conversation_id
int64
1
206k
help_channel
stringlengths
6
7
__rowid__
stringlengths
32
32
author_id
int64
62,061,868B
1,071,443,446B
author_name
stringlengths
2
32
timestamp
stringlengths
19
19
content
stringlengths
0
3.97k
reference.messageId
stringclasses
3 values
reference.channelId
stringclasses
3 values
reference.guildId
stringclasses
1 value
url
stringlengths
0
591
fileName
stringlengths
0
513
student
int64
0
1
helper
int64
0
1
references.id
float64
62,061,868B
1,071,056,124B
references.name
stringlengths
2
32
references.discriminator
stringlengths
4
4
references.nickname
stringlengths
1
32
references.isBot
bool
2 classes
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:38:48
cuz cos wouldn't start from origin
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:39:07
right...
0
1
200,013,547,491,688,450
a disappointing son
0540
a disappointing son
false
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:39:13
so possibly your other answer that is already correct is right lol
0
1
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:23
so I put 1.5 again?
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:26
1.5 and 1.5?
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:39:31
no
0
1
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:33
X_X
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:34
eh
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:39:36
it tells you to select the correct function
0
1
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:39:39
only one of those is gonna be right lol
0
1
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:44
ohhhhh
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:45
ok ok
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:39:59
omg lol
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:40:03
what a tricky sneaky question
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:40:07
that was bs
1
0
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:40:08
indeed
0
1
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
200,013,547,491,688,450
a disappointing son
02/01/2022 17:40:09
lol
0
1
null
null
null
null
null
428
help-10
a5d649ba14904bb792d3111e1df02b26
351,013,311,996,887,040
♡ nahitspanda ♡
02/01/2022 17:48:22
.close
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 17:56:14
since H_t must be a vector space, does t=0?
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 17:56:30
since the 0 vector must be within a vector space
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 17:57:45
and does that imply that s must remain a constant, since the vector that results from the subtraction of two points in an affine space must be contained within its tangent space?
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:07:56
H_t isn't a vector space in general
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:08:13
H_t is an affine space
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:09:42
?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:09:51
Or am I misinterpreting notation
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:10:01
<x, y, z> is just a normal vector or not
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:10:05
H_t is the tangent space and H_s is the affine space I think
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:10:09
and yea it's a normal vector
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:10:20
I don't understand what tangent space means in this context then
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:10:28
For us it was just defined as
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:10:30
Geometrically, isn't H_t flat?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:10:40
Subtraction of two points in H_s will result in a vector in H_t
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:10:54
and adding a point in H_s with a vector in H_t will result in a point in H_s
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:10:58
ohhhhhh ok I get it.
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:11:09
Then yes the tangent space is a vector space
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:11:25
In particular
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:11:34
Think about a general plane in 3D space.
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:11:46
the equation is **x**.**n** = **a**.**n** = D
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:12:01
Do you recognise this?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:12:09
What does the . represent?
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:12:12
dot product
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:12:37
No, not really if I'm being honest I don't think we've introduced the dot product in the class yet
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:12:51
This is university/college stuff or not?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:12:57
Yes but it's an intro class
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:04
Did you not see plane equations in high school
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:14
cartesian equations?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:13:15
Yea
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:28
ax + by + cz = D
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:13:33
Ok got it yea
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:38
But in vectors, you haven't seen dot product?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:13:49
Is that the inner product?
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:50
That's kinda odd
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:51
yes
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:13:54
Ok yes
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:13:58
ax + by + cz = D
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:07
(a b c) . (x y z) = D
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:12
if I write those vectors as columns
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:16
you can see?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:14:18
Yes
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:23
**x**.**n** = **a**.**n** = D
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:26
So we have this form
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:29
The (a b c)
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:31
is **n**
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
382,568,504,936,759,300
Hungry Kitten
02/01/2022 18:14:40
got it
1
0
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:45
For one sec, lets think if D = 0
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:14:50
**x**.**n** = 0
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:15:01
This means variable **x** is orthogonal to **n**
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:15:09
yea
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:15:14
Your plane is all vectors perpendicular to **n**
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:15:24
sorry I got off my phone I'm here now
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:15:25
So if D = 0, it turns out **n** is the normal vector to the plane
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:15:39
ok
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:15:57
That make sense so far?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:15:58
So what does this have to do with affine space and the tangent space exactly?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:16:02
yea I do get it so far
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:16:08
Because I think it's v. related
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:16:22
In this case uhh
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:16:34
I'm pretty sure you have a plane, do you not?
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:16:42
yea
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:16:46
since the z is constant
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:16:47
Right
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:17:06
So for a shifted plane
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:17:11
**x**.**n** = **a**.**n** = D
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:17:18
You are shifting the plane by vector **a**
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:17:24
If **n** is a unit normal vector
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:17:34
And D = **a**.**n**
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:17:55
So actually, I think H_s will be the shifted plane. H_t will be the unshifted plane
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:18:55
https://cdn.discordapp.c…7241/unknown.png
unknown.png
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:19:27
So back to this, H_s in general is the plane parallel to the xy-plane, s away from the origin
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:19:40
Sure
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:20:00
t is the plane at the origin
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:20:13
And I think Hs and Ht have to be parallel
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:20:23
Aren't they already parallel
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:20:27
yh I guess lol
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:20:30
since we define H_s and H_t with constant z
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:20:32
So t = 0 is a must
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:20:37
and s = any element of R
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:20:43
Yh
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
321,445,119,171,756,000
Shuri2060
02/01/2022 18:20:46
thats what I figured
0
1
null
null
null
null
null
429
help-10
a866d67a4e74491fbd334d04b918d41d
225,110,750,161,666,050
Neko
02/01/2022 18:20:50
is H_t just displacing it up and down then?
0
1
null
null
null
null
null