Damn you really said aight imma head out
#geometry-and-trigonometry
late frost
white cradle
✌️
slender nacelle
Have you been given any length? Like radius of the circle? @late frost
slender nacelle
At least you should give a length
halcyon dragon
Not enough information I think
late frost
Right
Idea #1 Because the angles are 45 deg, cegf and Qbdc are squares.
Idea #2 ef and bf are both radii of the circle
Idea #3 ef is the diagonal of a square
Idea #4 bfQ is a right-angled triangle
slender nacelle
Yes
late frost
What do u mean
slender nacelle
I mean, you are right
slender nacelle
Yup. They are correct statements
But I thought you were formulating this problem
slender nacelle
It should
Are you familiar with equation of circle?
If not, you can follow the hints and get the answer too
late frost
@slender nacelle Which equation is that
slender nacelle
Nevermind. You will probably learn it in conic section.
@late frost try to follow hints
slender nacelle
Can you apply Pythagorean theorem?
Or you can just use trigonometry if you know it
slender nacelle
Good
late frost
nvm
slender nacelle
What did you do?
slender nacelle
Okay
late frost
Nothing
slender nacelle
Can you find fg in terms of R?
slender nacelle
What's that?
late frost
R cos(45)??
slender nacelle
Yup
slender nacelle
Do you know value of cos45?
late frost
Half of sqrt(2) right?
slender nacelle
Great!
late frost
hold up hold up imma solve this
slender nacelle
Sure
slender nacelle
What is 60 degrees?
late frost
relevant**
slender nacelle
Or 30?
late frost
What is angle cfb
I mean cfd
ITS 45 DEGREES
FAHRENHEIT
no its not
so owhats cfb
slender nacelle
How do you know cfd?
late frost
I don't
slender nacelle
You also don't know cfb
late frost
Great
slender nacelle
But you know one thing
How does it help you?
That 45 degrees which you haven't used yet
late frost
It's in a triangle that cd is in
slender nacelle
Can you tell me which side will be equal to cd?
late frost
Qb
slender nacelle
And?
late frost
bd
slender nacelle
And?
late frost
Qc
late frost
No
late frost
Its a right triangle
slender nacelle
Can you apply Pythagoras to the triangle?
late frost
Which one
slender nacelle
Qfb
late frost
(fQ)^2 + (Qb)^2 = R^2
slender nacelle
Do you know what is fq? In terms of fc and qc?
late frost
fq = fc + qc
slender nacelle
But what's fc?
late frost
R cos(45)
slender nacelle
And what's qc?
slender nacelle
Great
slender nacelle
Now you're done
late frost
So it will be (R cos(45) + cd)^2 + cd^2 = R^2?
late frost
yes
slender nacelle
Tell me what answer you get!
late frost
Is this the correct equation:
R^2cos^2(45) + 2 Rcdcos(45) + cd^2 - R^2 = 0
slender nacelle
Yes, looks correct
late frost
How tf you solve that BS
slender nacelle
Only unknown you have is cd
And this is quadratic equation in cd
First put the value of cos45
And simplify the equation
slender nacelle
-0.5R^2 + sqrt(2)Rcd + cd^2 = 0
late frost
Oh Yah
slender nacelle
Do you know how to solve ax²+bx+c = 0?
slender nacelle
No. c is -0.5R^2
slender nacelle
It's okay. We all make mistakes
late frost
A is 1 right?
slender nacelle
Yes
slender nacelle
I don't think so 🤔
somber coyoteBOT
dissy:
slender nacelle
I don't think so
late frost
$$ solve:for:x,:x^2+\sqrt{2}y:-:0.5y^2=0
somber coyoteBOT
dissy:
Compile Error! Click the 
reaction for details. (You may edit your message)
late frost
that was my input into symbolab
slender nacelle
solve:for x :$x^2+\sqrt{2}xy-0.5y^2=0$
late frost
oop
somber coyoteBOT
oscillatingEquilibrium:
somber coyoteBOT
dissy:
Compile Error! Click the reaction for details. (You may edit your message)
slender nacelle
Looks correct
late frost
@slender nacelle Tysm for wasting your time for my mathematical education
slender nacelle
Lol. No problem!
Glad to help
Wait @late frost
I think you made the mistake
-0.5R^2 + sqrt(2)Rcd + 2cd^2 = 0 is the correct equation
late frost
Ok
slender nacelle
You forgot another cd!
late frost
$$ x=\frac{\left(\sqrt{6}-\sqrt{2}\right)r}{4}
somber coyoteBOT
dissy:
Compile Error! Click the reaction for details. (You may edit your message)
slender nacelle
Yup
deft barn
i have a question relating to trig. - for finding all solution of a equation in an interval, when do we use 2kπ and kπ?
tiny grail
doesnt matter aslong as the answer is right
eternal crag
brazen relic
(angle) + 2kpi for sine and cosine
brazen relic
Must've been tan
stark dock
https://www.youtube.com/watch?v=593w799sBms&list=PLmSGbjacooPfwaA5s3NYox9AIrXFwFsNW&index=3&t=1930s I have a question about this video, around the 29 minute mark. Why do these coordinates matter (eg. sqrt(2)/2) and how do we know to put them where they are on the circumference?
I understand the values are for sin, cos, etc, but they seem almost arbitrary to me. (I know they are not arbitrary, but that is how i am ignorantly perceiving them right now).
boreal light
@kraddict I found a good/brief visual video for you to help visualize "why the coordinates matter", as you asked. (https://youtu.be/Q55T6LeTvsA) The thing to remember here is that these values are not arbitrary - they are inputs and outputs of a function that can be plotted like a wave - sine, cosine, etc. The unit circle is a helpful way to measure these values and visualize them in contrast to other points on the wave. There are some additional helpful graphics under "Trigonometric functions on the unit circle" section of this wiki article: (https://en.m.wikipedia.org/wiki/Unit_circle)
The other part of your question - "how do we know to put them where they are on the circle" - relates to what I mentioned before about them being inputs and outputs. Each spot anywhere along the circle only corresponds to ONE input and ONE output on the interval (0, 2pi). This becomes a bit more complicated when you work in larger intervals because of whatever nth time around the circle you are on, but don't worry about that yet until you feel confident with the basic sine and cosine inputs and outputs
Hope that helps.
stark dock
@boreal light this makes sense now, thank you. I guess a better question I have now is, why do we use sqrt notation? why not decimal? (eg. why "sqrt(2)/2)" and not "0.707"? I understand that the former is one of the ones that students are expected to memorize)
boreal light
Yes, that's a good question. Basically, you can think of anything with a square root as the "exact number", and the decimal version of that number as... essentially an approximation of that number. The reason is because sqrt(2)/2 actually equals 0.707106781185...
Is it easier to write out that long decimal, or the sqrt(2)/2 every time? ALSO -rounding is not always accurate. If you are measuring the distance from here to the moon and you were using scientific notation, shortening any number to 0.707 is not accurate - you're missing a lot of information.
In general, decimals are not as accurate, and they are longer. One of my favorite profs used to explain notation by explaining that mathematicians are lazy 🙂
Also (in general) it's more common to use radian notation than degrees when you are doing trig. Radian notation is where you will see a lot of the pis and square roots.
Similar question you might like to read: (https://matheducators.stackexchange.com/questions/122/answers-in-exact-form-e-g-including-radicals-vs-decimal-approximations)
stark dock
Gotcha, thank you. Radian notation is kind of new to me, so mentioning that this will be useful for when i see more of radian notation helps
("newly" new to me...I learned all of this stuff decades ago and am trying to re-learn everything lol)
boreal light
Radian notation is arguably more important to know when doing trig than degrees... you obviously have to know both but the majority of problems you will be assigned in a trig class will be using that notation
idle bloom
degrees are kinda arbitrary but radiens have geometric meaning
rich wolf
Radians
idle bloom
oops
idle bloom
Ya
swift moth
devout harbor
upper karma
@swift moth your book is being silly
high breach
different calculators give me different answeres when I use the cosine func
eternal crag
that might happen because
- you're using degree/radian
- calculator are engineers, they approximate cosine function with polynomials
idle bloom
@high breach when happens when you plug in cos(90)
swift moth
@upper karma that's what I thought as well
clear haven
i dont understand the premise at all
how is it mirror symmetric and across what line is it so
oh shit
im dumb
lmfao
ignore me
cinder portal
lol @clear haven what app is that
tawdry pivot
if you want to feel stupid
clear haven
yuS
eager pendant
white cradle
holy shit this game is good
solar hearth
yeah thats how i proved it
solar hearth
although my alg was kinda dodgy so i wasn't sure if there was another solution lol
worldly wave
what could I use an equation of a sphere for in real life?
solar hearth
which equation
worldly wave
the
(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2
I understand equation of lines can be used to predict
stuff like
you know
stock market stuff
creating relations between two things
I've used them
We were tasked to do a problem relating to geometry
and if I do it with the equation of a line that problem will end in like 5 lines and it's just too easy
And idk what I can use a sphere's equation in
solar hearth
im underquailfied to talk about this
lol
although im sure there is a practical use for it
worldly wave
Ya.
And I'm under-qualified to make one on my own.
we're supposed to search it out but
I can't find anything xD.
solar hearth
welp i hope you get ur answer
sly marlin
@solar hearth If you are still stuck, you can think of circumcircle of ABC as an incircle.
bleak lintel
very basic question, how does one find the point where y = sinx and y = -x-(pi/2)-1 intersect
bleak lintel
yes
but wot
sinx = -x -(pi/2) -1 doesn't really seem that straight forward to me
might just be my stoved head
weak shoal
yea i don't think there's a way to solve for x. But it's just that x = -pi/2 is sort of an obvious solution
bleak lintel
yes
I came to that too just the way I got to it is by moving -1 to the other side
then evaluate at0
lmao
weak shoal
lol
bleak lintel
well they should be equal
but hey still got it, thansk tho
was to calculate my borders
for this boi
weak shoal
oh lol
rugged pebble
This is election seal of Taiwan, using on voting stamps, with its asymmetric property it allows voting station staff to distinguish wether or not the mark on folded vote is an actual stamp or just a wet mark, in that case this seal would be mirrored.
What I'm interested in is that it is said that the reason they choosed this particular sign, is because this is the simplest non point symmetric nor line symmetric symbol to be carve onto a seal (that means the circle is required), and I want to check if that is mathematically true.
dark sparrow
well it depends on what you mean by simplicity
i mean if you're carving then you want lines
and one line won't do
but two will
weak shoal
??
median crown
does anyone know an formula to find the length of that cord
weak shoal
The straight portion or the arc?
median crown
using some trig functions
median crown
yees
somber coyoteBOT
Abhijeet Vats:
weak shoal
Let L be the length of that chord
weak shoal
Well, their sum is $180-\theta$
somber coyoteBOT
Abhijeet Vats:
median crown
oh yeah
weak shoal
Yeap
So, let L be the length of the chord
Then, notice that:
$L\sin(90-\frac{\theta}{2}) = r\sin(\theta)$
somber coyoteBOT
Abhijeet Vats:
somber coyoteBOT
Abhijeet Vats:
weak shoal
So now, we have:
$Lcos(\frac{\theta}{2}) = r\sin(\theta) = 2r\sin(\frac{\theta}{2})\cos(\frac{\theta}{2})$
somber coyoteBOT
Abhijeet Vats:
weak shoal
So L is, then, just:
$L = 2r\sin(\frac{\theta}{2})$
somber coyoteBOT
Abhijeet Vats:
weak shoal
Okay?
median crown
k
weak shoal
Nice
tawdry pivot
cosine rule
weak shoal
Sure but i don't really memorize such rules, which is why i didn't present it as a method.
upper karma
@daring venture Cant help you much with the first one but for the seconds one, this is what I did:
sorry for sloppy handwriting
upper karma
since no one has replied
$sin^{6}x + cos^{6}x = (sin^{2}x + cos^{2}x)^{3} - ...$
somber coyoteBOT
A. S.:
upper karma
nice little hent for ya
idle bloom
sum of cubes
solar shale
What would I do next I don’t understand what it’s asking
weak shoal
Keep factorizing
solar shale
Ok
weak shoal
You have:
$f(x) = 0$
$100x^4 - 81 = (10x^2 - 9)(10x^2 + 9) = (\sqrt{10}x - 3)(\sqrt{10}x + 3) (10x^2+9) = 0$
Fkkkkk
somber coyoteBOT
Abhijeet Vats:
weak shoal
Anyways, if they're asking for all the real roots, then you just have 2 of them that are real. Since they're asking you for ALL the roots, you probably need to give the complex ones as well.
solar shale
So that’s good so far
weak shoal
Mmmh
solar shale
So now
weak shoal
If they're asking for the complex roots as well, you gotta factorize 10x^2 + 9
weak shoal
What do you mean?
weak shoal
Uh $10x^2 + 9 = 0$ has no real solutions for x. You can, however, still factorize it:
$10x^2 + 9 = (\sqrt{10}x + 3i)(\sqrt{10}x -3i)$
Where $i^2 = -1$
somber coyoteBOT
Abhijeet Vats:
solar shale
Oh my bad for not clarifying it more I meant that
weak shoal
So, now, your quartic polynomial has 4 linear factors and 4 solutions. 2 are purely real, 2 are purely imaginary.
solar shale
So I just leave the 4 functions? Or like how would I write the answer
weak shoal
Well, you could say that:
$100x^4 + 81 = (\sqrt{10}x - 3)(\sqrt{10}x+3)(\sqrt{10}x + 3i)(\sqrt{10}x-3i) = 0 \implies x = \frac{3}{\sqrt{10}}, x = \frac{3}{\sqrt{10}}, x = \frac{-3i}{\sqrt{10}}, x = \frac{3i}{\sqrt{10}}$
somber coyoteBOT
Abhijeet Vats:
weak shoal
You should place 'or' wherever i placed the commas
solar shale
Wait is this like where I say multiplicity of like 2 for example@or something similar=#
weak shoal
weak shoal
Uh yea i guess
solar shale
Last problem
solar shale
This time it asks for identifying all multiple roots
This is where multiplicity happens right?
I did some problems earlier before break and it says that I kind of forget how to solve tho
silent plank
factorise the (x^2 - 1) and (x^2 + 1) first
then distribute the exponent
silent plank
not what the questions is asking for.
you pretty much returned to the start and erased the ^2
from their factorisations:
$ (x^2 - 1)^2(x^2 + 1)^2 = ((x+1)(x-1))^2 ((x - i)(x+i))^2$
somber coyoteBOT
ramonov:
silent plank
and then distribute the exponents to those terms
solar shale
Wait so should I first multiply parenthesis then ^2
umbral snow
You don't actually want to multiply at all. Factoring is the right way to go. But, you're losing what the ² is applying onto
solar shale
I don’t quite understand
silent plank
$(ab)^2 = a^2 b^2$
somber coyoteBOT
ramonov:
umbral snow
[x² - 1]²
= [(x + 1)(x - 1)]²
= (x + 1)²(x - 1)²
weak shoal
See, there's a difference between:
$(x-1)(x+2)^2$
And:
$[(x-1)(x+2)]^2$
somber coyoteBOT
Abhijeet Vats:
weak shoal
So, you gotta be clear about that. That's why your parantheses are really important.
silent plank
there isn't much point expanding it again after you just factorised
did you understand:
$ (x^2 - 1)^2(x^2 + 1)^2 = ((x+1)(x-1))^2 ((x - i)(x+i))^2$
somber coyoteBOT
ramonov:
silent plank
including the necessary presence of all the parentheses
upper karma
Find the area of the square. Both circles have a radius of 1.
cinder portal
u want a hint? @upper karma
hasty flicker
It sounds like he set it as a puzzle for others
hasty flicker
nah
hasty flicker
you select the section you wish to hide, right-click it and press hide or whatever it is
mark as spoiler
upper karma
Which option?
hasty flicker
ah
you must be on the browser version
you can use double "||" before and after the chunk of text
rigid thunder
||B R U H||
rigid thunder
@upper karma I got approx 0.677
hasty flicker
^ same
although I'm sure there's a simpler solution
how did you find it @rigid thunder? I created equations for the length of a horizontal and vertical side of the square at a certain angle from one of the circle centres and solved where the horizontal & vertical sides are equal
hasty flicker
This is what I got and I had to get it to be solved by a machine
since I know not how to solve these 😛
rigid thunder
somber coyoteBOT
maxymczech:
hasty flicker
that is a lot smarter xD
I should've spotted that
well they seem to take a similar amount of working
you need a quadratic equation for this to get x right?
rigid thunder
yes, you get something like
somber coyoteBOT
maxymczech:
hasty flicker
ah cos135 = root2/2 that's convenient
rancid gust
I just got a physics take home test and im kinda lost
- Add the following forces: 20 newtons south, 30 newtons north, 40 newtons east, and 50 newtons west
How would I solve that>
?*
mint lion
Start with a free body diagram
hasty flicker
and then use trig to get 2 perpendicular forces
warm frigate
any tips to prep for trig
thorn talon
what's in the course?
hasty flicker
I don't know why but I find trig hard
It just doesn't feel that right to me
ambiguous case n that ugly stuff
rigid thunder
dark sparrow
??
sudden locust
First video of 2020, hope you like it ❤️ https://youtu.be/1VqO8MtoMJ0
frosty steppe
What's your strategy for getting 3?
frosty steppe
You can do better
torpid torrent
how 4
frosty steppe
Where do you cut to get 3?
frosty steppe
You can take cross sections anywhere in the shape, not just on its surface
torpid torrent
what?
i thought cross sections
where only through a shape
like this
like basically the base of the left figure
except through the shape
frosty steppe
Yeah you're right
torpid torrent
so that is 3 points
frosty steppe
With that definition, you can do 4
torpid torrent
how?
dark steeple
I don't understand the question
torpid torrent
i thought its only like one plane
buoyant forge
is there a place online i can learn geometry from the very beginning
wraith haven
just try to find a geometry textbook with a lot of problems and try to solve them
unfortunately i don't know any english textbooks, but maybe someone else here can recommend something
i know a good russian book that has ~5000 problems but that's the only geometry book i know
dusky cobalt
hm
quiet mason
theres this circles book from.russia
upper karma
hello i have a big problem with math. vectors
vague pagoda
What is your problem exactly
upper karma
it is this sheet of theory sorry that it is not in englisch but i can translate 🙂
i am trying to understood this formula since 2 days but i could not get the point
how can i do the excercises with the formula
D in the formula is the distance the line g to the point B
thorn talon
hmmm
the magnitude of the cross product gives you the area of that parallelogram
= base * perp. height
then divide by the base length
to give the perp. height?
@upper karma can you give a translation
upper karma
yes
of the theory or of the exercise
F4 Distance from point- Line
it says point P is given and g: also
and i need to find the distance d from the point B from the line g
There are several ways to address this problem. With the help of the vector product, a particularly elegant solution can be found. To do this, understand d as the length of the height of a parallelogram. In this way, the distance formula point-straight is obtained from the vectors v and AB
thorn talon
yes
so my interpretation was correct
what is troubling you?
@upper karma
you can pick any arbitrary points A and C that lie on the line
upper karma
yes but i have troubles with the second excercise
there it says
i should show that for every point p from the line g die distance AP is shorter than the distanze BP
the excercise is the last one on the screnshoot i sended
thorn talon
wait, where's B?
upper karma
B is P
thorn talon
then what is BP?
thorn talon
so B is not P?
daring venture
how do u do this
dusky cobalt
the two triangles are similar
daring venture
wanton kestrel
@daring venture
What does it mean for those triangles to be congruent?
upper karma
yeah
torpid torrent
im confused
pls help
its 80
if i wrote another aux line
parallel
ok
thank u
i dummy
this makes sense right
wb this
this too
pls someone else help
thorn talon
How would add those fractions?
silent plank
parentheses
thorn talon
Yes
torpid torrent
you never just keep the numerator
thorn talon
And also yes to parentheses
torpid torrent
sorry it was just a disconnect from taking those fraction principles into variables
thorn talon
A simple checking method that can eliminate answers
Is to remember that you can just sub certain values into and see if it holds
Obviously not a good way to solve the problem
But alright for checking
eager kraken
I just took a semester off after algebra and im about to go into trig
thorn talon
Nice
green roost
Stupid question because I've not touched triangles in a long time and I cant remember, do perpendicular bisectors have to bisect through the midpoint of a line in a triangle?
green roost
Too much work on logs and calculus has made me forget everything lol
So should I just pick a point from the line it bisects, rather than using the midpoint?
wanton kestrel
oop my brain got rekt there
by perp. bisector u mean that a line perp. to another line bisects that line
perp. bisector or angle bisector?
green roost
I mean a line that intercepts another line at right angles, so m1×m2=-1
wanton kestrel
where does a perp. bisector meet the other line?
green roost
That's what I'm asking, I've to find the equation of that line, but I dont remember if I can use any point on the line that it intercepts (on the triangke) or the midpoint of that line
wanton kestrel
by definition a segment bisector meets another segment at its midpoint
hence "bisect" ["in half"]
so your perp. bisector meets a side of the triangle at a point on that side
you can use both points
green roost
So it doesnt matter what point i use?
I seem to remember that being the case, but I've not did this in a while
wanton kestrel
what's the original question?
i'm not sure how you can get the slope of the bisector just by using the coordinates of one point
green roost
A is the point (2, -1), B (10,-5) and c (2,-5), find the equation of the perp. Bisector of AB
I know that the gradient of the bisector is 2
But when I sub into y-b... I dony remember if i can just sub in the point A or if I need to use the mid point of AB
wanton kestrel
i see
but the perp. bisector of AB doesn't intersect AB at A
so you clearly can't use A
but you can use the midpoint on AB ofc
since that's part of the bisector and A is not
green roost
Ok thanks, just been a while since I did this so I'm rusty
green roost
Same, just too many names to remember, I spend more time trying to remember what I'm supposed to ge working out than I do actually working it out lol
green roost
Calc, logs, functions, quadractc theory, all fine, but god I hate geometry
sudden locust
The Area of a Circle Proof - This proof made me get an "aha-moment", I live for these! Hope it can provide some value! 😊
random aurora
how do i calculate the POI of a exponential and sinusoidal function
daring venture
weary drift
pts of inflection? find where the second derivative changes sign
vague pagoda
No
He said that he meants points of intersection algebraically and said that he hasn’t took calc yet
daring venture
g
primal saffron
There’s a unit cube ,1 by 1 and an ant starts on one corner and wants to travel to the furthest corner away . He can only travel across the faces of the cube , what’s the shortest distance he needs to travel ?
would i have to split this up into a 2d net?
clear forge
2d net yeah
calculate straight line distance
prove it’s the shortest as well for fun
primal saffron
is there a certain way to do that? or would you just have to show all the possible different paths?
primal saffron
@clear forge
upper karma
can someone help me
rich wolf
sure
silent plank
,rotate
somber coyoteBOT
upper karma
kinda
hallow brook
🤦
frank sail
In the Parallelogram isn't (3)=50°?
Cause of some rule or another which I don't remember the name of...
soft gulch
it is 50
interior angle
1 is 32
2 is 98
- 1=38=4, 2=90, 3=90,
- 3=54=2, 4=1=72
@upper karma
frank sail
How did you get the rhombus' angles?
robust socket
$2(\sin(x)\cos(\frac{\pi}{3})+\cos(x)\sin(\frac{\pi}{3})=2\sin(x+\frac{\pi}{3})$
somber coyoteBOT
Umma.Gumma:
robust socket
can someone explain me this factorisation please
dark sparrow
sin(a+b) = ?
robust socket
damn, the other way round, thanks
how long did you take to get fluent with trig identities? this one was trivial but in general I feel I am not fluent enough
and I really want to move to limits, I'm not a big fan of trig tbh
dark sparrow
idk i didn't measure
robust socket
right
sudden locust
Intuitive Proof of the Area of a circle! https://youtu.be/vHs7vvD52oI 🔵 👈 😳
jaunty sail
silent plank
those 4 triangles would be congruent
jaunty sail
Alright so then
silent plank
you'll probably need to know that to solve this.
have you tried looking that up?
(and the derivations)
jaunty sail
I’ll look it up
I saw this problem on social media
And I wanted to learn how to solve it
tiny moon
you have the hypotenuse of the triangle as 10
jaunty sail
Ya
eager kraken
Is a modulo operation really just the remainder of the division?
frosty steppe
Yes, if you’re trying to calculate it
turbid rain
say i have an arbitrary segment, i.e. x1, y1, x2, y2
how can i obtain a 'margined' area around the segment?
for horizontal and vertical segments it's easy, i just need to add the margin m to corresponding x and y coordinates of the segment
i'm having difficulty with segment with slope
how is the margined area defined for them?
like this?
or this?
upper karma
I'm confused what you mean by 'the margined area' like are you lookign for some numeric value or a subset of the plane?
twin prawn
If you're trying to ask which definition makes more sense, then there's a lot of reasons we could give for either, but in the end it might not be able to help you answer whatever question or project you're working on 
turbid rain
@upper karma @twin prawn i'm working on a project where this segment is given, and the margin (or padding). and i need to find the objects (shapes) that intersect the segment or are within the "margined" area...
currently i take (xmin - margin, ymin - margin) for margined area lower left and (xmax + margin, ymax + margin) for upper right coordinates
but it doesn't work well with above segments
upper karma
@turbid rain wouldn't the margin at the end be a semicircle?
turbid rain
@upper karma
but how would i get the coordinates of that surrounding object from segment's begin and end coordinates?
upper karma
I'm really confused as to what you want if I'm entirely honest
if this is for computing the problem is that it's an infinite set lol
do you want a function saying if itis within the range?
buoyant forge
So im going over basic geometry and im being introduced to all these trapezoids, kites etc..
Am i supposed to remember all this?
buoyant forge
oh ok
do they give a sheet on how to do em?
Im most likely not gonna remember how to find an area of a kite in a big test including everything not only geometry and trigonometry in a test
upper karma
Hello i was wondering if someone could help me with something
Im actually trying to install something and need to add some tension to my pole
But there's an object in the way
I measured the box 4.5' tall but im trying to give it some leeway so other people can open the box (opens on the right side), so i wanna have the downguy at least 10' (5.5' above the box)
can someone tell me what equation i should use? been trying to google pythag theorem stuff but couldnt find something similar
foggy island
earnest phoenix
feeling real stupid, as a near college graduate, not knowing what this question is expecting of me
but like
idk, do they want me to pull out a pixel ruler and measure the sides perfectly?
arctan(1/2) = .4636 rad
upper karma
what they're asking is ridiculous
maybe try a lower accuracy but you only get 6 tries lol
earnest phoenix
yeah, I'm sweating bullets lmao
somber coyoteBOT
Requested by A. S.#7247
upper karma
yeah, try 0.4?
marble parcel
turbid rain
@upper karma yes i need some function maybe? with the semicircles as margins, yes it's not easy. so the previous approaches i presented maybe should be used?
turbid rain
these are the polygons that i identified as margined areas, i suppose there isn't any other one...
upper karma
@turbid rain dude, I legit don't understand what you're trying to return though
like can you simply state what it is the function returns
turbid rain
@upper karma i didn't make a function... i'm not sure how to do that. i just wrote the functions for each case i guess
upper karma
oh my god
whati s the object you are trying to return?
sorry for sounding frustrated
uneven halo
I am wondering if a point in any-dimensional space has width, length and other alike properties set to 0 or it is aproaching 0
did anyone wonder too?
upper karma
iterally what does that mean
uneven halo
well i think if it is 0, then points could overlap
upper karma
points in 1d space have 0 width 0 length
uneven halo
and the entire space could be just one point in another space
upper karma
it's true in any dimension lol
uneven halo
but if a line has unlimited points within it
and i encountered some definition that the power (dunno if I translate it good) of array of these points in another line is larger, then a line is longer
if length of a point is 0, wouldnt it be arbitrary?
turbid rain
@upper karma hmm well. what i need to do (overall) is to find the shape overlaps with the segment, and the margin is the margin around the segment.
i need to handle this for all segment types
vertical, horizontal etc
uneven halo
btw. I spent some time searching and it is said simply that points dont have such properties. It resolves the ambiguity
funny though
intuition dictates something like 0 length
@turbid rain is it 3d?
turbid rain
here even though segment and rect don't overlap, taking into account the margin, i need to consider this shape (rect) for something
@uneven halo 2d
uneven halo
what about the objects you mentoined,
do you have to find all of them,
are there any constraints?
upper karma
@turbid rain I'm sorry you're being so incoherent
Do you want to return a boolean for if there is overlap?
uneven halo
for what I understood so far, it has to be exactly within the area he describes as margined one
turbid rain
actually yes, but for that i need to determine the coordinates of the margined segment. which is what i'm asking
upper karma
what do you mean by 'the coordinates'?
turbid rain
the rect or polygon enclosing the segment with given margin
upper karma
so you're not going to have rounded ends of your margin
even though that would be the most appropriate?
i.e. all points within a distance r of your line segment
turbid rain
yes, that's the semicircle as you mentioned earlier
but with that approach i find it difficult to find the overlaps
upper karma
yes, it is a lot more difficult with rounded parts lol
so you want to return as an array the points defining the rectangle of the overlap?
turbid rain
there is existing algorithm which works incorrectly
i need to fix it
enhance to take into account the margined area
uneven halo
you wrote some ymin, xmax etc. onto your drawing, you didnt explain what's it
upper karma
I'm gonna go insane
what does this algorithm return
if you feed it input
what is the output
uneven halo
it it's IT problem, wouldnt it be faster (in terms of writing the code, performance would be a little worse) and more readable to copy the shape and just enlargen it, then pass to the working algorithm?
upper karma
... no
uneven halo
no rounded edges remember, so it should be vailable, shouldnt it?
upper karma
you want a human to look at hte image and feed the intersection points into a computer?
rather than just calculating the intersection points?
uneven halo
@turbid rain the things that are obvious to you arent obvious to us, feed us more data so me might be able to help you
upper karma
^ I agree 100%
turbid rain
i'm sorry, i will try to explain bette
so i have a canvas consisting of rects
the user should be able to "inspect" the rects in some area
to do that, the user can draw a segment and specify a margin. the area to find the shapes should be the area around the segment with given margin
currently i need to "find" the coordinates (?) of the margined area
around the segment
upper karma
how are you treating these rects?
are they just a 4x2 array?
or do you have some object?
turbid rain
rects are just 4 points (or 2)
upper karma
oh yeah, you only need 2 lol
so I'll write this all in vague terms
intersection_rectangle(line_segment[2,2], rectangle[2,2], margin):
for each point in rectangle, check if it's near line-segment (i.e. it's x and y coordinates are within the valid range)
if none: no intersect
if both: it fints entirely within the margin
if one: find which coordinate 'runs out' for want of a better word (i.e. hits the boundary of the margin) and choose the point defined by that
makes sense?
uneven halo
lets say your segments has two points: (x1, y1), (x2, y2)
the line user draws has slope = (y1-y2)/(x1-x2)
the same would have the line that connects point to the margin corner
now if you wanna you can calculate x = arctan(slope) from it and you can use then sin(x) cos(x) functions but there's a more optimal way with divisions:
calculate length of your segment
length = square_root((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2))
calculate the ratios:
marginx = margin*((x1-x2)/length) (it is equal to cosinus(x) * margin)
marginy = margin*((y1-y2)/length) (to sinus(x) * margin)
Corners of the area you want would be
(x1 - marginx, y1 - marginy) (x1 + marginx, y1 - marginy)
(x2 - marginx, y2 + marginy) (x2 + marginx, y2 + marginy)
but please first ensure x1-x2 and y1-y2 arent zeros
those are the cases you resolved by yourself
Was that what you wanted @turbid rain ?
turbid rain
@upper karma @uneven halo thanks and sorry, i was out, i will check it out now
uneven halo
If I have an axis, where I give a real number to every point on it...
is it correct to say that two points are x distant away, given x -> 0?
turbid rain
@uneven halo thanks that's helpful. but i think the corners aren't correct.
i worked it out on example and it isn't correct
turbid rain
okay
uneven halo
try now
if x1 < x2
and if y1 < y2
(x1 - marginx, y1 - marginy) is left top corner
(x1 + marginx, y1 - marginy) right top
(x2 - marginx, y2 + marginy) left bottom
(x2 + marginx, y2 + marginy) right bottom
those need to be meet
ensure x1 < x2
and y1 < y2
you can swap variables in your algoritm, make temporary ones to hold mininum and maximum seperately, or use function that will choose, w/e it's up to you
uneven halo
make a variable that holds minimum value
int minx, maxx, miny, maxy;
if (x1 > x2)
{
minx = x2;
maxx = x1;
}
else
{
minx = x1;
maxx = x2;
}
if (y1 > y2)
{
miny = y2;
maxy = y1;
}
else
{
miny = y1;
maxy = y2;
}
its cpp, make it work in your language
then put these variables instead of x1,x2 and y1,y2 in the algorithm
it should work then
ping me if it doesnt
uneven halo
pm
turbid rain
ok
upper karma
Can someone help me with this proof?
I know the first and third are given
The further is reflexive
Fifth*
Not further, my b
And I think the sixth is triangle vwz is similar to triangle xyz
And the seventh is transitive property
So I’m just unsure with the second and fourth
remote heart
I think that the forth is because triangle VWZ is similar to triangle XYZ
upper karma
But that’s the sixth
Because those triangles are similar by AA similarity postulate
And the fourth statement is stating a congruent angle between those two triangles
But I just don’t know the reason why those two angles are congruent
But you’re literally the goat
For trying 😭
No one else did yett 
SO THANK YOU
remote heart
XY is parallel to VW
upper karma
Yea, but that’s not a theorem or postulate
I can see that, but still..
For the reasons side, you have to write a theorem or postulate
And it already states that in the third statement
And in the given part
remote heart
I am sorry
upper karma
NOO DONT BE SORRY
You tried, that’s all that matters
But this proof is a life and death situation
The teacher said
Whoever gets this
Gets a Hershey kiss 😄
remote heart
wowooo
remote heart
if you know that the hypotenuse and the legs are straight, then don't you know that VW, meets YZ at the same angle XY does?
upper karma
Wait whut??
What postulate or theorem is that?
I don’t understand
Rip ;-;
Like it kinda makes sense
I just don’t know what to put for the reasons side
upper karma
Ah
This is at my home
On my pillow
Because
I don’t have a desk in my room
Because I have to share a room
So yea
Point is
I’m doing it at home LOL
So yea, I got abt 2 hrs before I go night night
eternal crag
nice username
upper karma
hAHa, thanks
I will always remember that day when nothing happened 😔
And nice profile picture
You are the goat at Euclidean geometry if you could solve this
marble topaz
Well, you've already got the dimensions for one triangle
And you can use law of sines to get the angles for said triangle
From there you can just work your way back until you get to line segment BD
@upper karma Do you see what I mean?
upper karma
Wait, please no sines, I didn’t learn that yet
marble topaz
Oh, my bad
marble topaz
What is the most recent thing you've worked on?
marble topaz
Oh that's like the precursor to the law of sines
upper karma
marble topaz
Gimme a sec to refresh my memory on how those work, because once you learn what I'm referring to you'll never use that again
Actually I don't remember how to use these, haha
Do you possibly have any notes on you?
If not, I guess I can tell you what I've been referring to
upper karma
Ah, its no problem
marble topaz
Sine A/a=Sine B/b=Sine C/c
where the little ones are the line segments directly opposite the angles
upper karma
That’s my textbook lesson I’m learning
I don’t know sine or cosine
yEt
So I have to stick with using the things ik
marble topaz
oh yikers
cobalt turtle
(psst, properties of an altitude)
marble topaz
I assume you've already noticed the other right angles, right?
upper karma
Right
marble topaz
aaaaa wow it's been so long since I've used these tools ahah
Straight geometry was never my strong suit, I only got better once I got more into trig
upper karma
Yea, a lot of people forget this
I swear, everyone says that
Everyone’s like the same person lmaoo
marble topaz
It's the worst feeling!
upper karma
!!
I bet haha
But this is like critical thinking
And open mind
And big brain
marble topaz
Well, go ahead and write down the rest of what you know
I already see one more similar triangle
And you have the length of the line segment. Do you see which one it is?
upper karma
I split ac into 81.6-x and x
marble topaz
If you can't see
upper karma
And ad and ab
marble topaz
It's AD. AD is the same length as--
upper karma
They’re marked by tick marks
marble topaz
Okay yeah you caught that
upper karma
It’s by diagram lmaoo