geometry-and-trigonometry

[rare talon]

After that we're goin to the 2nd problem

Now

What is the area of the triangle?

[sacred vessel]

3 times 3.9 divided by two

wait a sec

[rare talon]

No

Do you see the base of the triangle that has height of 3 dm , is 1.3 dm ?

[sacred vessel]

oh

[rare talon]

If you don't, try to rotate the shape, so you can see it

[sacred vessel]

wait a sec

1.95 dm^2

i think

@rare talon

[rare talon]

Yeah

Now

See it on the other side

You know that Area of the triangle = 3.9dm . H ./ 2 = 1.95 dm^2 right ?

[sacred vessel]

yeah

[rare talon]

Try to find H now

[sacred vessel]

wait what does 1/2 mean

?

😛

cuz i need to A=1/2(b)h

@rare talon

[rare talon]

k

Just let it 1/2 (3.9 dm) (H) = 1.95 if you want

[sacred vessel]

yeah

wait a sec

[rare talon]

It's the same though

=tex a . \frac{1}{b} = \frac{a}{b}

[sacred vessel]

the height is 2.6

[rare talon]

Really?

[sacred vessel]

is it 0.9

[rare talon]

Show me your work

[sacred vessel]

1.95 times 2 = 3.9

3.9-1.3=2.6

because i just followed the formula back

and then subtracted the one i knew to get height

[rare talon]

What

1/2 (3.9) (H) = 1.95 | Multiply the equation by 2
(3.9) (H) = 3.9 right?

[sacred vessel]

yeah

[rare talon]

I don't even know why you put 1.3 there

Find H from that

[sacred vessel]

i dont get it

is 5.85 the area

im supposed to find

[rare talon]

No

[sacred vessel]

im not getting any of this

[rare talon]

Do you get why the area is 1.95 ?

[sacred vessel]

because 3.9 divided by 2 is 1.95

[rare talon]

It's actually because you've find 1/2 (b)(h) = 1/2 (3dm)(1.3dm) = 1.95 dm^2

You did it in your first step

Remember?

[sacred vessel]

yeah

[rare talon]

Now

[sacred vessel]

i get it a little now

[rare talon]

Yeah you've agreed that 3 dm can be interpreted as the height of one triangle, and 1.3dm is the base

[sacred vessel]

teag

yeah

[rare talon]

Now we know that: SEEING 3.9dm as the base, and H as the height

The area of the triangle = 1/2 (3.9dm)(H) right?

[sacred vessel]

oh yeah yeah

right

[rare talon]

Now hey! We know that the area of the triangle is 1.95 dm^2

[sacred vessel]

yeah

[rare talon]

Then we get the equation:
1.95 dm^2 = 1/2 (3.9dm) (H)

[sacred vessel]

and now i can get height

[rare talon]

There you go just find H

Let me actually do it for you

The 2nd problem is pretty similiar

1.95dm^2 = 1/2 (3.9dm) (H)

You multiply the equation by 2 to get rid of the fraction.
2 * 1.95 = (3.9) (H)
3.9 = (3.9) (H)

Finding H should be easy right? 😛

[sacred vessel]

yeah

H is

3.9

no

wait

[rare talon]

Okay

I'll wait

Are you using calculator?

[sacred vessel]

its 2.6

i believe

[rare talon]

I hope you get rid of it

No

[sacred vessel]

i was

now im not

[rare talon]

Good

But it's not 2.6

3.9 = (3.9) (H)

I hope you're getting until this

Aren't you?

[sacred vessel]

i am

[rare talon]

Good

[sacred vessel]

but i dont understand can you write like i was

like divided

multiplied

its easier then

subtracted and added

like that

[rare talon]

Oh okay

[sacred vessel]

cuz if i understand the process i can do it on my own next time 😃

[rare talon]

3.9 = (3.9) (H)

We are dividing that equation by 3.9 (the coefficient of the H, so we can get H)

Now the eq becomes:
3.9 / 3.9 = (3.9) (H)/(3.9)

3.9 divided by 3.9 is?

[sacred vessel]

1

[rare talon]

Good

Now (3.9)(H) / (3.9) is?

[sacred vessel]

1

[rare talon]

H

[sacred vessel]

oh

[rare talon]

You still have H there 😛

[sacred vessel]

yeah

[rare talon]

Then H = 1

[sacred vessel]

1h

[rare talon]

Yep

[sacred vessel]

thanks

ill try the next one on my own

[rare talon]

Now can we go to the 2nd one?

Oh good! That's the spirit!

[sacred vessel]

and ill keep you posted

so we can check

[rare talon]

Yeah just mention me, but if I'm not around just mention @ help

I can go anytime soon

[sacred vessel]

kk

so first its 16 times 24

[rare talon]

Good

I hope you know the reasoning why you multiply 16 * 24 😛

[sacred vessel]

yeah

its

height times base

[rare talon]

Okay good

[sacred vessel]

because thats how you get area

[rare talon]

The area of parallelogram

= b . h

[sacred vessel]

yeah

[rare talon]

So far so good

[sacred vessel]

so now its 384 divided by 19.2

i think

[rare talon]

What do you try to get by dividing 384 /19.2 ?

[sacred vessel]

dunno 😛

[rare talon]

Ah okay

I want to make it clear

[sacred vessel]

im following what i did last time

[rare talon]

But here is the better step you should do

[sacred vessel]

what is it

[rare talon]

The area of the parallelogram = 19.2 (h)

Agree?

[sacred vessel]

i think

wait but isnt the area

[rare talon]

See 19.2 as your base, h is your height

[sacred vessel]

384cm^2

[rare talon]

Yeah

Just keep 384 cm^2 aside for now 😛

[sacred vessel]

okay

😄

[rare talon]

I'm sticking by the formula

The area of the parallelogram = 19.2 (h)

Agree?

[sacred vessel]

yeah

[rare talon]

Good

Now we know that the area is 384 cm^2

As you mentioned

[sacred vessel]

yeah

[rare talon]

Then
384 = 19.2 (h)

What should you to get h?

[sacred vessel]

384/19.2

wait no

[rare talon]

Divide it by 19.2, that's what I want to hear

[sacred vessel]

that not it

wait

😄

[rare talon]

Oh sorry 😛

[sacred vessel]

i was right

[rare talon]

You was

[sacred vessel]

but i dont trust myself

[rare talon]

But you need to keep yourself know why you do that

I'd like things to keep organized

[sacred vessel]

yeah

its 20

h is 20

[rare talon]

384 = 19.2 (h)
Divide the equation by 19.2

You get:
384 / 19.2 = 19.2 (h) / 19.2

Okay good

😛

20cm to be exact

[sacred vessel]

yeah

[rare talon]

If you have the other kind of that problem

Try to solve it by your own 😛

To make yourself sure that you understand

[sacred vessel]

ill try

😄

i need help with a circle problem

cuz it involves pi

and im not good with math

[rare talon]

Okay

Post it

[sacred vessel]

its sorta

a written thing

i have to fill in the blanks

so help me with one and ill try the others

[rare talon]

Okay

[sacred vessel]

so the radius is 2 m

and i need to find

other things

one is area

but the others i dont remember in english

1 sec

its lenght

[rare talon]

Perimeter?

[sacred vessel]

i rememberd

[rare talon]

Diameter?

[sacred vessel]

i think

[rare talon]

Which one

[sacred vessel]

r is the radius C is lenght S is area

and r is given

[rare talon]

C is what length?

Wait

I'll post the pic

[sacred vessel]

span maybe

but im not sure

[rare talon]

Which one is your length?

[sacred vessel]

im not sure

im just given info

[rare talon]

Then I can't answer that

Try to look that at your book or something

[sacred vessel]

could it be span

[rare talon]

idk what span is sorry

😛

But okay

[naive scarab]

C usually stands for circumference

[rare talon]

I'll answer the area

[naive scarab]

if you're doing things with circles anyway

[sacred vessel]

lenght is the black line in the midle

[rare talon]

@sacred vessel do u know what is the area of the circle?

Oh it's diameter

[sacred vessel]

yeah

i just checked the book

cuz im doing these off a sheet

[rare talon]

Okay

[sacred vessel]

i know how to calculate area

of these

[rare talon]

Now what is the formula for finding the area of a circle?

[sacred vessel]

waith

[rare talon]

Oh good

[sacred vessel]

yeah

i do

[rare talon]

r = 2m

[sacred vessel]

its A=pi times (d/2)^2

[rare talon]

It's okay

Then

Can you find d for me?

What is d?

[sacred vessel]

d is r i think

[rare talon]

It's different 😛

[sacred vessel]

oh no

[rare talon]

d is diameter

[sacred vessel]

d is the circles height

[rare talon]

d = 2r , do you get it from your book?

There's nothing called circles height 😛

[sacred vessel]

well the thing

[rare talon]

d is 2 times the radius

[sacred vessel]

wait

thats d

lenght of the circle

[rare talon]

Yeah d is that

= my black line

It's the same

The exact same thing

[sacred vessel]

yeah i guess i overlooked

[rare talon]

Okay diameter (d) is 2 times the radius

[sacred vessel]

yeah

[rare talon]

You know the radius is 2m , then d = ?

[sacred vessel]

2/2

so 1

[rare talon]

No

d = 2r
d = 2 . 2 (subtitute r = 2)

😛

[sacred vessel]

4

yeah

its late for me here

its like 4 in the morn

😄

i cant think

[rare talon]

Oh do you have test?

You should rest

[sacred vessel]

yeah but its next month

on the 24th

[rare talon]

You should rest

If you're tired

I can't think math on a scrambled mind

[sacred vessel]

until then i have to get practicaly the entire 8th grade down or else ill have to repeat a year

and i dont want that

[rare talon]

Oh I see

Okay

Now you get d = 4m

[sacred vessel]

this is my summer practice

[rare talon]

Now find the area

Yeah next time, don't overburn yourself, it's not an effective learning of learning math

[sacred vessel]

A=3.14 . (4/2)^2

[rare talon]

Okay

[sacred vessel]

its just im so busy during the day that i cant really sit down to do maths

[rare talon]

You let pi is equal to 3.14, I'm okay with that for now

[sacred vessel]

but im making time now

for the day

[rare talon]

Oh okay

[sacred vessel]

so yeah pi is 3.14

[rare talon]

Find A

pi isn't actually 3.14, but that's what you'll learn later, now just stick to the problem

I don't want to confuse you sorry B(

[sacred vessel]

😄

its ok

i got 6.28^2

[rare talon]

What?

Wait2

A=3.14 . (4/2)^2

Order of operation:

1. Evaluate things in the parantheses first

[sacred vessel]

yeah

i got 3.14 time 2^2

[rare talon]

Oh good

Now 3.14 * 2^2 = 3.14 * 4 right?

[sacred vessel]

yes

[rare talon]

You should do the exponent on the 2^2 first

[sacred vessel]

oh

[rare talon]

Yeah you can't say 3.14 * 2^2 = 6.28^2 😛

[sacred vessel]

sorry

[rare talon]

Don't worry

[sacred vessel]

i slept during class

well not literaly slept

[rare talon]

Just take a look over that next time

[sacred vessel]

but i wasnt paying atention

12.56

[rare talon]

Good

Now you can fill in the blank

The "length" of the circle is ...
The "area" of the circle is ...

"length" = diameter as you're telling me before

[sacred vessel]

the area is 12.56

[rare talon]

m^2

[sacred vessel]

yeah yeah

im simplifying

😄

[rare talon]

Okay I just don't want you to forget that

[sacred vessel]

i havent

😄

and then the lenght is just 4

i think

[rare talon]

Yeah

[sacred vessel]

yeah

so now i got 2 more ill try

[rare talon]

I hope the length is not the circumference of the circle, or it will be marked wrong

[sacred vessel]

the teacher will check and if some of its wrong ill ask for another day and come back here to get help on the explanation

but she said i can visit any time

for help

but learning like this seems more usefull (not to be mean to the teacher

im keeping notes

aswell

also*

[rare talon]

Keep your notes , the best way to learn math, is to understand, not memorizing 😛

[sacred vessel]

yeah

now i just got to do something else but the D is 14 pi dm

[rare talon]

Anyway you should try some more problems on your own

D is what?

[sacred vessel]

so i need r and area

14 pi symbol dm

[rare talon]

Diameter?

[sacred vessel]

yeah

so just follow back what i did before

[rare talon]

Length = C ?

[sacred vessel]

yes

[rare talon]

Oh

Holy

C = circumference

[sacred vessel]

crap

we did it wrong

😦

[rare talon]

xD

[sacred vessel]

😄

[rare talon]

But the area is right

At least

[sacred vessel]

yeah

😄

[rare talon]

Now

Let's go back to that problem

Oh I should mention you

The area of the circle is usually denoted as pi * r^2

If you haven't that in your book

It's much more simple than you're doing it with the diameter (pi * (d/2)^2)

Now what is the C formula?

In your book?

[sacred vessel]

wait ill check

C=pi symbol d

[rare talon]

pi * d

[sacred vessel]

yeah

[rare talon]

Okay

You know what d was right?

[sacred vessel]

so it is circumfrence?

[rare talon]

Yeah

[sacred vessel]

yeah

[rare talon]

I assume so

[sacred vessel]

yeah it tottaly is

i looked up the def of circumfrance and thats what its asking for

[rare talon]

Okay good

[sacred vessel]

wait a sec

[rare talon]

Now what is circumference = pi*d ? 😛

[sacred vessel]

🚽 bathrom break

[rare talon]

Ok have your time

[sacred vessel]

im back 😛

😄

[rare talon]

Okay

[sacred vessel]

C=2Pi times r

[rare talon]

Yeah they are the same thing

[sacred vessel]

yeah

so

by that logick

one sec

going over book and notes

so i understand

[rare talon]

At my previous test about circle, we were asked the definition of the circle

I'm at uni now

*though

[sacred vessel]

its just a line that was turned 360 degres

😄

[rare talon]

Good that you know it, it's quite important imo

But okay

Go back to your problem

[sacred vessel]

well this is easy

common knowledge

😄

kk

omg

[rare talon]

Yeah but it is sometimes overlooked by the student

[sacred vessel]

i did not mean to press that

[rare talon]

Anyway what is the circumference?

[sacred vessel]

3.14 times 2

6.28

is the circumfrence

[rare talon]

Well

No

[sacred vessel]

crap

😄

[rare talon]

circumference = 2 * pi * r = 2 * 3.14 * 2

😛

Don't forget you have 2 in the front

[sacred vessel]

ohh ok

yeah

so its 12.56 ?

like the area

[rare talon]

Well the numerical is same

But the unit is different

Is only 12.56 m

Not m^2

[sacred vessel]

ohh

so C=12.56

?

[rare talon]

Yeah

We can go to the 2nd problem

[sacred vessel]

yeah

circumfrence is given

soooooooo

by that

i can calculate r

[rare talon]

Isn't d = diameter?

Or is it c?

Anyway what was the problem again? Would you mind to post it again?

[sacred vessel]

yeah the thing is writen c but im writing like for you

so you can understand

im writing d for you

and marking it as c

[rare talon]

Oh whatever then

[sacred vessel]

😄

[rare talon]

I'll just solve the problem given 😄

By you

[sacred vessel]

k

😄

[rare talon]

Okay you know the circumference is 7 pi?

Or what? I forgot

[sacred vessel]

14 pi dm

decimeters

[rare talon]

Oh okay

[sacred vessel]

so by that

[rare talon]

You can find r, how?

[sacred vessel]

i just divide by 2 and then 3.14

?

[rare talon]

Okay

I'll actually write the exact step

To see if you're right or not

[sacred vessel]

kk

[rare talon]

2 * pi * r = 14 pi (circumference of the circle)
Divide the equation by 2 * pi
r = 14 pi / (2 pi)

Yeah you're good

[sacred vessel]

21.98

dm

[rare talon]

I believe, no?

[sacred vessel]

cuz when i divided by pi

it was weird

like super long and weird

[rare talon]

Okay so you get
r = (14 * pi) / (2 * pi) = (14 * 3.14) / (2 * 3.14)

Okay?

[sacred vessel]

okay 1 sec

i got this

[rare talon]

Good!

I usually don't write pi = 3.14

I leave it as pi

[sacred vessel]

7

its 7

[rare talon]

Yeah

Good

Now you can find the area easily

[sacred vessel]

yep

[rare talon]

Usually I keep pi as pi, not write it as 3.14 , to keep thing simple (unless your teacher wants pi = 3.14 in the test)

[sacred vessel]

its not specified

so im just putting numbers so its easier

but i think on the test it will be

[rare talon]

Yeah it might be easier for you to put number

Whatever, it works anyway

[sacred vessel]

i got

153.86 dm^2

[rare talon]

Good

😄

[sacred vessel]

last ones easy

im given the area

and need to find r and C

so i got this

[rare talon]

Try to do that by yourself

[sacred vessel]

😄

yeah

[rare talon]

I won't give any hints

[sacred vessel]

k

[rare talon]

😄

[sacred vessel]

ill just say what i got

😄

[rare talon]

Okay

What is the problem?

[sacred vessel]

but its weird

can i ask something

[rare talon]

Yeah?

[sacred vessel]

why is it 49 pi

cm^2

[rare talon]

Well

It's fine technically

😛

[sacred vessel]

so i dont need it on the others too

?

[rare talon]

I can give you another problem

Let the area is 100pi cm^2

Find the radius and circumference

If you want

[sacred vessel]

ok

1 sec

so r is 50

and c is

1 sec

[rare talon]

r is not 50

Note that the area = pi * r^2

Not 2 * pi * r

[sacred vessel]

wait ill show my work

and you tell me where i went wrong

i wrote

[rare talon]

Okay good

[sacred vessel]

r=(100 times pi) divided by (2 times pi)= 3.14 :6.28

equals 50

[rare talon]

No

[sacred vessel]

314

i mean

not 3.14

[rare talon]

You don't divide by 2 * pi

[sacred vessel]

so what do i divide by

[rare talon]

I am not sure if divide is enough

Let's see here

100pi = pi * r^2 right?

[sacred vessel]

yeah

[rare talon]

Because 100pi is the area of the circle (which the formula is pi * r^2)

[sacred vessel]

wait

[rare talon]

Now find r^2 first

[sacred vessel]

r^2

is just r times r

[rare talon]

Yeah

[sacred vessel]

so to get r

i need

1 sec

so pi divided by (r^2)

[rare talon]

Ah not that

I'll just show you okay?

[sacred vessel]

ok

[rare talon]

100pi = pi * r^2

I hope you get this 😛

Have you got algebra lesson?

Anyway

[sacred vessel]

yeah but as i said i didnt listen i was zoning out during class

which was stupid on my behalf

[rare talon]

Oh I see, next time try to review some of them

It's quite important

[sacred vessel]

and i will never do that again

in my life

😄

[rare talon]

Anyway
100pi = pi * r^2
314 = 3.14 * r^2

Got this?

[sacred vessel]

yeah

[rare talon]

I just changed pi to 3.14

At that step

[sacred vessel]

so wait

it is 50

[rare talon]

No

[sacred vessel]

r is 50

[rare talon]

It's not 😛

[sacred vessel]

1 r is not 50?

😄

[rare talon]

I make the problem so I know xD

[sacred vessel]

Okay

😄

[rare talon]

314 = 3.14 * r^2
Divide the equation by 3.14
r^2 = 100 right?

[sacred vessel]

yeah

so 100 /2

[rare talon]

It's not 100/2

r = square root of 100

[sacred vessel]

oh yeah

thats right

its not r times 2

its r times r

[rare talon]

Yeah 😛

[sacred vessel]

😄

crap

[rare talon]

You need to square root it

[sacred vessel]

yeah

[rare talon]

If you find like r^3 = 1000

You need to cube root it

So r = ?

[sacred vessel]

so 10

[rare talon]

Good

[sacred vessel]

r is ten

😄

[rare talon]

Now find the circumference

[sacred vessel]

yay

😄

[rare talon]

Try to be familiar with algebra, to make sure you're familiar with the things why you did this and that

[sacred vessel]

10 times pi times 10

right

[rare talon]

Oops

[sacred vessel]

is the circumfrence

[rare talon]

No

What is the circumference formula?

Once again!

[sacred vessel]

2 * pi * r = 14 pi

but the 14 is not that

[rare talon]

Well r is 10

Not 7

[sacred vessel]

its just your formula

yeah

[rare talon]

2 * pi * r = circumference of the circle

[sacred vessel]

yes

[rare talon]

Try to take a look at your book again

[sacred vessel]

so 2 times pi times 10

[rare talon]

Okay

😄

[sacred vessel]

6.28 times 10

62.8

is C

[rare talon]

Yep

But

Don't put that on your sheet

Because, it's my problem

[sacred vessel]

yeah yeah

[rare talon]

Not the sheet problem 😛

[sacred vessel]

ill just get the formulas

because thats what it comes back to

😄

Back to formula

[rare talon]

Okay

[sacred vessel]

so ill try my own one

and check with you

[rare talon]

The area is 49pi right?

[sacred vessel]

yeah

[rare talon]

Okay

I'll check

[sacred vessel]

whats the r formula again

ill write it down

so i dont forger

forget

[rare talon]

Okay

[sacred vessel]

so can you tell me

😄

?

oh wait

:

😛

thats my job

rn

[rare talon]

Try to look it at your own book B(

[sacred vessel]

yeah yeah i know

😄

[rare talon]

I can give you ofc but you won't learn

I think you mean the formula for the area and the circumference of the circle

Just to make sure you're not confused

[sacred vessel]

i was looking r

formula

but its my job rn to find it

so i got this

[rare talon]

Well "r" is considered as a very basic element of the circle

I don't think I ever use formula for that

[sacred vessel]

yeah its just c/2

i think

[rare talon]

d/2 in my case

[sacred vessel]

yeah

[rare talon]

Okay

Good

😄

[sacred vessel]

😄

1 sec

im cracking it

after this one its bedtime

cuz its 5 am

😄

[rare talon]

I believe you should go to bed now tbh, but okay

[sacred vessel]

i could send over the sheats but you wont understand cuz theyre in lithuanian

😄

[rare talon]

Oh I see

[sacred vessel]

here the learning your expected to do is crazy

but its no excuse to be lazy

either so

😄

so 49/pi

and i think i get C

wait no

[rare talon]

No

[sacred vessel]

c is 2 times pi times r

i need r

[rare talon]

Try to find r first

[sacred vessel]

i need to square root it

1 sec

7

i remembered

😄

its getting crazy early in the morning no sleep and work all day
how am i even awake

😄

[rare talon]

I don't know

¯_(ツ)_/¯

[sacred vessel]

its 7

r is seven

[rare talon]

Yeah

Then?

You need to get your job done, finding c

[sacred vessel]

2 times pi times 7

easy

😄

[rare talon]

Okay

[sacred vessel]

1 sec

43.96

[rare talon]

Yeah

[sacred vessel]

thanks

[rare talon]

np ~

[sacred vessel]

im gonna go to bed but you have been a great help 😄

thank you a thousand

[rare talon]

Okay rest yourself!

[sacred vessel]

i will thanks

😄

[cedar prawn]

It's only a few levels because these calculations are a lot of work XD

That is a regular septagonal tiling, but i think it's only a few rings' worth

you can tell it's tending towards a circular boundary though

and I made all that by hand so sorry it's not bigger and more filled out :3

Actually I didn't link some of the outer points yet, blargh - some of them are missing

[mighty epoch]

Making these things by hand is probably difficult lol

[cedar prawn]

I'm not sure about the way you label tessellations but each point has seven edges

It's not as hard as you think - Photoshop's rotate function is my friend

I really only have to make each section once then rotate it seven times around

but the calculation involved to find the points takes time

[dark sparrow]

@cedar prawn do you mean order-7 triangular?

[mighty epoch]

Ah lol, what language are you going to use to draw these?

[cedar prawn]

Python

[mighty epoch]

Ah okay

[cedar prawn]

I've already got the program working with a regular hexagonal tiling, it just doesn't work with any others yet XD

Um I think that's what it is √2

I really look forward to having it working all the way so that I can give the points a small but nonzero probability of having more or fewer edges than their neighbors, walk around in that semirandom tiling, and see how it moves between curvatures as you go around

[dark sparrow]

7 triangles to a vertex

[cedar prawn]

Yes exactly

That's the ultimate goal - have the plane be, I don't know the word for it, non-homogeneous? That doesn't seem like the right word. But the tiling itself is going to be randomly generated and shifting over long distances

Is there a word for a plane where the curvature is not the same at every point?

[dark sparrow]

surface of non-uniform curvature?

[cedar prawn]

Oh duh :3

Like imagine you're wandering around on that hyperbolic plane I started drawing and eventually you come to a line where all the points have six triangles instead of seven, and when you cross that line you're in a Euclidean plane

I want to be able to envision how that transition would look

Each point is a place the player of the "game" could stand and you're moving along the edges

My issue right now, besides getting the program to work, is that the algorithm is only capable of drawing it with the center of the screen being on a point, but it wouldn't be fluid looking if you're just hopping directly from place to place - it should warp as you go over an edge to the next point.

I just don't know how to calculate that

[lofty python]

Hey guys. Hope you're having a good day.

I have a question on this problem here. https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.591304.html

When combining 1/cosx - cosx how come it is (1-cos^2x)/cos x not just (1-cosx)/cos

Its on the link after "Combine the first and second..."

[haughty prawn]

Cosx=cos^2x/cosx

[lofty python]

I still don't understand

[haughty prawn]

1/cosx - cosx = 1/cosx - cos^2x/cosx = (1-cos^2x)/cosx

[lofty python]

Ok thanks that makes sense. I forgot I had to multiply cos(x) by cos(x)/cos(x) so I could add them together.

[haughty prawn]

👍

[lofty python]

Cheers thanks

If I'm multipying sin(s-t) * cos(t) how would i do that?

cossin(s-t^2)?

[haughty prawn]

sin(s-t) = sin(s)cos(t) - cos(s)sin(t)

[lofty python]

Oh ok for the difference identity

[sacred vessel]

@rare talon you here? 😄

[sacred vessel]

i need help with a problem

can someone help

[rare talon]

Ok

Just post your problem, someone will help

[dark sparrow]

what are the geodesics under the L^4 metric?

i.e.

if the distance function is defined as follows:

=tex D = \sqrt[4]{\Delta x^4 + \Delta y^4}

[dark sparrow]

then, given a point (x, y), what curve connecting it to the origin will have the shortest length?

obviously if xy = 0 then the geodesic is either a horizontal or vertical line

but that probably isn't the case for other lines

[final prairie]

Oo interestingg

[dark sparrow]

fun fact: if we measured distances using this formula, π would be around 3.3969

wait

nvm

rip

[quiet orbit]

it will always be a straight line, no?

[dark sparrow]

somehow i'm not really sure of that

[quiet orbit]

D(A,tA+(1-t)B) + D(tA+(1-t)B,B) = D(A,B)

and you also have the triangle inequality, since it's a metric

so it follows that if the curve contains a point that's not on the segment joining A and B the overall distance will be greater

[dark sparrow]

hmm

you're right

[quiet orbit]

what's the value of pi as n approaches infty for the metric (Dx^n + Dy^n)^(1/n) ? :\

[dark sparrow]

i think it's 4

in the L^∞ metric it's 4

[quiet orbit]

interesting

[dark sparrow]

the L^2 metric actually minimizes it

[upper karma]

Quick quesion Im(j) = sqrt(3)/2 right ?

[azure storm]

1st third root of the unity?

[upper karma]

Yeah

Its correct 😄

[azure storm]

Yeah (j is also used to replace i sometimes so I got confused a few seconds)

[dark sparrow]

do you mean the engineers' jmaginary numbers

[azure storm]

exp(2pi/3)->Im=sin(2pi/3)

jmagjnary

[upper karma]

Its usedby math people here

[dark sparrow]

engjneers

[upper karma]

Hmm in physics j is i no ?

[azure storm]

Depends

[dark sparrow]

physjcjsts

[upper karma]

Haha

[azure storm]

If i is something else (intensity) then yes

[upper karma]

Wellyeah

But there is always something else in physics

😛

[dark sparrow]

current

[restive moat]

Im(j) = sqrt(3)/2 i didn't understood 😦 what is j?

@dark sparrow

[dark sparrow]

j is SEV's notation for e^(2πi/3)

it seems

[restive moat]

ahhh ok xD

thanx

[azure storm]

its a "common" notation

[dark sparrow]

the only one i saw was ω

[quiet orbit]

same

[cedar prawn]

what is the name of a manifold (I think that's the term) which is like an infinitely long cylinder "squared" - as in, four dimensions, two of which are infinite and flat, and two of which are circular?

I have been thinking about such a shape, all the possible surfaces on / in it - there are cylinders, tori, and even flat euclidean planes, depending on how you orient yourself in the four 4D rotation axes

but I don't actually know what to call it

I've been referring to the dimensions in my mind and writing as x, y , θ₁, and θ₂ - x and θ₁ are the linear and circular dimensions of one infinite cylinder, y and θ₂ are the dimensions of the other, and the manifold/space/thingy that I am considering is the product of the two

I imagine I am saying some things in incorrect ways of course, but I can see it in my head

whoever can help, thank you 😃

I probably ought to study lower math before trying to understand complex 4D spaces but you know me... my mind goes in strange directions...

[vapid kettle]

Infinitely long cylinders are the same as a cylinder if you remove the border

Can use that for some visualization

Also the thing you described is a torus crossed with a "patch"

Patch can also be though of as R^2

You can see that by your theta 1 theta 2 and x and y

so a way to view your space

is to view a plane

and a torus next to it

and imagine a little point star on your torus

and a point on the plane

these two points together totally describe the space

*a point on the space

and as you move a point on the plane continuously that is moving continuously

same for the point on the torus

or you could move both at the same time

[cedar prawn]

Yes I am completely aware of that

All that

I figured it out on my own

My issue isn't how it works - I can see it all in my head perfectly

My issue is: what is it CALLED?

[vapid kettle]

well I don't work much in topology

buttt

doesn't seem like that special a space to me

just a torus cross a plane

[cedar prawn]

Well the reason I found it interesting is that there is a plane in that four-dimensional space which is both positively curved at every point, and infinite

which is what I was considering to begin with

if you take it as a pair of those infinitely long cylinders, and have two helices, one on each

take any two points, one on each helix

(which is a straight line on the cylinder space)

and they are equivalent to one point on a surface which is infinite, but positively curved everywhere

and it is that surface that I found interesting enough to consider all this

[vapid kettle]

ok

[cedar prawn]

but do you like understand what I mean?

am I getting something wrong?

[vapid kettle]

each cylinder

R cross S1

S1 is circle

and put curve (t,t) on each cylinder

then look at the image of the cart product of those curves in R^2 times T (T for torus)

that's how I read it ~

[cedar prawn]

the problem is I know how to envision this in my head but I don't know what some of those words mean or how to express any of it in symbols 😦

[vapid kettle]

hmm

well I'm sleepy so cross is the wrong word xD

should sat times or cart...

[cedar prawn]

To me, it's just a surface where all the "lines" are helixes

which cannot be completely embedded in 3-space

[vapid kettle]

well helix

as a word to me means it has two strands

[cedar prawn]

not a double-helix

a single-helix

[vapid kettle]

so I'ce been reading what you mean as single strand

[cedar prawn]

DNA has two connected helices, I am referring only to one on each cylinder

equations of the form f(z)=(cos z, sin z, z) for instance

I may not have said that right but you get the picture

[vapid kettle]

well it's a space

and uh

put a plane in that space

fun to play around with such things

[cedar prawn]

I know, it's wonderful

[vapid kettle]

and also mm

[cedar prawn]

In my mind I was standing on the origin rotating in various 4D directions, looking at all the different plane surfaces to be found in the space of R2*T

[vapid kettle]

a sphere has positive curvature everywhere

[cedar prawn]

but it's finite

[vapid kettle]

well

[cedar prawn]

I think my helical space is infinite

[vapid kettle]

"finite/infinite"

doesn't really mean much in topology

[haughty prawn]

^

[vapid kettle]

like I poined out

[cedar prawn]

I'm not thinking of this from a topological perspective

[vapid kettle]

you can view your space as "finite"

[cedar prawn]

but a geometrical one

[vapid kettle]

mm all terms you've mentioned are things in differential topology ~

and

I can take my sphere asss

complex plane

and add a point at infinity

and then bam

it's infinite

geometrically

[cedar prawn]

But it has a radius which is so large it acts like a flat plane

That's not useful for having any particular amount of curvature

[vapid kettle]

known as projective complex line ~

[cedar prawn]

I'm thinking, can I make a plane which I could tile with polygons that only tessellate in positively curved space

and there would be infinitely many of them

[haughty prawn]

R^2-(0,0) is pretty infinite, but its lowkey a sphere

[cedar prawn]

they require a set radius which is very finite

I don't know these terms though so you have to break it down for me...

[vapid kettle]

R^2 - (0,0) a sphere?

in what way?

[cedar prawn]

How can something be a sphere, and be infinite?

[haughty prawn]

Hmm, lemme check my definitions lmao

[vapid kettle]

cause like

[haughty prawn]

I thought it was homeomorphic

[cedar prawn]

Are you referring to the complex projective line?

[vapid kettle]

R^2 - (0,0)

is his infinite cylinder :p

topologically

[cedar prawn]

Uhhh

Oh I see

Take an infinite plane, cut a little hole, stretch it, it becomes a cylinder

Interesting!

[vapid kettle]

R^2 - (0,0) isn't homeomorphic to a sphere ~

[haughty prawn]

Lmao gj me

[cedar prawn]

Yes! It's composed of an infinite series of concentric circles

and if you squish them and extend into the Z dimension

it becomes an infinite cylinder

that is amazing

I would never have thought of that

[vapid kettle]

uhhh

sure

[cedar prawn]

Why the uhh?

Am I wrong somehow?

(I am still learning all this so please correct me where possible 😃 )

[vapid kettle]

oh just

hand wavey arguments in topology

mmm

don't that often translate into rigorous proofs

[cedar prawn]

Well, I know there's more than intuition

[vapid kettle]

but the idea seems fine to me ~

[cedar prawn]

But I have to be able to see things in my head in order to understand them

[vapid kettle]

just

an example is

there is an idea known as the fundamental group

and

once you know the idea

it's extremely intuitive that the fundamental group of the circle

is the integers

butttt

the intuitive way to heuristic argue that

doesn't work so well

intuition is very useful in mathematics ~

but it can lead astray in certain things

[cedar prawn]

Well, I am a completely visual and tactile thinker, so I have to use metaphors like that with the squished concentric circles to understand things

I can imagine moving things around with my hands and looking at them with my eyes

but it's hard to handle pure symbology

[vapid kettle]

well

most mathematicians don't work just with symbols ~

[cedar prawn]

I know

[vapid kettle]

like stuff we can visualize

[cedar prawn]

That's why I'm attracted to geometry and topology, they're very tactile and visual

Number theory, not so much - though it is interesting in its own ways

Honestly I love all math