Tan 90 value approximation, just take a look about my new analogy

[robust falcon]

Tan 90 sure it big but it's not infinity and cam be approximate as an infinite decimal, check this new idea, the answer is not 2 but the method is correct

[dusty yacht]

It is neither big nor defined

[robust falcon]

How do u say

[robust falcon]

I'm not talking in the typical method of 1/0
Check out my concept first

[dusty yacht]

Your concept does not work because you have incorrectly defined tan for angles above 45

How are you defining all your theta btw?

[robust falcon]

Lemme tell u

Take a square ⬛️ whose side length, let it be "a"
Now draw a line from the left bottom vertex to the top right vertex which makes the angle between that and the bottom side 45°
Now draw another from that same vertex to the mid point of the right side of the square, that makes the angle smaller. So if we consider the tan value of it it would give , tan theta2= ((1/2)a)/a = 1/2

So then draw another line from the same vertex to the right side as the opposite side of the angle becomes 1/4th of the right side , so the tan value for that angle is ((1/4)a)/a=1/4
And then draw lines from the same vertex to the right side until the hypotenuse of the substended Angle touches the bottom side, so the angle is nomore,
Considering the tan values of those angles we get the sequence,
1,1/2,1/4,1/8,1/16.....till infinity
For the angles,
Tan theta1,tan theta 2, tan theta3.... so on
Do u see that first

[dusty yacht]

Till infinity or did you mean till zero?

[robust falcon]

Till the angle becomes zero

[dusty yacht]

So $\theta_n=\arctan2^{-n}$. Ok

[balmy fern]

SWR

[dusty yacht]

And $\lim_{n\to\infty}\theta_n=0$. Sure

[balmy fern]

SWR

[robust falcon]

For the tan values, the last value is

$1/(2^(♾️)$

[balmy fern]

nahsed2712

[dusty yacht]

There is no last value

[robust falcon]

For the last angle , so it is zero or negligible

[dusty yacht]

But you are trying to say that $\lim_{n\to\infty}\tan\theta_n=0$, which is correct so far

[balmy fern]

SWR

[dusty yacht]

There is no last angle. Just limiting behavior

[robust falcon]

Yeah yeah

But it's not about the angle that gets smaller and smaller

Do u agree on how I took the tan values? First of all

.@dusty yacht do u agree

[dusty yacht]

How you took them? I mean, you defined each $\theta_n$ to satisfy $\tan\theta_n=\frac1{2^n}$. You didn't really do any calculations with tan yet

[balmy fern]

SWR

[dusty yacht]

@robust falcon

[robust falcon]

Yeah, took the tan values from opp/adj

[dusty yacht]

Okay. Anyway, what next?

[robust falcon]

, then input them to the tangent sum formula

I need help on that

[dusty yacht]

This one?

Is the basis of your proof based in the assertions that $$\sum_{n=1}^{\infty} \theta_n=90^{\circ}$$ and $$\sum_{n=1}^{\infty}\tan\theta_n=2$$
?

[balmy fern]

SWR

[dusty yacht]

@robust falcon

[robust falcon]

This one's for 2 angles

Look for the general formula for an number of angles

[robust falcon]

All the angles get summed up to 90 caz the angles are same no matter what we do to them
And the tan values are also just as I told

[dusty yacht]

The angles, in fact, do not sum to 90

[dusty yacht]

@robust falcon wdym "no matter what we do to them"?

@robust falcon I'm off to bed. If you care to discuss more, it shall be tomorrow

[robust falcon]

Why not

[robust falcon]

Okay

[dusty yacht]

, w pi/2=sum k=0 to infinity arctan(2^(-k))

[balmy fern]

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[dusty yacht]

Off i go now until tomorrow. I'll leave you to think this over until then

[robust falcon]

, w sum k=0 to infinity [pie/2^(k)]

[balmy fern]

Results provided by WolframAlpha

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Requested by nahsed2712

[dusty yacht]

What is this doing for you?

@robust falcon

[robust falcon]

Thank you bro for your enthusiasm, I think I found where the error is , the angle sum exceeds 90° so the angle isn't 90° means this calculation is kind of flawed , imma fix this as I can

Thank you again

[dusty yacht]

Good luck to you. And respect for at least trying something. That's how we all started around here

[robust falcon]

Glad to hear bro, I thought this would make some difference but seems like my geometry kind of tucked, can I add you DM

[dusty yacht]

Nah I don't really discuss math through DM. If you have more math questions, you'll be better off just asking here

[robust falcon]

Not maths stuff bro, as friends,

U think I get this sort of weirdo ideas very often enough ti discuss them trough dm

[dusty yacht]

Sorry. I don't really add people here. But if you get ideas (about math), just share them here.

[robust falcon]

Alright dude , thanks for telling me where I did wrong, I'll debug the errors, maybe I can get 90 degrees if I got the exact sum of the all angles and then substract the required amount to reach 90

[dusty yacht]

You would -I am quite confident- end up with an undefined value

@robust falcon, as a gentle reminder to you, do not pigeonhole yourself into believe that tan90=+infinity.

[robust falcon]

Alright bro thank for the advise

[dusty yacht]

that's only true if you approach it from the left

but from the right, it diverges to -infinity

,w plot tan(x)

[balmy fern]

Results provided by WolframAlpha

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Requested by spelwerdzrite

[robust falcon]

But nothing should be either undefined or too big , everything s got their limits

[dusty yacht]

Having things be undefined is okay

If you try to define everything, you end up breaking a lot of structure

if you try to define 1/0, then you are going to break something else that is far more useful than defining 1/0

[robust falcon]

I know, but not everything is undefined , it maybe undefined for now, just because we can't imagine how its limit can be , maybe we will In the future

[dusty yacht]

We can precisely define the limits of 1/x and tan(x) though. It is from these limit definitions that we say its limits do not exist.

[robust falcon]

Yep, caz we have build a lot laying on this undefined thing

[dusty yacht]

And as well, they are undefined because they involve division by zero, which itself is undefined because it breaks several properties of basic arithmetic

[dusty yacht]

wdym?

[robust falcon]

Alright alright I'll believe in you

[robust falcon]

We have developed a lot of concepts believing in the fact that 1/0 is undefined

[dusty yacht]

you don't need to believe me. The facts of math do not need to stand on authority.

By all means, you are free to explore yourself and see your own ideas.

[robust falcon]

Yeah alright

[dusty yacht]

But I (and others) will be ready to scrutinize them

[robust falcon]

I guess so, I just wanted to see what it meant when I randomly spawned that in my mind

[dusty yacht]

The things I am telling you, my intention is not "believe them because I know more math than you", I am simply sharing my own experience with you and letting you know the similar pitfalls I have faced

Like, when I was younger, I tried solving the quintic equation, fully aware that it was proven unsolvable

[robust falcon]

I know , u re an undergraduate right? I'm still a high-schooler

[dusty yacht]

I foolishly believed that I could think of something really really clever

but no, proofs are proven for a reason

[dusty yacht]

I graduated a very long time ago

[robust falcon]

Everyone does until some point in their life, somethings work out to be true, somethings don't

[robust falcon]

Well ur dm says that u re an undergraduate

U seem to be older than 25 I guess

[dusty yacht]

Those roles indicate the level of math you have studied, not where you are in education

[dusty yacht]

Or maybe I graduated at 6 years old. Who knows?

[robust falcon]

Oh sorry, dear I signed up today, so u don't know how these things work

[dusty yacht]

what?

[robust falcon]

So u are probably older than me, caz ur dm says u joined discord in 2017, where I was doing 1+1=2

[robust falcon]

I mean I signed up for discord today

[dusty yacht]

ah

[robust falcon]

How old are u actually

To which university did you go

[torn ermine]

bro explain me one thing why the sum off all thetas gives 90? I'm sure it's not 90

[robust falcon]

Oops sorry bro , I had a miscalculation and I recognised it now, I thought this would work but it doesn't in this way sorry bro

[dusty yacht]

[dusty yacht]

[robust falcon]

U sound like a 6 year old who graduated at 4

[torn ermine]

ok, but can u pls explain me the tg(theta_1+theta_2.......theta_n) sum formula?

[robust falcon]

Well I'll send u a clearer image of it

[torn ermine]

ok

[dusty yacht]

[dusty yacht]

Or maybe a 4 year old who garduated at 6

That would be pretty advanced

[robust falcon]

So he should have started studying from it's pre- cellular age

What a luck, or maybe u re just a teenage like me

[dusty yacht]

🦠

[robust falcon]

@torn ermine here

[robust falcon]

Of course I didn't prove this, I took this from a book

[torn ermine]

Jesus it looks pretty difficult and which book?

[robust falcon]

A local one, by a phd
I took it from the town's library

[torn ermine]

I can't find any books in English in my town, where are you from?

[dusty yacht]

Yikes that is a brutal formula

[robust falcon]

It wasn't in English bro, I'm srilankan

[robust falcon]

I wonder how he took that

[torn ermine]

I'm sure it's pretty easy but so tiring

[dusty yacht]

Induction, I would assume, but doing it sounds unfun

[robust falcon]

I don't know , maybe it's easier, when you have studies for a phd lol

[torn ermine]

yeah I guess

[robust falcon]

Must have taken a couple of weeks

Mind if I ask you a riddle guys

[dusty yacht]

How is $\sum_{1\le i<j\le n}$ working? Are you iterating $j$ from $1$ to $n$, and in each iteration, doing an inner iteration of $i$ from $1$ to $j-1$?

[balmy fern]

SWR

[robust falcon]

Where are u from actually ? So that u can't find English books

[torn ermine]

nopr go ahead

[torn ermine]

I mean related with math. Azerbaijan

[robust falcon]

I have heard of that

[dusty yacht]

i.e. if n=4, then your (i, j) iterations are (1, 2), (1, 3), (2, 3), (1, 4), (2, 4), (3, 4)?

[torn ermine]

yeah think like it's a python loop

for i in range(1,n+1):
for j in range(i,n+1):
print(i,j)

[robust falcon]

Well a hunter , shoots down a bear from a distance.then he goes to it's body, then he travels 100m south, then 100m east, then 100m north. And you have got to where the year's dead body lays
So what colour is the 🐻 bear

[robust falcon]

I guess so

[dusty yacht]

https://tenor.com/view/beardance-gif-6830159389639305176

[robust falcon]

I know it sounds irrelevant but it does make sense

[torn ermine]

ok guys I gotta sleep

[robust falcon]

Alrighty

[torn ermine]

sweat dreams

[robust falcon]

Ah same to u bro, the answer to this riddle is north pole,