geometry-and-trigonometry

[exotic yarrow]

,w tan x+cot x=4

[somber coyote]

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[exotic yarrow]

[long geyser]

Exactly!

i really love geometry, i just proved to myself what the missing side length of a rectangle has to be to fit a rectangle with a perimeter of 16 units based off of the information that one of its sides is 3 units wide.

That same logic can be applied to anything and everything, an angle for two lines can't exceed 180 degrees because of the underlying definitions. You can deduce things and induce things using knowledge that you know and don't know.

Maybe I'm just late to the party but does everyone see it like that? That picture applies to many other aspects outside of math/just-drawing-stuff on graphs

[long geyser]

i feel like i got reincarnated as aristotle by learning what i know so far in school

[wanton yacht]

Some people can do it better than others

[long geyser]

mhm

[long geyser]

this is so much fun!!! this is just like a puzzle

I don't understand why the long line in a triangle for example has a decimal/fraction for it's length, intuitively wouldn't it be a whole positive integer?

[wanton yacht]

Would it have a whole length?

[long geyser]

i mean whole integer

[wanton yacht]

Yeah, would it?

[long geyser]

Hm

[wanton yacht]

What if you rotated it to be in line with one of the other sides?

[long geyser]

well take a wall for example and a ground, if you want to calculate the length of something leaning on it then it would be like duplicating the wall or the ground and rotating it in a direction

[long geyser]

it has to be longer than both individual sides

because otherwise it won't connect both points

[wanton yacht]

Right. Who's to say its length should be an integer though?

This is the idea of the pythagorean theorem

$a^2+b^2=c^2$

[somber coyote]

pebble

[long geyser]

nobody i just mean intuitively it's a bit odd if you don't think about it and randomly see it and then you ask (Why is it a fraction/etc?)

[wanton yacht]

Yeah, I get that.

[long geyser]

Well the pythagorean theorem only matters so long as we can use it right? so long as we have constructions such as lines and coorinate planes right? i mean not necessarily the latter but maybe you get what i mean?

[wanton yacht]

I mean, you can calculate the distance between any two points using it as well

[long geyser]

i suppose my relevance to that is that you're bringing the Pythagorean theorem into discussion but what if you didn't already know it?

[wanton yacht]

Mhm

[long geyser]

Yea! but i think that's a property of math rather than um

[wanton yacht]

I can see how it would be a little confusing, in which case, it's time to learn it!

[long geyser]

im not sure

[long geyser]

I've learned it before and i know it and i've used it but, i think as with many other formulas it's better to get an idea or grasp on the whats and whys first

before you generalize something

right?

[wanton yacht]

I generally agree with that. That's what I always try to do with physics. Getting an intuitive understanding of what you're doing and why you're doing it and why it works helps you better understand and solve new problems.

In that way, it's less formulaic and more logical

[long geyser]

i suppose an analogy to this is that you're telling me what f(10) in a formula is, but generally you start with the first integers of a function and expand from that/generalize

[long geyser]

Absolutely

i watched a video of a math teacher explaining that if you think calculus is just formulas then you don't know calculus

as in calculus is the study of something specific

rather than just a bunch of operations abstractly

[wanton yacht]

Yeah, I think calculus is a good example. You can understand the definition of a derivative, you can learn the formulas for differentiation, and then you can learn integration, but if you don't understand what those operations represent, it's no good, you can't apply it to anything. That's another thing I like about physics, it takes these ideas and applies them directly to the real world in ways that make it clear what calculus is useful for.

[long geyser]

If we label these coordinates as A, B, and C respectively, then we can devise properties about these vertices and the whole shape through the tools that we've built before

[wanton yacht]

Yep

[long geyser]

Yea

[wanton yacht]

That triangle specifically is special though because it's a right triangle.

[long geyser]

I suppose any triangle is special then, because the angles stay the same no matter what in math, i mean 90 degrees isn't the same as 110 for example of course but a triangle with a certain degree still has properties such as adding up to a certain degree right?

[wanton yacht]

I mean, in Euclidean geometry with shapes that have straight lines, all triangles will have angles that add up to 180 degrees, sure. You can have a right triangle with one of those angles being 90 degrees, you can also have other triangles where that's not the case, in which you can always break the triangle that's not a right triangle into two smaller right triangles by constructing a line perpendicular to one of the bases and having it intersect the opposite vertex.

[long geyser]

i'm feeling way more comfortable with the coordinate plane and points on the plane and what happens to them now that i'm learning geometry, because before it was scary and i didn't know a ton of these properties that i'm learning in geometry such as rules of lines maybe

[wanton yacht]

Lol ,yea

Just wait until you get to trig, that's fun

But anyway, what makes a right triangle special is that the basic trigonometric functions apply to them nicely

[long geyser]

Yesss, but i suppose that in the same vain trigonometry is just geometry but one that deals with "tri" or triangles, so 3 angles.

[wanton yacht]

Yeah

[long geyser]

i think i understand a bit

[wanton yacht]

Yeah... in situations like this it doesn't hurt to have a white board, lol

[long geyser]

Yea that's what i meant, so i think "anything" can be special because yes it would be "nicer" for trigonometry and stuff, instead of having to make like 14000 different stuff that you have to memorize

so it's definitely special in the case of studying trig and implementing it

but in general, angles probably don't care about what you call the shape right?

[long geyser]

Yea it's just i haven't seen lots of those words in action before

[wanton yacht]

Right. An angle is only between two lines

I gotcha

[long geyser]

i suppose that the study of geometry is the properties that this has when we for example add another line etc or close an object

because we start with certain premises or axioms, in euclidean geometry. Correct?

[wanton yacht]

Yup

[long geyser]

yea

[wanton yacht]

And then if you do spherical or hyperbolic geometry you change those a bit to get different behaviors

Veritasium makes a good video on that

[long geyser]

ooo

[wanton yacht]

https://www.youtube.com/watch?v=lFlu60qs7_4

[long geyser]

i've seen this video before

a while ago

[wanton yacht]

Yup

[long geyser]

omg i remember i didn't understand a lot of geometry, but now i'm doing some geometry in general

[wanton yacht]

I mean, you probably should get through a bit more euclidean geometry before you worry about noneuclidean geometry, lol

[long geyser]

Yea

in higher level math euclid's axioms are replaced right?

with high level math logic?

ZF and ZFC

[wanton yacht]

I'm not entirely sure. From what I gather, the axiom that says that lines can only have parallel line is changed to where lines can either have no parallel lines, or multiple parallel lines.

[long geyser]

no i mean as a whole

in mathematical analysis

https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

maybe this?

[wanton yacht]

Maybe?

I haven't learned any of that yet, lol

Mathematical analysis from what I understand is more deriving formulas rather than just memorizing

[long geyser]

my friend told me it's like useless to for anyone other than someone like specifically studying this or something that needs it

[wanton yacht]

yeah

I've mostly just done more applied math for my physics courses

[long geyser]

i can't wait to reinvent the wheel for so many formulas!

it's like a puzzle

no, it is a puzzle!

[wanton yacht]

Lol. It's fun to do

[long geyser]

Fair enough

[long geyser]

Yes! it stimulates my brain so much!

[wanton yacht]

I will say, it's even funner to do when you're finding formulas that nobody has found before on the front lines of math and physics

[long geyser]

That can take a while

and what if you reach dead ends

I mean, you're bound to realistically, even way before your journey to discover something new

But road blocks haven't stopped society as a whole from developing new things, new ideas

i sometimes forget formulas for algebra and i'm at a bit of a dead end, but then i can just remember them or find a new path

in algebra, multiple paths lead to the same solution, and one answer has multiple paths that can be taken to achieve it

or i can ask those more knowledgable than me for help, etc

[wanton yacht]

Yeah. There's always dead ends that you will come across, but that's what makes it a challenge. I imagine what people like Einstein and Shrodinger had to go through when they made breakthroughs in their field. Up until them, our standard physical model of the universe only described some things with good accuracy, not all things with perfect accuracy. Will we ever get to that point? I don't know

[long geyser]

People like these spend years studying something specific, sure they did this over 80 years ago, but they spent each day thinking about the same thing rather than in 1 second simply find and formulate a solution because they wished to

[wanton yacht]

yep

[long geyser]

it doesn't matter whether i wish to find a solution to a simple quadratic equation, it exists whether or not i like it, and i have to respect its properties to find it, so i have to actually do work and thinking

i suppose this could maybe be generalized even further, such as if i'm a mathematician and i want to discover something new

[wanton yacht]

Yeah, I mean, geometry, algebra, calculus, linear algebra, these are just tools for these problems. That's how I like to imagine it

[long geyser]

Precisely

i was talking with my brother today, and he told me about how in his time when he was learning geometry and trig it wasn't as easy as now because he's revisited them and seen why for example the identities work and why they were created

i believe that's the only way to master something, it's to essentially discover it for yourself

seeing why it works

knowing what happens when you change something, etc

[wanton yacht]

Yeah, that's a good way to look at it. That's why I said desmos would be really good to learn from because it forces you to just play around and see how things work yourself

[long geyser]

Precisely!

[wanton yacht]

See how different variables change things

[long geyser]

Yes

[wanton yacht]

I mean, I think that if you can teach yourself things, you'll probably know them better than if you only learned from someone else. I'm not saying you shouldn't learn from other people, in fact, people are a great resource! I think you should find ways to do both. That's what I do in physics. If in class we learn something from our teacher that I don't fully get, I take it upon myself to figure it out. That's what works for me, and I think I probably have a better intuition for things than most kids in my class, which shows on my test scores, yada yada.

[long geyser]

It's doing both that gets you to heights that people back then with no resources and were pioneers could only dream of

[severe crypt]

not replaced, Euclid's axioms are for geometry and geometric consructions. ZF axioms are for set theory

[long geyser]

Ahhhh

Thank you, i see

That's mind blowing to me

[long geyser]

it's so hard for me to reinvent the wheel, but if i get tools from teachers and tutors then i can have a better understanding of formulas etc

i'm not a genius in every subject, nor was someone like Euclid

[wanton yacht]

Yeah, it's definitely more difficult to discover things yourself, but when you think about it, that's all that matters. Soo, yea

I mean

I guess discovering new things and applying what we already know to things like engineering, what not

[long geyser]

Yea

i want to cry so bad, because geometry is the most beautiful thing ever to me. it doesn't simply just exist in pen and paper, but it's all around us if you think about it

and i don't just mean houses and cities, but trees too, and stars

it's really symmetric

[wanton yacht]

Math is all around us, always

[long geyser]

Yea!

[wanton yacht]

...

[long geyser]

im sorry

[wanton yacht]

Sometimes I feel that way too, lol.

[long geyser]

i've spent all of my aware life (since i started thinking) viewing objects and symmetries

the neurons in my brain abstracted and quantized things around me into variables and sets

There are so many types of trees for example, but they're all under the set "tree"

[wanton yacht]

Yup

That's good

[long geyser]

i feel like i'm a reincarnate of philosophers of the past. i feel like when i'm not in the earth anymore that my legacy will still persist, that people will still try to figure out things

[wanton yacht]

Yep

[long geyser]

is this essentially math

[wanton yacht]

There will always be that human curiosity

[long geyser]

Yea

Biology

[wanton yacht]

I think the reasoning you need to do math is very structured like how you're describing. I think reasoning like that helps with things other than math too, like programming, engineering, etc, which aren't all just math subjects, but, they're related

[long geyser]

Yes

[long geyser]

I really advise this article that i recently found, it's like a metapsychologist wrote it https://www.britannica.com/topic/thought/Creative-thinking

i dont agree with everything in it personally, but it's so interesting to think (wow) that my thoughts (ironically) are in some way supressed actions/behavior

when you think in your head, you suppress your tongue a bit from talking because you don't want to verbally talk

[wanton yacht]

I'll check it out

[long geyser]

i think this is a bit relevant to geometry in that we think a ton, and so we problem solve, we try to figure out new approaches based on stuff that we've already seen

does that ring any bells /genq

[wanton yacht]

Yeah, that about summarizes things. At least in my own experiences, I find that my solutions seem inspired by what I already know, which is sometimes good, sometimes it worries me because sometimes solutions demand completely different perspectives, and those take time to come up with.

[long geyser]

Someone like me doesn't always mind that though. Although some people prefer not to think, I despise those kinds of people (even though i'm usually very lazy) those people are not lazy but just refuse to think

[wanton yacht]

Lol, I know what you mean

[long geyser]

Yea, do you think geometry has a ton to do with problem solving in general?

[wanton yacht]

I think it depends on the kinds of problems you're doing and the type of experience you have in geometry

[long geyser]

i see, so then would you say something like just applying a formula that you already know be less problem solving and more just time?

But if you're trying to invent something from scratch logically, then that's as problem solving as it gets?

Maybe?

[wanton yacht]

If you know little to no geometry and you're doing geometry, even simple problems, there's lots of problem solving to be done. If you know lots of geometry and you're doing simple problems, there's probably not as much problem solving being done. If you know lots of geometry and you're doing difficult problems, then there's plenty of problem solving to be done. As for whether I think applying a formula that you already know, I think that depends as well on the complexities of the specific problem you're trying to solve.

[wanton yacht]

Yes

[long geyser]

Yea!!!!

Honestly yea, it just depends.

Some formulas are just plug and play while others still require like doing a lot of algebra for example, right?

[wanton yacht]

Yeah. But sometimes it is good to practice and play around with formulas you already know, especially if you have ideas you want to try with them

[long geyser]

Mhm! After all, we still haven't discovered everything about math

Right?

[wanton yacht]

Well, I don't know if I would describe it like that. It's not like math is discovered, it's created

[long geyser]

Even on an individual level, probably nobody knows everything about math right?

[wanton yacht]

Yea

[long geyser]

i believe it's both. in some really vague sense 🤷‍♀️

[wanton yacht]

Maybe. In the context of physics, I think it's a better perspective to have that mathematics is a tool used for modeling the universe. Our models aren't perfect, they're just theories that experiments seem to align with, and they can be improved. Whether it's discovered or created, well in this context, I would say it's more accurate to say that math is created for the purpose of creating better and better models.

I mean

however you want to look at it I suppose

[long geyser]

But either way, with our axioms there's still a lot of properties that we don't know the solutions to right? maybe like complicated things that we only have approximations for possibly?

[long geyser]

Sure

[wanton yacht]

Yeah, like the Riemann hypothesis, lol

[long geyser]

Interesting

[wanton yacht]

Nobody has proven the Riemann hypothesis, in a sense we don't know 'the solution' to it

[long geyser]

Right

This is the most interesting stuff ever though

do you love geometry

since you practiced in desmos too

[wanton yacht]

I would say I love geometry, yea

[long geyser]

Nice!

[wanton yacht]

It is very interesting, lol

[long geyser]

idk why but i used to draw random shapes in my art notebook, i don't mean random shapes but like for example a pentagon with circle tiling's inside of it, and a circle with pentagon tiling's inside of it etc, and colored them

Since i was really young i was interested in shapes!

i suppose because it's easier than just randomly being able to draw whatever you want perfectly

Like if you want to draw a tree as perfect as possible from one angle

But a tree can be seen from multiple vantage points

[wanton yacht]

Sounds like fractals

[long geyser]

When i was a bit older, i started drawing those

Like infinite triangles, infinite pentagons stacked inside of each other, etc etc

[wanton yacht]

Yupp

Or like the Mandelbrot fractal

[long geyser]

it's the coolest thing ever to me!

[long geyser]

that one is terrifying to me, the black areas

i'm scared of darkness and voids, that's my biggest fear

[long geyser]

But the colorful areas that show amazing geometry is the coolest thing ever!

[wanton yacht]

Hm, well unlucky for you most of the universe is just a dark void full of ionizing radiation

[long geyser]

The mandelbrot fractal is in the complex plane correct?

[long geyser]

Does that mean it's in 4d?

[long geyser]

Yeah but the thing is that's only because it's dark to our eyes, in reality it's the most beautiful thing ever, minus black holes

black holes are the scariest things ever

light doesn't enter them from our perspective

[wanton yacht]

No

[long geyser]

Can you render the mandelbrot set in 3d and travel in it with a 3d camera?

[long geyser]

oo

[wanton yacht]

Yep, that's relativity

[wanton yacht]

Maybe, I haven't looked into it

[long geyser]

What do you think is at the other end?

[long geyser]

that'd be so cool!!!!! it'd be so nice to the eyes!

[wanton yacht]

It's probably just a super dense ball of neutrons to be honest

[long geyser]

Makes sense!

[wanton yacht]

I'm not really sure what would happen to matter if it's that dense

[long geyser]

Another universe?

big bang?

[wanton yacht]

No idea

[long geyser]

black holes have a really long lifespan right?

[wanton yacht]

I mean, relative to what?

[long geyser]

to the time axis?

[wanton yacht]

I think if you compare relative to other types of stars, yea

[long geyser]

when values explode in the complex plane, is that like a big bang?

[wanton yacht]

What do you mean by explode in the complex plane?

The complex plane is just one that is perpendicular to the positive and negative number line

[wicked peak]

help 💔

[long geyser]

how is this not just 3d

[wicked peak]

i did

[long geyser]

there's a million dollar check to the person who solves it

[wanton yacht]

I think they define like 3 different imaginary numbers that are all kind of perpendicular to each other

[wicked peak]

bro answer my question so i can leave you

[wanton yacht]

In that regard, you can make it as many dimensions as you want

[wanton yacht]

I will

damn

[wicked peak]

hurry

[wanton yacht]

What is this for the SAT? lol

[wicked peak]

yur

but listen its an ego thing lets not bring it up

pretend im einstein

[wanton yacht]

ughh I haven't solved a problem like that since I was in geometry

Let me sketch it out

[wicked peak]

good

job

[long geyser]

That's insane!!!! 🤯

[wanton yacht]

Come on it's not that hard, GM and GN are of length that's equal to the radius

[wicked peak]

its easy ik but i cant get it

bruh what

whats the answer then genius

[wanton yacht]

I could be wrong, I haven't really looked into it much

I just know things like Quaternions use multiple imaginary numbers

[long geyser]

But it's still probably something like that even if that's not correct

[wanton yacht]

yeah

[wicked peak]

on gang you're no help

[long geyser]

the help channels are really good!

you can try one too

[wicked peak]

this is the geometry and trig channel and you guys are over here talking abt your love for geometry i dont get it

[long geyser]

i get help there all the time

[wanton yacht]

I'm thinking, lmao

[wicked peak]

forget i even asked someone my age got it in 2 seconds

[long geyser]

i LOVE geometry

[wicked peak]

with all due respect

[long geyser]

You're really mean

[long geyser]

So rude

[wanton yacht]

Ahh, yep

I think I got it

[long geyser]

you're really nice!

[wicked peak]

im not i said with all due respect

[wanton yacht]

Meh

[wicked peak]

see im respectful

[long geyser]

mhm mhm...

[wicked peak]

bro take this to the dms

[wanton yacht]

You have the radius, you have the perimeter, you can solve for the distance between M and H, and since angle GMH is 90 degrees, you can just use pythagoreans theorem, right?

[long geyser]

I haven't done geometry before and I can probably solve this if i tried. are you too stupid to solve this yourself?

What use is bickering with your fingertips if you can't even solve a simple SAT question

[wanton yacht]

Haha

[long geyser]

You have access to the internet yet you can't solve this.

and on top of that you are rude to others

You're pathetic

[wanton yacht]

lol

That was a fun little problem, that honestly woke me up

[long geyser]

my heart rate is really high

[wicked peak]

degrees has nothing to do with this

[wicked peak]

bro what

[long geyser]

How old are you?

[wanton yacht]

What are you talking about?

[wicked peak]

why are you talking look at your bio 💔 chronically online ahh

[wicked peak]

67

[wicked peak]

90 degrees has nothing to do with this because the rectangle is inscribed into the circle

[wanton yacht]

No it doesn't...

H is outside of the circle

[long geyser]

So insolent

[wicked peak]

you would do patheogrean theorm and do 168+168 which is 336 i forgot the whole number subtract that from 3368 (something like that) and you would square both (adding them of course) and then square root then the answer is 1768

[wicked peak]

took bro a while to google the word

[long geyser]

you couldn't google this?

[wicked peak]

what

[long geyser]

What does that say about your brain?

Tell me

[wanton yacht]

That's what I did

lol

Anyway

[wicked peak]

you just used keywords "distance" "radius" 90 degrees which you said it was which it is

nt

[wanton yacht]

What?

[wicked peak]

saying its 90 degrees would make it an isolesce triangle and its not

[long geyser]

the next time you look at a mirror, remember what you are, okay?

[wicked peak]

even if u cut the rectangle

[wicked peak]

.

[wanton yacht]

First of all, draw a picture of the situation and lets see if we agree

[wicked peak]

im quite fond of myself

[wanton yacht]

Because you said the quad is inside the circle, I'm saying it's not entirely inside

[wicked peak]

i gave u the steps to my own question bros cooked 😭😭

[long geyser]

i wouldn't have guessed, now do that alone.

[wicked peak]

its A RECTANGLE

[wanton yacht]

I already got the right answer, what?

[long geyser]

You are a disgrace

[wanton yacht]

No it's not LOL

[wicked peak]

read the question

bros stupid

[wanton yacht]

???

[long geyser]

Please ignore them @wanton yacht

[wanton yacht]

Are we real?

[long geyser]

they're a waste of time

please

[wanton yacht]

Clearly

Anyways

I was going to say, yeah, I think we just define i, j, and k as all between positive and negative 1, they're just all perpendicular to each other

[wicked peak]

its ok continue talking to an underage girl

[wanton yacht]

That's how quaternions work

[long geyser]

you can't insult someone and expect them to help you

[long geyser]

you have eyesight but for how long?

how long can you have pupils for?

[wicked peak]

aurora hop off

shes going insane

or

he

idk

[long geyser]

Why are you looking at your screen right now?

Tell me

[wicked peak]

because i can!

❤️

[long geyser]

ok

[wicked peak]

im ragebaiting dont take it to heart

anyways

bye

[long geyser]

bye

[wanton yacht]

👋

[long geyser]

raising my heartrate for what

im shaking

[wanton yacht]

It's all good

Everything is fine

[long geyser]

im just a blowfissh

im weak

[wanton yacht]

You get used to it

[long geyser]

i hope i wnt have to interact with someone like that agian

thats insane

so disrespectful at the start

insane

[wanton yacht]

Yeah, I mean, this world's full of people like that soo

Good luck

[long geyser]

true

:((

[wanton yacht]

But that was a fun little math problem

[long geyser]

Yea!

[wanton yacht]

I remember struggling with problems like that when I took geometry, but I solved it really easily

[long geyser]

outside of their bickering, it was nice

[long geyser]

it's so beautiful the symmetry of problem solving

[wanton yacht]

Yeah

I think doing physics has helped me with my geometry

[long geyser]

Nice!!

[wanton yacht]

In physics you have to do a lot of vectors and lines and trigonometry

[long geyser]

interesting

are vectors part of geometry?

[wanton yacht]

Technically yes, but I'm not sure if you would learn them in a geometry class.

[long geyser]

i see

[wanton yacht]

You more learn them in a physics class, or like a linear algebra class

[long geyser]

mhm

[wanton yacht]

A vector is just a coordinate though

[long geyser]

from the origin?

[wanton yacht]

Well, it could be, but usually we write them as being relative to another point

[long geyser]

oooo

can you describe the motion of someone through vectors and a 3d axis?

[wanton yacht]

Yea

[long geyser]

thats insane

[wanton yacht]

I mean, think about it, they have a position, that's clearly a coordinate in space. Then they might have a velocity which a vector representing how their position might change over a given unit in time, which is also a vector, then you have acceleration which represents how velocity changes over time, (how much they speed up or slow down.)

[long geyser]

Right!

how about the movement of the sun and earth and other planets

[wanton yacht]

Yep, you can describe all of that with that sort of stuff

[long geyser]

trajectories too?

[wanton yacht]

Yup

That's all physics

[long geyser]

whats the relation between physics and geometry

[wanton yacht]

It's hard to explain, it's kind of something you have to see for your self through examples. Most physics problems involve trigonometry because you have to consider like, just the x coordinate of a vector or something, and if you only have a magnitude and an angle, you need trigonometery for that

[long geyser]

i see!

[wanton yacht]

But then there's geometry in calculating things like moment of inertia, you need sometimes the areas or volumes or different objects, things like that

[wanton yacht]

But I mean, there's multiple different ways to write the same problem. For example, this COULD be explained using vectors, forces, velocities, etc, but it could also be explained using relativity and curved spacetime.

And it could also be explained using energy and lagrangian mechanics which is completely different than newtonian mechanics

I mean, it solves the same thing, but it does it using energy instead of forces

[long geyser]

and how about just a 2d graph and an ellipse?

[wanton yacht]

Yeah,

[long geyser]

ooo

[wanton yacht]

If I recall correctly, showing that the trajectory for a planet around its orbit to be elliptical is actually pretty difficult though

[long geyser]

did euclid have a z axis back then? for pyramids and cubes?

[wanton yacht]

He probably considered it

[long geyser]

i see

[long geyser]

did he know that pyramids existed?

the 3d pyramid

[wanton yacht]

Are you talking about like a geometric pyramid?

[long geyser]

Yes

and a cube etc other 3d objects

[wanton yacht]

I mean, I suppose he might have considered them

[long geyser]

right

did they only do 2d stuff?

[wanton yacht]

Maybe. I'm not sure

[long geyser]

Fair

do you play with the z axis in high school math?

or is that only in calculus

[wanton yacht]

Uhh, I mean we've talked about how to do like vector calculations for vectors that have higher dimensions than 2d, and it comes up when you're doing things like cross product in physics, but it mostly shows up in Calculus 3 and beyond

Lots of applied math in AI and what not involves many more dimensions than just 3 though

[long geyser]

Wow

is that harder

[wanton yacht]

No

The jump from 2d to 3d just adds one more coordinate component. The jump from 3d to 1000d just adds more and more components, but all the math is the same.

[long geyser]

i see

n d?

[wanton yacht]

Yep

[long geyser]

Nice!

.5?

[wanton yacht]

Hmmm

Maybe

Not sure how fractional dimensions really work

[long geyser]

this is so insane

[wanton yacht]

Yep

[long geyser]

does gravity work like this

[wanton yacht]

I've never really thought about it like that

I don't really know to be honest

[long geyser]

Fair!

i want to learn all about this

[wanton yacht]

Shoot for the moon land among the stars

[long geyser]

exactly

[wanton yacht]

I had that same thought when I learned that quote

[long geyser]

Tysm for talking with me!!!!!!

[wanton yacht]

But nope, that's how it's written

Yep. Good luck with geometry

[long geyser]

shoot for aristotle become better than him in reality

[long geyser]

Ty!

[wanton yacht]

😅

[wanton yacht]

Good luck

[long geyser]

Ty

you too!

shoot for albert

become the next albert

[wanton yacht]

Yep, maybe that's part of the plan

[long geyser]

im gonna try to master this, this is the foundations of geometry right?

[wanton yacht]

It's definitely an important part of it, yea

[long geyser]

cool!

i'll be sure to pay attention

[wanton yacht]

Probably a good idea, lol

[frosty trench]

heblooo

[long geyser]

hii

[green gyro]

Can I ask for help with this task here

[edgy seal]

Don't shitpost here

go to #chill or #discussion

[exotic yarrow]

In the future, please show what you've done so far when asking for help. It gives us more context and saves time. \ \

As a hint, think of the ntersecting chords theorem. If you extend $OE$ to meet the circle at $P$ and $Q$ (where $P$ is closer to $E$ than $Q$), then what are the lengths of $EP$ and $EQ$ in terms of the radius?

[somber coyote]

Civil Service Pigeon

[edgy seal]

If you continue to be unhelpful/obstinate I will just

[vapid tide]

RIP. 🙏

[edgy seal]

I try to be nice and just warn the troll instead of banning them smh

[vapid tide]

It's aight man you're just doing your job...

[exotic yarrow]

mods good

🍪

[wanton yacht]

What's the problem?

That depends on what the homework is.

[grave pond]

No, you cannot in fact ping 300,000 people.

[wanton yacht]

For part a, I think we can both agree that if we had the point that the cable was going to attach to, specifically on the sloped ground, it would be a simple distance formula calculation to get the total cable length, right?

Yes, but does what I've said make sense to you though?

[grave pond]

That still won't let you ping everyone ...

[wanton yacht]

Alright, so the question now is, how do we find that point?

Do you agree this is what we've got?

And then like, you've got the point where the cable attaches which is at the top of the tower

So if I was just like, alright, lets say that T = (0,650 ft) for simplicity, and I said that the point at the base of the tower was (0,0), if we can find P, we can use distance formula between P and T to get the length of the cable.

So how do we find P? Any ideas?

What did you get for a final answer?

I got a different answer for part a

What exactly did you do?

Well, that triangle isn't a right triangle though

I mean

You wrote it had a 90 degree angle in your diagram

What am I looking at?

That's right, sure, but how does that help you find the point where the cable attaches?

[wanton yacht]

I like my diagram better

That's not possible

Or actually

I mean, that's not the answer I got

Does it say that's the right or wrong answer when you type it in?

Is this a test?

So am I helping you cheat right now?

Alright

Is it an assignment you can ask for help with?

[wanton yacht]

.

[wanton yacht]

I mean, I'll just say that from my diagram, tan(10deg) = y/100ft, so the y coordinate for p is 100*tan(10deg), and if you then do the distance formula between (0,650ft) and (100,100tan(10deg)), you get a different answer than what you said

[frosty trench]

hello

[wanton yacht]

I got 640 ft

Yeah

[frosty trench]

Vrochacho just search it up 🥹

[languid talon]

divide this man by 0

[peak turtle]

Alr

[languid talon]

multiply him by i 😔✌️

[peak turtle]

I think I could do better but this is what I have rn ✌️

[rustic girder]

btw

[lime crown]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[peak turtle]

My bad

[hazy aspen]

need help

[worthy folio]

Question and its solution

Now how I'm supposed to do questions like this which require simple but not very obvious trickery.

||I'll certainly not even get to the first step of writing 1 = sin^2 A + cos^2 A||

[obsidian harness]

I agree that method is a bit artificial

let $u = \sin^2 \alpha$ (cause we can find $\csc^6, \sec^6$ in terms of $u$)

we have $10u^2 + 15(1 - u)^2 = 6 \implies u =\frac{3}{5}$

so we just need the value of $\frac{27}{u^3} + \frac{8}{(1 - u)^3}$

[somber coyote]

south

[obsidian harness]

ping

[worthy folio]

I see

Thank you

[obsidian harness]

no worries!

lmao given this method, the book has a terrible solution

[loud geyser]

So there is a circle radius 6, inside contain 4 quarters of a circle also radius 6 spaced evenly. Center of the outside circle lies upon all 4 circumferences of those circles. Find the shaded area

[lime crown]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[loud geyser]

tbh no idea

I meant first step

[grave pond]

If you have no other ideas, a very natural place to start would be to define an appropriate coordinate system and start figuring out coordinates for some of the relevant points.

While you do that, you can also start thinking about which tools you have that could be used to calculate the areas on one of the shaded regions.

(My first instinct would be integration, but you probably don't have that available when you're asking here. Perhaps you have some formulas for the area of circular segments, so you can divide each of the red "fan blades" into a triangle and two segments?)

[loud geyser]

I do have access to integration actually, but I kinda hate making all the equations

I think a found a way

oh wait, that isn't 3

Okay ig I would just use integration atp, it seems more complicated using only geo

Yippe

[grave pond]

I think my first approach would be that ABC, AEG, DFG are all half-segments which I could derive a formula for; then
ABD = ABC + AEG - CDEF - DFG.

(Whoops, sorry for using different letters).

[loud geyser]

Oh I was doing that then it seem to be required finding a lot of others areas to derive to those 4

[grave pond]

Well, whatever works for you -- I'm not claiming any particular superiority of my dissection.

[loud geyser]

Thanks for the help 🩵

[warm shuttle]

Notably, red area is necessarily equal to the white area

[grave pond]

Nice observation.

Though it's not clear that the white area is easier to calculate.

[warm shuttle]

Seems like a nasty problem either way tbh

[green gyro]

Okay thanks. It’s just that my way of solving was totally wrong since I mixed up some theorems

[obsidian harness]

https://www.youtube.com/watch?v=-Gmw_DjgyYw

if anyone wants to try (or watch)

[odd edge]

could anyone help me w/ trigonometry, I don't really get it, even the basics

[upper karma]

which concept?

do you know about circles and right triangles?

each one builds on one another, so you can take the last lesson and think in terms of its relevance in the next one

[silk socket]

Hi guys got a quick question

Which topic should I start when I'm relearning analytic geometry

[vapid jay]

In the triangle ABC where AB=4, AC=5, and cos(∠BAC)=1, as shown in the figure, point D divides segment BC in the ratio 1:2. Let E be the point other than A where the line AD meets the circumcircle of triangle ABC. When the foot of the perpendicular from point D to segment CE is F, the length of segment FC is p/q√11. Find the value of p+q. (Here, p and q are coprime natural numbers.) PLS HELP

[long geyser]

Tysm! I haven’t learned trigonometry but this was a really fun video!

[obsidian harness]

no worries!

most of it is actually just coordinate geometry though

[long geyser]

I see! Thanks

[obsidian harness]

idea behind the approach (spoilers!):
||take the intersection point to be the origin; you have three points that lie on the circumference of a circle, so the standard approach is that the two perpendicular bisectors intersect at the centre, then the radius is just the distance formula||

[long geyser]

I thought maybe you could transpose the angle and line somehow by like shifting it until it’s equivalent to the center, and then doing calculations

[long geyser]

||But how can you know if the circle still has the same radius?||

[obsidian harness]

there's a unique circle that passes through any 3 points (that don't lie on the same line)

by taking the intersection point as the origin, you're only translating the circle, not enlarging it or anything else

[obsidian harness]

that doesn't work without finding the new lengths

[long geyser]

I see, so it has to specifically have 3 points on the radius of the original circle for this to work?

[obsidian harness]

3 points make a circle passing through them

there's no "original circle"

[long geyser]

Interesting, what prerequisites would I need to solve similar questions? I’m only beginning in geometry right now

[obsidian harness]

you need to go through algebra 1 material

do you know how to plot points on the coordinate plane?

[long geyser]

Yep I’ve finished algebra 1

Is that enough?

I just don’t know like the theorems and stuff like that, I believe

[obsidian harness]

cool, then I think it's about developing the geometric intuition to connect algebra and geometry

[long geyser]

Okay thanks! I recently figured that a rectangle with missing bottom coordinates with a given area can be figured out algebraically, it’s so beautiful to implement what I learned so far in math into geometry

[obsidian harness]

https://www.youtube.com/watch?v=G6C0lbELl2Y&list=PLg2tfDG3Ww4s6Bjp17m9xjv4AIDX0xK3b
this might be new to you, but the algebra should be straightforward

[long geyser]

Ty! I’ll definitely watch it

[obsidian harness]

there's a whole part of coordinate geometry just on circles

[long geyser]

I see

[obsidian harness]

the tangent is always perpendicular to the radius

what else, the perpendicular bisector of any chord always passes through the origin

these are results from geometry

[long geyser]

Does that deal with infitisimals? Or is that just logic

[obsidian harness]

but how you find those lines is through algebra, of course

[long geyser]

Nevermind I see it in my head right now, that makes sense

[obsidian harness]

you're splitting this vertical line into two equal halves, so each angle is 180/2 = 90

[long geyser]

A ray that points in a direction from the origin of a circle has a perpendicular line to it at the vertice of the thing

[long geyser]

Yep!

I was trying to see it from the 45 degree angle

So I was wondering how would you know that

[obsidian harness]

lol

[long geyser]

Haha

[long geyser]

What’s a bisector and chord?

[long geyser]

Makes sense

[simple vigil]

@long geyser which class ?

[obsidian harness]

bisector - a line that cuts an angle / another line into two equal halves

[long geyser]

I just finished 9th grade algebra 1

[obsidian harness]

chord - a line that connects two points on a circle

[obsidian harness]

yeah so you'd be doing geometry next semester or what?

[long geyser]

I see!

[long geyser]

Isn’t that just the diameter or would that be any 2 points on the circle at all?

[long geyser]

Yep!

[simple vigil]

You have whole circles or just basic

[hoary totem]

any 2 points

[long geyser]

Okay

[hoary totem]

a chord is the line segment

[long geyser]

What’s a line segment

[hoary totem]

the infinite line is called a secant

[long geyser]

I’m not sure

[hoary totem]

a segment of a line
basically a line that starts from point A to point B and stops

[long geyser]

The one that points towards the x axis?

[hoary totem]

no

[simple vigil]

You have tangents in syllabus?

[long geyser]

No I haven’t taken geometry in school yet

[long geyser]

Ah

[simple vigil]

This is a weird system for me

💔

[long geyser]

For the notation of the ray do you have to always point the arrow to the right?

[hoary totem]

mhm

[long geyser]

I see!

This is so easy!

[simple vigil]

Two rays form and angle
You must be knowing this

[simple vigil]

💀💀💀

Beware when you will have to use triangles and circle together

[long geyser]

I believe you mean two connected rays, because it is not necessary that they make an angle right?

[simple vigil]

Yes my mistake

[long geyser]

I’m just referring to the notation like for example writing AB and then a line over it because I’ve seen that before but I wasn’t sure when to use it etc

[long geyser]

How about disconnected rays? Can you still trace an angle between them?

And for example parallel lines?

[simple vigil]

It's used
But most of the times in question you need not to mention

[long geyser]

I see, so you can just write AB and it’s okay?

[simple vigil]

You can measure
But you will have to extend the original

[simple vigil]

Yes but it depends ask your teacher first

[long geyser]

Ah I understand

[long geyser]

Okay thanks so much!

I’m new to this

[simple vigil]

In between parallel lines
Angle is always 180°

[long geyser]

How about when they are placed on top of each other

0?

[simple vigil]

I think you should first look at
Postulates and axioms of Euclid they will be used everywhere

[simple vigil]

Yes
And they are called
Co-incident lines

[long geyser]

I saw them on Veritasiums channel if you know him

[simple vigil]

Yes it was in my syllabus in 9th 😂

[long geyser]

I see

[long geyser]

Your teacher made you watch him?

Or the axioms?

[simple vigil]

No it was part of a chapter

[long geyser]

Ah

[simple vigil]

Which chapter you have studied till now

?

[long geyser]

Transformations of points on Khan Academy, definitions of a circle line etc and how to find the coordinates

I’m going to learn the axioms soon

[simple vigil]

🤯

Are you in 9th for sure?

I think I studied these in 6-7th 😭

[long geyser]

Yeah they’re prerequisites for geometry but I’m not good with them

So I need to learn them again

[simple vigil]

I m in 10th
Just send me the question if you want help
I m good in geometry 😂

[long geyser]

Thank you! 🙏

That’s really nice of you

[simple vigil]

No problem

[long geyser]

That’s really intuitive, I was wondering why in the other video the person used the x-x0 and all of that and it makes sense now!

[dusk wharf]

is this a good place to talk about graphs

[obsidian harness]

try #precalculus

[wild wolf]

how can I start precalculus or What do I need to know to start studying precalculus ??

[opaque dock]

I’m stuck on number 2

[flat fox]

Aren't quadeladeralls the same on both sides

[odd edge]

parallel on both sides, doesn't have to be the same side size

[flat fox]

oh

[obsidian harness]

1. practice on Khan Academy

2. https://www.hood.edu/sites/default/files/A Quick Algebra Review.pdf
   you should be familiar with all of the material in this document to proceed

I know there are harder concepts in geometry / alg 1 / alg 2 so that document really has the barebone essentials

oh yeah, IXL is pretty decent too: https://www.ixl.com/math/precalculus

[long geyser]

Khan Academy is brilliant, i'm going through geometry and it's all very digestible

[long geyser]

is this in algebra 2?

[obsidian harness]

yes

[long geyser]

omg i think i took this in iraq, it wasn't easy

i took that in 9th grade, i think the curriculum in the middle east is advanced

[odd edge]

uh what do you mean by concept?

[spice axle]

Somebody plz check my answer.

[viscid gorge]

how can i find the eccentricity of this ellipse (F is the focal point) based on the given parameters ? (aka like a formula for e)

[obsidian harness]

https://www.desmos.com/calculator/ektc6odc06

I've used technology to do all this algebra and you have $n = \frac{e \cos t - 1}{e \cos t + 1}$

[somber coyote]

south

[obsidian harness]

rearrange this to solve for e

well my t is not the same as your theta (t = pi - theta), but you should be able to work it out

[viscid gorge]

how would a geometric approach be like ?

like not analytical geometry

[obsidian harness]

I doubt this is possible synthetically

[viscid gorge]

alright thanks!

[obsidian harness]

no worries!

[somber badge]

Can yall explain to me why cos(-θ)=cosθ, and sin(-θ)=-sinθ I still can't understand

[short obsidian]

u know that cosine is an even function and sine is an odd one right

with respect to the y-axis

[somber badge]

Yes

Oh shoot I completely forgot about that

[short obsidian]

so cosine of a negative angle is the same as cosine of a positive angle

due to it being symmetric (even)

but sine is not symmetric and we cannot say the sin(-x) looks the same as sin(x)

[somber badge]

Wait, but on the Unit circle, lets say the triangle is 30° and the other triangle 210°, we see that the triangles are opposite of each other and flipped over the x and y axis, sine would be (1/2) in the 30° triangle and sine in the 210° triangle would be (-1/2) they are not equal as due to the identity sin(-θ)=-sin(θ)

[short obsidian]

yes

if u want an explanation using the unit circle i think thatll be more understandable

so theta moves anticlockwise if its positive, and clockwise when its negative, right?

[somber badge]

Yeah

[short obsidian]

right and we know cosine correlates to the x-axis, and sine for the y-axis right?

so imagine terminal going clockwise (-x)

cosines value is still positive here (positive x)

but sine changes since its dipping down (y axis)

[somber badge]

Ohh, wait so we are talking about the 4th quadrant, the cosine is going in the negative direction, but still is positive, and sine goes down, so its negative

[short obsidian]

yes we are in the 4th quadrant

but if we dip into the 3rd quadrant as in the terminal keeps going, we hit the negative x-axis, so both our cosine and sine values will be negative

and when you continue in this clockwise direction, youll end up in 2nd quadrant where our cosine and sine values will be..?

[somber badge]

Cosine is negative and sine is positive

[short obsidian]

yup

[somber badge]

And so this why the cosine function starts at one and descends in both sides until negative in the y-axis when it goes down

[short obsidian]

i dont understand what u mean

wdym in "descends both sides"

[somber badge]

By that i mean y-relative on the both sides of the x-axis, so -x and x, y descends equally until it reached its point where it becomes negative and keeps going down until it reaches its point where it can go back up

[short obsidian]

🤔 i think i am just not understanding this

could u perhaps do a small drawing of what u mean

[somber badge]

Yeah, I have the paper right in front of me

[short obsidian]

or if someone else whose understood could verify what u said lol

[somber badge]

Alr, so we have the cosine function, at 1 on both side of "x" which is negative and positive, y dipps down equally until it reaches zero there, because as you said before when the focus line goes down x is still positive and y is negative.

Wait, but how can we represent "-x" or positive x now? Its always negative

And on the positive side, y is getting bigger and x is getting smaller because its going counterclockwise, how is y getting smaller on the function?

[short obsidian]

if i try explain further i might mess up what you have understood, i think its best i leave someone else to explain this

trig is not my forte either sorry bro 😔

[limber atlas]

please help me

it's fisica

[somber badge]

Its really hard to actually understand, I can feel the toughness

[short obsidian]

when you have the graphical intuition it all clicks

its tough but it all is tied together and there isnt anything that cannot be explained

[warm shuttle]

Can't you just mark all the intersections and use series/ parallel resistance formulae to solve for equivalent resistances between them?

[somber badge]

Yeah, that's what I find all the time, going from basics to creating your own things, you have to think of like every single possibility that the functions can be used for

[warm shuttle]

I don't think I learned how to do this

[short obsidian]

https://youtu.be/R6JCwzA8xX4?si=DirCkdQo7JEekx5B check this video out if you have the time to do so

i think ur confusion stems from the difference between the unit circle and the graphs of cos and sin as functions

[warm shuttle]

I think this is correct

[somber badge]

You are right, I figured it out, lets say you go back, cosine is not negative, because its still positive in the fourth quadrant, but the y goes down because its negative, and then it keeps going down because it's still negative, however cosine is cosine, its just a measure at this point, you can only have a negative cosine when you go back, but when you go back you go counterclockwise which means that cosine will be technically negative here but now instead of cos(-θ)=cosθ, its cosθ=cos(-θ) which is still the same thing and says that cosine is actually positive but you are going the negative direction, by the symmetric property of equality, and then everything also has to be the same, so in the y-axis, the y value would drop, which also makes the line go up back to zero and to its starting point because we are still in the fourth quadrant.

[short obsidian]

that all sounds correct hell yea brother

[somber badge]

Im copying this, its literally my greatest prove ever

[autumn star]

yo guys

need ghelp

in dutch but

calculate that without ict

[flat fox]

this might be wrong but it seems right

[grave pond]

What is "ICT"?

In particular, is it a name for particular trigonometric identities that should be avoided?

[autumn star]

calculator

[grave pond]

So the double-angle indentity is fair game?

[autumn star]

yes

i found it

what it need to be

thxcx for responding tho

[elder ice]

Hey guys any suggestions on how to get better or master geometry

[real sentinel]

practice as many questions you can

And ur pfp is super nostalgic

[worthy folio]

First get your notes organized. So you can revise quickly.

Mark hard questions.

[warm shuttle]

That's a good advice

(I think)

[wispy urchin]

ICT means Information & Communication Technology

[warm shuttle]

sin(2x) = 2 cos(x) sin(x) => sin(x)cos(x) = sin(2x) / 2

[hearty kite]

1+sin2x = (sinx + cosx)²

[slim plinth]

Famous identity: sin² (x) + cos²(x)=1

Derived from a²+b²=c²

[somber badge]

Can someone explain to me how in the world sin(x+y)+sin(x-y)= 2sin x cos y how it should be, but sin(x+y)-sin(x-y)≠2cos x sin y, my book tells me that, to prove the Sum-to-Product identities, but this is impossible, because in reality it equals 0💀

[grave pond]

Do you claim that sin(x+y)-sin(x-y) does not equal 2cos x sin y? Do you have examples of x and y that make them different?

[somber badge]

Well the book then says "Let x+y=a and x-y=b"

[grave pond]

Huh. That's not a counterexample.

But it's not clear to me whether you're actually claiming that sin(x+y)-sin(x-y) differs from 2cos x sin y. Could you clarify, please?

[somber badge]

I will try my best

[grave pond]

I'm not (at this point) asking for an explanation, just for a yes or no.

[somber badge]

Oh, lol, mb

Yeah, I do not claim that sin(x+y)-sin(x-y) equals to 2cos x sin y

[grave pond]

You're not claiming that they are equal, okay.

Are you claiming that they differ?

[somber badge]

Yes

[grave pond]

Okay, then do you have an example of a particular set of values for x and y that makes the two expressions have different values?

[somber badge]

Well, in one equation you subtract the two equations and in the other one you add both. I can conclude that the signs make the two different values different: sin(x+y)+sin(x-y)=sin(x)cos(y)+cos(x)sin(y)+sin(x)cos(y)-cos(x)sin(y)=2sin x cos y, ok
Then sin(x+y)-sin(x-y)=sin(x)cos(y)+sin(x)cos(y)-sin(x)cos(y)-sin(x)cos(y)= 0 somehow

[grave pond]

I'm asking which particular numbers for x and y make the two expressions have different values?

[somber badge]

Oh, there is no number, its a proof

[grave pond]

If it's a proof then it should not be a problem for you to find some numbers that one can plug in to see a difference?

Wait, are you claiming that sin(x+y)-sin(x-y) is 0, no matter what x and y are?

[somber badge]

Let me check

[minor zealot]

Can someone help me with this. The question is find w out calculator the exact value of cos(13pie/4)

Pls

[somber badge]

Aha, I found something interesting, I was able to confirm that if the degrees are equal in the the x and y for both of the equations in sin(x+y)-sin(x-y), then it will of course equal 0, but if the question is like sin(x+π/3)-sin(x-π/6) there is a solution, however I was not able to calculate it, because you can't with this identity, you need to use the sum-to product identity, I figured this out by using math solver for the last question, checking for any mistakes that I may have made.

I can't prove the identity with the identity though, makes no sense

[glass robin]

do any of you know any course books on fractals?

[river wigeon]

Finishing a book on chaos theory rn

[warm shuttle]

Technically, that's false

Just because you can prove something, doesn't mean you can construct an example

[gentle drift]

can any one prove why (x-h)^2 +(y-k)^2= r^2

[gentle drift]

dud see let the pie be x cos (13x/4) which can be written as cos(x+9x/4) since x is 180 so according to the cast rule it is -cos 9x/4 then you can write this as -cos(x+5x/4) same as we did in the before it will be -(-cos 5x/4) which is cos 5x/4 again you can write is as cos(x+x/4) which is -cosx/4 since x is 180 degree we can write -cos 180/4 which is -cos 45 we know it is 1/root 2 so -1/root 2 is ans

[obsidian harness]

it comes from Pythagoras

[hearty kite]

I once calculated tanx=i/root(8)
I don't even know how i did thay but it was funny

[wanton yacht]

What?

Prove what about it? It's just an expression

[grave pond]

Right. In this case I was trying to get them to plug in any numbers at all.

[coral gulch]

My geometry teacher gave me this do any of yall know how to shade it in

[flat fox]

Some of that is logic

[short obsidian]

something like this could help you solve these, perhaps?

thats borderline giving you the answers but theres not much other than knowing what these mean and how to shade in venn diagrams

[meager flax]

Yo guys is there any books like Stewart's calculus book for geometry?

[humble fable]

A(ABE)=9.A(EDC) ==> A(ABE)-A(EDC) = ?

[lime crown]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[upper echo]

use similarity of ABE and DCE

[humble fable]

tried it already

cant

[pallid arrow]

Guys what's 1+1 (Boolean)

[slender dragon]

1

[warm shuttle]

Depends on what + means

if it's OR, then 1. If it's XOR then 0.

[slender dragon]

tru tru

[gentle drift]

hey is infinite by infinite can be written as 1

[warm shuttle]

No, usually not

[obsidian harness]

under normal definitions of (cardinal) infinity, infinity * 2 = infinity, infinity * 3 = infinity, and so on

that's why infinity/infinity is undefined

[warm shuttle]

in my head it should be 6, should I check on paper?

Nah, you right

it's 5/6

[tender arch]

are you turkish?

[obsidian harness]

nice problem btw

[humble fable]

perhaps

[meager flax]

Would be happy if someone answers

[vast iron]

How do you calculate the area of this semicircle R1 with two fillets R2?

[warm shuttle]

Well, It's kind of difficult to get an exact answer, but possible.

Important thing to note is that the line from the radius of the big circle and through the center of a small circle also passes through the point where the curve of the big circle stops, and curve of the fillet starts

To simplify set R1 = 1, set center of the big circle at origin, and only seek to find area of the right side

then solve for the center of small circle in terms of R2

Then divide the whole area into a triangle and two circle sectors

This should work

[eternal rivet]

this had to be graphed I imagine (just asking)

[dire ridge]

integrals

[dire ridge]

ARE YOU?

because i am and so is he

[simple vigil]

Is this possible with geometry?

[dire ridge]

no

[simple vigil]

Then ?

[dire ridge]

you need to find a function that describes these

and integrate at correct bounds

[simple vigil]

🤯

[dire ridge]

the substract excess area

[simple vigil]

This means it is above from what I have studied

[dire ridge]

look at my account creation and server join dates

[simple vigil]

Oct 3 2025 I m older than you in this server 😂

[simple vigil]

But what you want to show me from this ?

[dire ridge]

same day

[tender arch]

yeah

[jovial creek]

F1???

[simple vigil]

Yes a bit

[simple vigil]

Dedication for maths 🗿

[jovial creek]

What do you think of yesterdays Qualifying ?

I also stole that tag its clean

[simple vigil]

Not able to watch
Because of the time

[jovial creek]

Aw damn

Will u watch todays gp?

[simple vigil]

Maybe
Because it will be 9:30 pm for me
I have to study also

I think I will manage somehow

[jovial creek]

Don’t study studying won’t entertain you like max winning the title

Hope he does

I hate egoistic norris

When is his car gonna explode already

[simple vigil]

Come in chill channel

[queen venture]

i found the crisp sol 🤤

but i need sol of this rn

[warm shuttle]

That's just not true. In fact it's harder with calculus

[queen venture]

oh everyone is sleeping

[upper karma]

Anyone willing to help for problem C

please

[dusk wren]

I'll get u bro 🙂

Wait

[obsidian harness]

you should recognise the expression inside the product as being one of the compound angle formulas

[dusk wren]

Yes

And use the trig formula for that product series:
tan( θ- ϕ) = (tan θ-tan ϕ)/(1+ tan θ × tan ϕ)

[vast iron]

How do I calculate R2 segment?

[vast iron]

I think I'm on it, but I'm stuck again.

Anyone know how to do it?

[obsidian harness]

like this

in this case you have $(r_2 - r_1)^2 = r_1^2 + BO^2$, so that's the length of the base of the triangle

[somber coyote]

south

south
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[obsidian harness]

woops, the area of the triangle is 1/2 * BO * ...

= 1/2 * r2 * BO * sin(AOB)

[vast iron]

Thanks for the working out. Did you fix the mistakes in your original text?

[vast iron]

I'll need some time to work through it, so I can understand it. But I'm not sure where this goes " 1/2 * BO * ...
= 1/2 * r2 * BO * sin(AOB)"

[vast iron]

Also where did you get the number 3 and 4 from in the diagram.

[obsidian harness]

they're not part of the diagram

[obsidian harness]

do you know A = 1/2 ab sin C? I just used that on triangle COB

[vast iron]

okay. So to get segment 2 would I do Sector(COD)-AOB-ABC?

[obsidian harness]

just sector COD - triangle COB

[vast iron]

I see, I'll give it a go, thank you.

[obsidian harness]

no worries!

[vast iron]

I think we got it. Does this look right. Sorry for the mad scribblings.

It's a big one.

[meager flax]

Does anybody have any idea??

[eternal rivet]

thx

[flat fox]

yes https://www.amazon.com/Best-Sellers-Geometry/zgbs/books/491546

[viscid gorge]

ABCD and EFBG are Squares.
If the area of triangle BNF is 9 and area of trapezoid BNEG is 27, What's the colored area

Anyone got a clue ? i suck at geometry very much

i had a idea of drawing a line from G parallel to ED

[river dirge]

well BG = EG = sqrt(36) = 6

so BE = sqrt(2) times 6

[viscid gorge]

ok makes sense

[river dirge]

we also know that FN = 1,5

cause 9 = FB * FN/2 and FB = 6

so the value of BN is going to be sqrt(38,25)

[viscid gorge]

wouldn't that be FN = 3 ?

[river dirge]

ah

youre right

my bad

now we have two equations from the Pythagorean theorem

[viscid gorge]

BN sqrt(45)

[river dirge]

for the ANE triangle and AEB triangle

so like (AB^2 + AE^2) = 72 right

[viscid gorge]

yea makes sens

[river dirge]

and EN = FE - FN = 3

so AE^2 + (AB - sqrt(45))^2 = 9

so AB = 18sqrt(5) / 5

now that we have AB, we can get AE and AN, so we have the area of the triangle ANE, and value of the area of ABCD

so value of the pink area is going to be [ABCD] - 27 - [ANE]

([ABCD] is the area of ABCD)

[viscid gorge]

ok let me do the rest of the calculations

i am upto AB

[river dirge]

i made a little jump there

[viscid gorge]

i did it myself

no worries

[river dirge]

nice 👍

[viscid gorge]

AN = 3 * sqrt(5) / 5

[river dirge]

yep

[viscid gorge]

so AE = 6 * sqrt(5) / 5

[river dirge]

r u sure?

[viscid gorge]

AN^2 + AE^2 = 9
9/5 + AE^2 = 45/5
AE^2 = 45/5 - 9/5 = 36/5
AE = sqrt(36/5) = sqrt(36)/sqrt(5) = 6/sqrt(5) = 6 * sqrt(5)/5

[river dirge]

then we have a mistake somewhere

[viscid gorge]

i got area 0 lol

[river dirge]

there AE = 6 * sqrt(2)/5

[viscid gorge]

AB = 18 * sqrt(5) / 5 is correct right ?

[river dirge]

i am 99% sure

ill double check

let AB be x

we have x^2 + (x- sqrt(45))^2 = 63

yeah its my mistake

AB isnt 18 sqrt(5)/5

[viscid gorge]

wait let me check

[river dirge]

ive got that AB is (3sqrt(5) + 9)/2

[viscid gorge]

i got the colored area = 36

with AB = 18 * sqrt(5) / 5

[upper echo]

square roots are not needed

[solid gate]

hey all
Im trying to solve the attached problem and im a bit confused. a cube is put in a sphere with a volume of 1.
now i understand their explanation on how they got the relationship between the length of the cube and the diameter of the sphere. however i assumed that from the center of the sphere (and cube) to the two vertices shown would be right angles and as such i can calculate the length of the side of the cube with pythagoras but that is not correct.

Can someone please explain why that is not correct as i cant see why

[upper echo]

That's because the diagonal section of the cube is not a square but a rectangle (with the ratio of the sides sqrt(2)). So, that angle in the center is not 90

[solid gate]

makes sense ! thank you !

[hybrid frost]

Can anyone please explain to me and make a few or just one example of Midline Theorem/square?

[viscid gorge]

the key says the purple area is 36

[upper echo]

oh, yes, There is a mistake in my drawing.

[leaden chasm]

Hey guys

[upper echo]

here is a correct version

[naive bay]

yall my teachers doing it on purpose at ts point😭

\

[obsidian harness]

doing what on purpose?

[naive bay]

solve for z ull see

[obsidian harness]

oh LMAO

I thought you were talking about there being an issue with the question

[keen marsh]

Can someone help me with this problem, I feel so confused: vertex in (4,-3) axis parallel to the x-axis passing through (0,3)

thx!

I need to find the equation

Of the parable

[grave pond]

Could you show the entire problem you're solving, including all instructions, please?

[jade sierra]

anyone know what is hsa? my text book uses hsa but my teacher say like hl

[finite drum]

what would i do for 12√3??? i want to know the steps

[jade sierra]

you want to simplify 12 sqrt 3?

[finite drum]

yes

[jade sierra]

you can think of it was 12 * sqrt 3
you can rewrite sqrt3 as 1.73
so 12sqrt3 is 20.78

[finite drum]

ohh that's it ???

[jade sierra]

yea lol

[finite drum]

but tysm 😭

[obsidian harness]

ask your teacher

is it something about surface areas?

[desert gust]

@everyone hi