i can't understand math.

[1337]

I don't know what I'm doing when I study math. I just got into trigonometry and blew it. There are terms that sound weird even when pronouncing them and I don't even understand exactly what they do. This is a triangle topic, but suddenly the x,z coordinate system appears. I passed my first and second years of high school without studying mathematics or studying very little. But I'm in my third year of high school now and I'm aware that if I want to get into a good university in the future, I have to work. For example, I can learn any physics, chemistry or biology subject whenever I want by memorizing it and spending some time. But the same is not true for mathematics. I don't understand the point directly. I feel like an idiot when I don't understand the topic. I go to a relatively good high school, and it drives me crazy that even the stupidest kids around me understand math topics. If people who do not even have the intelligence to understand what is being said at once can do mathematics, this shows that mathematics has nothing to do with intelligence in the real sense. Since I am not mentally retarded, I should be able to do it. For example, I don't get bored with probability and geometry topics. I can easily understand and solve it. But I look confused at issues such as polynomials or functions. What the hell is this stupid trigonometry and sine cosine tangent? I started trigonometry for the first time today, but I seriously don't have even the slightest enlightenment in my mind. Am I unable to find someone who explains it properly or am I not studying correctly? Maybe what I do can't actually be called working. I can grasp the topics very well in a short time after I barely understand them a little. But it takes me a long time to learn that little bit. People learn a little at a time and gradually grasp it very well. But hours pass before I grasp the subject and sometimes I don't know the subject directly. This is how I spent my last year. How can I find where I made a mistake? Have a nice day

[1337]

I think the paragraph is a little long sorry about that.

[Leo Gura]

Trig is quite simple and intuitive.

If you take a circle of diameter 1 and you move your finger along that circle, if you stop at any point you can draw a line to the center. You can also draw a horizon and verticle line to the x and y axis. These three lines always form a right triangle. The ratios between the lengths and angles of three lines in the triangle vary in a very consistent and proportional way to each other no matter where along the circle you are. The trig functions of sine, cosine, and tangent simply represent the way those lengths and angles change as you move along that circle.

Trig simply allows you to predict what the lengths and angles of all the possible right triangles are for any point along that circle.

This is literally all trig is:

You are not going to be able to understand higher math (anything beyond trig) without hours of very hard rigorous study. Your days of being lazy and just winging it in math are over.

Edited September 9, 2024 by Leo Gura

[Keryo Koffa]

@Leo Gura Is Trig a prerequisite for the more advanced alien metaphysics courses at your actualized.academy?

[Epikur]

You said you are good with geometry. It seems like trig and functions are part of geomety. 

Maybe math is a sign of intelligence. In the old greece there was at the academy that said. You are not allowed to come in if you can't do geometry. That is why flat earthers can't understand evidence for the globe.




You young guys have it so much easier in many regards. You can let yourself explain it with chatgpt. There are so many online courses which explain stuff but it is definately not for everybody.




 

Edited September 9, 2024 by Epikur

[Nemra]

24 minutes ago, Leo Gura said:

You are not going to be able to understand higher math (anything beyond trig) without hours of very hard rigorous study.

@Leo Gura, did you study it, or was it part of the curriculum?

[Davino]

37 minutes ago, Keryo Koffa said:

Is Trig a prerequisite for the more advanced alien metaphysics courses at your actualized.academy?

This is not Plato's Academy

[Joshe]

@1337 Thinking back to high school, I had a hard time understand algebra because I didn't even know what it was for. All they had to do was teach me what it was and what it was for and I could have understood it much easier. 

You need to know what the thing even is, why, where and how it's applied. You need to build "structure" around the "content" for the content to make sense. 

IMO, you need to first collect as much structure as you can before manipulating the content/components.

### What is it?
- A branch of mathematics that studies relationships between angles and sides of triangles
- A tool for measuring and calculating distances, heights, and angles
- A way of understanding circular and periodic motion
- A fundamental concept used in many fields like physics, engineering, and navigation

Trigonometry is the study of triangles and their properties, especially the relationships between angles and sides.

### Essence
Trigonometry uses the properties of triangles to solve real-world problems involving distances, angles, and periodic motion.

### Practical Impact
- Used in construction to calculate heights and angles of buildings and structures
- Applied in navigation to determine positions and plot courses for ships and planes
- Fundamental in physics for describing waves, orbits, and oscillations

### Significance
- A core branch of mathematics that bridges geometry and algebra
- Essential for understanding and describing circular and periodic phenomena
- Crucial in various fields from architecture to space exploration

Now, let's address the specific questions:

### Origin and Evolution
1. Primary field of origin:
   - Ancient mathematics and astronomy

2. Evolution of application:
   - Started as a tool for astronomical calculations
   - Expanded to navigation and land surveying
   - Now used in physics, engineering, computer graphics, and signal processing

3. Key figures:
   - Hipparchus (ancient Greek astronomer)
   - Ptolemy (Greco-Roman mathematician)
   - Aryabhata (Indian mathematician)
   - Leonhard Euler (Swiss mathematician)

### Fundamental Understanding
4. Fundamental purpose:
   - To solve problems involving triangles and circular motion
   - To calculate unknown distances or angles using known information

5. Key components:
   - Sine, cosine, tangent functions
   - Radians and degrees
   - Right triangles and the unit circle
   - Trigonometric identities

6. Understanding context:
   - Can be understood on its own for basic applications
   - Part of a broader mathematical framework for advanced applications

### Current Applications or Manifestations
7. Relevant industries/fields:
   - Engineering (all branches)
   - Physics and astronomy
   - Computer graphics and game design
   - Navigation and GPS technology
   - Architecture and construction

8. Top 3 practical applications:
   - Calculating distances and heights in surveying and construction
   - Modeling periodic phenomena in physics and signal processing
   - Determining positions and trajectories in navigation and space exploration

9. Practical engagement reasons:
   - To solve real-world problems involving angles and distances
   - To model and analyze cyclical or wave-like phenomena
   - To perform calculations in fields like engineering and physics

### Users and Adoption
10. Primary adopters today:
    - Engineers, physicists, and mathematicians
    - Computer graphics programmers
    - Surveyors and architects
    - Navigation specialists

11. Usage breadth:
    - Widely used in STEM fields and related industries
    - Taught in secondary and post-secondary education globally

12. Prerequisites and barriers:
    - Prerequisites: Basic algebra and geometry
    - Barriers: Abstract nature, need for practice to master

### Teaching and Dissemination
13. Teaching methods:
    - Standard part of high school and college mathematics curricula
    - Textbooks, online courses, and educational videos
    - Practical exercises and real-world problem-solving

### Significance and Impact
14. Problems addressed:
    - Calculating unknown distances or angles
    - Modeling periodic motion and waves
    - Navigating in three-dimensional space

15. Main strengths:
    - Provides tools for indirect measurement
    - Enables analysis of circular and periodic phenomena
    - Bridges geometry and algebra in powerful ways

16. Broader impact:
    - Foundational for many areas of science and engineering
    - Essential for modern navigation and spatial technologies
    - Key to understanding wave phenomena in physics

17. Expert regard:
    - Highly regarded as a fundamental mathematical tool
    - Considered essential in many STEM fields

### Related Concepts and Terminology
18. Top 10 jargon terms:
    - Sine, cosine, tangent
    - Radian
    - Unit circle
    - Pythagorean theorem
    - Trigonometric identities
    - Inverse trigonometric functions
    - Amplitude
    - Frequency
    - Phase
    - Periodic function

19. 3 most closely related concepts:
    - Geometry
    - Algebra
    - Calculus

### Criticisms or Limitations
20. Main criticisms/limitations:
    - Can be abstract and difficult for some students to grasp
    - Limited to Euclidean geometry in its basic form
    - Computationally intensive for complex problems without technology

### Future Directions
21. Key areas for exploration:
    - Applications in quantum computing and cryptography
    - Integration with machine learning and AI algorithms
    - Development of more intuitive teaching methods using VR/AR technology

 

[Keryo Koffa]

45 minutes ago, Epikur said:

You young guys have it so much easier in many regards. You can let yourself explain it with chatgpt.
There are so many online courses which explain stuff but it is definately not for everybody.

That's a teacher competence aspect, not an existential reality.

Reality is: you understand geometry intuitively, that's how your mind simulates the world.

The problem is translating that understanding into skillful cognitive overlays.

Everything is geometry, intelligence is just paying attention.

[Jacob Morres]

51 minutes ago, Epikur said:

You young guys have it so much easier in many regards

Yeah but at the same time, so does everyone else. It increases the skill needed to be competitive when everyone has access to the tools 

[Joshe]

This might help: https://brilliant.org/courses/trigonometry/

[Keryo Koffa]

I gotta sleep but I like condensing stuff, here's my 1% brainpower quick summary because it was unreasonably long

5 minutes ago, Joshe said:

@1337 Lemme help ya get this crap

What? part'a maths measuring shape ratios & circles waveyness to construct n' navigate stuff
Signi: glues shapes n' equations, cycles, architecture & mars rockets
1. origin: greeks & stars
2. evolution: astrolognomy, make maps, now pixels & tech
3. pioneers: Hippo, Pito, Arya, Leo, I mean Euler (maths people)
4. purpose: measure stuff
5. components: triangle sides, angles etc.
6. context: apply math, basic & less-basic
7. Relevant: engineers, astroneers, IT guys, gps tools, architecs
8. practical apply: construction dist., cyclical stuff, space!
9. reasons: *already mentioned*
10. adopters: *already mentioned*
11. Usage: STEM, highschool
12. Prerequies + barriers: construct equation-awareness, too abstract
13. methods: school textbooks, youtube, workshops
14. Problems: unknown dist., waves, 3d
15. strengths: ∞ measuring overlays + *already mentioned*
16. impact: *already mentioned* + physics
17. Expert: elementary, watson!
18. jargon: co/sin/tan, rad, abc², equi, inverse, Frequency, Phase
19 Shapes, Equations, Gradients
20 Nays: hard, no hyperbolic fun, blows AIs RAM
21. Legacy: Quantum woo-woo, AGI, meta-learning

[LastThursday]

It really depends on working out how you learn best. Do you like diagrams, do you like doing practical experiments, do you like to be told stuff? Sometimes stuff only clicks once it's presented in the right way. Sometimes stuff only clicks if you go over it a thousand times, it can vary a lot. If your teachers are not helping, then you'll have to either find a mentor or go find things out for yourself.

As Leo says, all trig just boils down to right angled triangles inside circles. More importantly it is about RATIOS a.k.a fractions. All trig functions are just ratios of things. Each trig function is based on an angle, it gives you the RATIO of two sides for a given angle. There are three sides to a triangle, if you pair up the sides there are three pairs, so there are three functions: cosine, sine, tangent - one for each pair. Each pair can also be reversed to get the reciprocal of those functions: secant, cosecant, cotangent. So just memorise which pairs give you which functions and you'll be nearly there (hint use the right angle as an anchor point).

If you're practically minded go out and measure height of a building using trigonometry, to get a feel for it.

[Joshe]

52 minutes ago, Keryo Koffa said:

I gotta sleep but I like condensing stuff, here's my 1% brainpower quick summary because it was unreasonably long

Thanks! That duplicate info is a problem with my prompt. I'll have to fix that.. Good to know you have a compulsion to organize and condense information. I could make use of that 😉

Edited September 9, 2024 by Joshe

[Ero]

4 hours ago, Keryo Koffa said:

@Leo Gura Is Trig a prerequisite for the more advanced alien metaphysics courses at your actualized.academy?

It is the first encounter of periodic functions (one period). Wait till you discover elliptic functions, which are doubly periodic in complex space - they serve as the foundation for modular forms and many hyperbolic geometries - that’s where you will find the aliens, having mastered the curvature tensors👽

[Keryo Koffa]

[Michael569]

13 hours ago, 1337 said:

If people who do not even have the intelligence to understand what is being said at once can do mathematics, this shows that mathematics has nothing to do with intelligence in the real sense.

The ego doesn't like to be shown its inadequacies so the ego creates a delusional fantasies about the subject of interest having nothing to do with reality because it hurts less that way. 

How do you know those "less intelligent" do not spend hours in self study which is why they get it and you don't. 

Swallow your pride and if you really care about understanding math, do more home studying. If you don't care, do bare minimum to get by, just don't point fingers and blame the system, the intelligence of others and the teachers. 

Take responsibility, study harder, get private tutorship if you must, ask a friend for a help in exchange for something you're good at.

This is a phenomenal lesson for you and one that has proved true over and over in my life as well as I watched how all of us 90s kids progressed through life. Some who were exceptionally smart in the elementary and high school and got used to passing by didn't make it far in life. Others who were a bit slower and got poorer grades learned early on that unless they do 5 times as much they won't pass, In the end it was those who were consistent in their approach not those who got used to passing by effortlessly who got further in life because that sort of mentality then penetrates in other areas of your life - your finances, your health, your personal development, your relationship, your family. You realise that unless you work consistently on things, you don't ever get results or only unsatisfactory results. 

Life rarely gives you things because you are blessed with some natural intelligence, life gives you thinks because you put time, energy, willpower and soul into something and do it consistently and repeatedly for years, specially the boring mundane tasks such as taking trigonometry exercises 30 minutes a day for a whole month in order to advance your knowledge. 

And so once you embrace that mentality, you become unstoppable. And even tho it takes you longer than others who were maybe more intelligent to achieve results, when you do, those results last longer because you had to build up your entire character and you had to develop yourself around those problems and that cannot be taken away from you. 

Edited September 10, 2024 by Michael569

[1337]

@Leo Gura Thank you for the explanation. gif helped. I studied a little more today and I think I'm slowly starting to understand the subject. At least I don't look at the screen like an idiot anymore when I see trigonometry

@Epikur I heard that trigonometry is also a part of geometry, but we never had to use it until now, and it was not in our curriculum. I think I opened this post in a bit of a hurry. Yesterday was the first day of school and I wanted this year to be epic in terms of classes. I was a little devastated when I came home and sat down to study mathematics first thing, and then found myself looking at strange terms that I didn't understand. Now I'm slowly starting to understand the issue. I felt like an idiot when I didn't understand it the first day. Everything is fine now, about trigonometry

@Joshe Thanks for the link. As far as I can see, the course is free, right? For now, I will look at the trigonometry subject explanations in my native language, but thank you anyway. I have difficulty understanding subjects such as mathematics or physics when I listen to them in English.

17 hours ago, LastThursday said:

If you're practically minded go out and measure height of a building using trigonometry, to get a feel for it.

I always wanted to do this when I was little, but I didn't know how. If I leave the house, I will definitely try it But for now, I'd rather be equipped with theoretical knowledge and solve tests I don't like going out. But I'll try this tomorrow while I'm already out during lunch break at school.

7 hours ago, Michael569 said:

How do you know those "less intelligent" do not spend hours in self study which is why they get it and you don't.

Yes, many of them make serious efforts at home, but they also seem to grasp the new topics covered in class very quickly. Maybe you're right, my ego might just be making excuses. There are general reasons why I say "less intelligent". I really don't judge people by calling them stupid. That would be childish. Probably anyone in the world can learn enough mathematics to get into a good university with enough study. While writing this, the idea that I was deceiving myself became more prevalent It's best to keep working. I wish you a good day.

[Judy2]

maybe you can try to find a tutor from a higher grade?

[1337]

@Judy2 Good suggestion but expensive. I get a weekly allowance of $15 from my family. Even if I agree with a 12th grader for a lesson, he will ask for at least 15 dollars per lesson I tried Khan Academy today. He explains it very well, I will finish the topics for now and solve a lot of questions. If I solve many questions, I will probably reinforce the topic. But still thanks for your suggestion. Have a nice day