are we just too tunnel-visioned to see the right perspective?

It’s a known fact that people want to be right. It makes you look credible. If you’re right, it makes you look better and everybody definitely wants to look better in front of different people. It makes you a more reliable person. But that has an unfortunate consequence that sometimes we can’t admit that we are wrong. It’s the reason why sometimes different political parties don’t compromise on decisions even when they need to. If they think they are right, then they definitely will back their opinion up.

So what do we need to do to make us more open-minded to different opinions? Simple: we need to be able to admit that we are wrong. If we admit that we are wrong, then that helps us change our opinions easier. That lets our brains know that, yeah, he’s right and I’m wrong, helping you change to that side.

It’s definitely difficult for people to change opinions just because it is hard for them to admit that they are wrong. So help yourself and widen your view. It helps everyone around you and it makes you more humble and gives you a wider view of the world.

Why are people’s opinions so hard to change?

Other interesting things about the Pythagorean theorem

I had analysed the Pythagorean theorem a bit ago and noticed a pattern and wrote a decent page on it. I liked it, and it got lots of views and I haven’t gotten that in a while. So here are some other very interesting things about this simple equation.

Apparently all Pythagorean triples are divisible by 60. Now there are proofs using number theory, all about how using modular arithmetic can be used to figure out that at least one of the numbers must be divisible by 3, 4, and 5 to figure out this. This is actually interesting, but if you want to see an actual proof, click this link:

For the proof: 000000000

Basically, there are a lot of things you can do with the Pythagorean Theorem. There are so many different proofs, different weird things, it is bizarre. If you know anything quite bizarre about any math concepts, then comment below. I hope to see your interesting topics down below.

Other interesting things about the Pythagorean theorem

The Continuum Hypothesis

So, once there was a theory proposed by Georg Cantor that proposed that there were many types of infinities, some larger and smaller than others. How does this make sense though? Enter the continuum hypothesis: an interesting way in how we think about infinity and how our brain lacks the ability to comprehend it.

So, to explain what the continuum hypothesis is, there are multiple ways we actually think about infinity, but most mathematicians usually said that there is the infinity of the natural numbers, which was the sum of all the natural numbers. That was called infinity. But as you could see, we were leaving out other numbers like irrationals and fractions and all decimals, which led to this interesting question: would there be a difference between an infinity with the natural numbers and an infinity with all positive real numbers?

Let’s describe both sides of the argument. First, it would seem clear that people that supported the continuum hypothesis thought that since there were different kinds of infinity, they should not be equal, like the example above. there would be other infinities, like all the rationals, or all the irrationals, and what if we added infinities together? These things could support their claim but there was counter evidence to also cancel this out.

People who said that this was not true looked at the fact that infinity was such a big number, that it cannot become any bigger because it was just too big. After all, most people do say that you can’t get any bigger than infinity. this is a logical conclusion and it just comes to show why this theory isn’t a theorem right now.

So that’s the gist of the continuum hypothesis. It is one of the greatest unsolved problems in math history. It is a very interesting problem ,and even though it may have no real value, it is an interesting to think about and how our brains really conceptualize infinity.

The Continuum Hypothesis

The High School Math Sequence: pt 2

So I discussed yesterday that high school math’s second and third year should be a mesh between geometry and algebra two. But what would that look like? Let’s find out what we should teach in each year and what time of the year we do it in.

So first, we should start developing and reviewing algebra one concepts in the first unit. Next, try to gt the ball rolling with quadratic equations in the next unit. Then start switching to geometry with concepts like angles and logic to help review for later reference. Next, start learning radical equations and some counting units next. Finally, finish the year with triangles.

In the second year, first start off strong by going directly into quadrilaterals and area. Next, go into exponential and logarithmic equations. Next, probably go with constructions and analytic geometry. Finish Algebra II by going into previews into precalculus and finish geometry with trigonometry.

I think this is how these two high school math courses should be like. But of course, there could be differences in when to switch in geometry and algebra, but let me know what your idea is.

The High School Math Sequence: pt 2

Which should be taught first in the high school math pathway: geometry or algebra II?

In high school, things were a lot different. Schools were different from each other and it’s just not the same as being a middle schooler. Another debatable thing is the math course geometry and algebra II. Which should come first? Should it be consecutive years in the field of algebra or a break between the algebra classes?

To first judge our answer, we must take a look at the classes before and after this weird two-year period of debate. Before taking either of these two classes, you take algebra I. After both classes, you will usually take precalculus. So, let’s take a look at these classes and see what they have in common with these two classes.

Algebra I deals with the basics of algebra, like solving equations, graphing linear equations and other basics. They are introduced to many topics that will be further elaborated in algebra II, like solving and graphing other types of equations, like quadratic, exponential, logarithmic, radical, and rational equations. Geometry, on the other hand, is more like middle school math, a year before algebra I.

Precalculus is more of a balance between both algebra II and geometry, due to the fact that calculus is a broad subject and it requires both elaborated concepts from both geometry and algebra II. Precalculus focuses usually more on trigonometry, solving harder equations, and harder geometry.

Using this analysis, putting algebra II first forces precalculus teachers to review algebra II concepts at the beginning of the year, while putting geometry first makes more sense, this puts losing key parts of geometry at risk, due to geometry being more of a memorization subject of math compared to others. there aren’t any real choices here than just to mesh them together, maybe?

There isn’t any other good way to keep students fresh on both subjects unless you kind of teach half and half in each of those two years. It can lessen review for precalculus teachers and allows students to memorize more important geometry concepts without being forced to review lots of algebra concepts. To me, this sounds like the best solution. But is this right? Well, it’s just my opinion.

Which should be taught first in the high school math pathway: geometry or algebra II?

What is needed to be a good orator?

I think most of us, especially now in schools today, are now learning that students need to learn more than just the common core curriculum to succeed in life. There are other skills that people need to be good at life. One of these skills is speech. I believe that a lot of schools now assign presentations and the students have to create their own presentations and explain them orally. But back to my question of the day: what makes a good orator or speaker?

Definitely the first thing that comes to mind is composure. If you can’t handle yourself, then how are you going to handle others watching you present? Orators with good composure can handle themselves and can correct themselves without much nerve adding on to them. They are fearless and don’t freeze up when they make a mistake, which is important, because you can make a mistake quite easily in speech.

The next important skill when it comes to speaking is the ability of speech manipulation. Now, that may seem a bit strange, but here’s what I mean: It’s the ability to control how you speak. Orators need to express themselves or make their points across and they don’t want to bore their audience. Using different voices or volumes can help separate different moods of the speech you’re saying or help draw the attention and increase your audience’s attention span.

These two traits were not the only, but definitely the most important parts of oration and, if these skills were to be mastered, the person would be a fantastic orator. It is definitely true that schools do need to teach their curriculum, but surely these skills must be just as important, right?

What is needed to be a good orator?