Lilly Astar
@nasaexploration.space
Hi I am NasaExploration but call me Lilly ! I am french and euhh yeah that's it !
This wolf needed a home, I gave him one… hope he’ll be happy !
Thanks @andre.moraph.art for the amazing merch :D
Thanks @andre.moraph.art for the amazing merch :D
September 23, 2025 at 9:03 PM
This wolf needed a home, I gave him one… hope he’ll be happy !
Thanks @andre.moraph.art for the amazing merch :D
Thanks @andre.moraph.art for the amazing merch :D
April 20, 2025 at 12:16 PM
Happy birthday from France @yonkagor.fish !!!!!
February 26, 2025 at 11:28 PM
Happy birthday from France @yonkagor.fish !!!!!
I saved some of @andre.moraph.art’s arts on my phone to show them to a good friend and my phone made a freaking video on it ! I found this so funny
December 27, 2024 at 5:43 PM
I saved some of @andre.moraph.art’s arts on my phone to show them to a good friend and my phone made a freaking video on it ! I found this so funny
Hey @andre.moraph.art out of curiosity, I have three questions for ya :D
1 - Is the text at 1:09:10 in the left corner intentional?
2- You switch between a beautiful script and cursive, is it your handwriting ?
3- At 4:24 in the vocal it's To linger in the what? Just need that to complete the sub :D
1 - Is the text at 1:09:10 in the left corner intentional?
2- You switch between a beautiful script and cursive, is it your handwriting ?
3- At 4:24 in the vocal it's To linger in the what? Just need that to complete the sub :D
December 10, 2024 at 11:27 PM
Hey @andre.moraph.art out of curiosity, I have three questions for ya :D
1 - Is the text at 1:09:10 in the left corner intentional?
2- You switch between a beautiful script and cursive, is it your handwriting ?
3- At 4:24 in the vocal it's To linger in the what? Just need that to complete the sub :D
1 - Is the text at 1:09:10 in the left corner intentional?
2- You switch between a beautiful script and cursive, is it your handwriting ?
3- At 4:24 in the vocal it's To linger in the what? Just need that to complete the sub :D
@andre.moraph.art and @luiroi.bsky.social YOU BOTH GOT A PLACE AT FAUNTASTIC. Jeez 34 seconds I couldn’t even grab my phone TwT. Hopefully next week I can grab a residential pass…
December 1, 2024 at 8:28 AM
@andre.moraph.art and @luiroi.bsky.social YOU BOTH GOT A PLACE AT FAUNTASTIC. Jeez 34 seconds I couldn’t even grab my phone TwT. Hopefully next week I can grab a residential pass…
:3c
The Speckely Goober just arrived. Wonder if more of my French fellows received theirs :D
The Speckely Goober just arrived. Wonder if more of my French fellows received theirs :D
November 27, 2024 at 4:25 PM
:3c
The Speckely Goober just arrived. Wonder if more of my French fellows received theirs :D
The Speckely Goober just arrived. Wonder if more of my French fellows received theirs :D
Everyone it’s happening !!! It took about 10 days of transit to finally reach France ! I don’t know what took it so long when some French lads already have it it’s so weird ! It might come on my birthday that’s approaching very soon hehe
November 22, 2024 at 10:39 AM
Everyone it’s happening !!! It took about 10 days of transit to finally reach France ! I don’t know what took it so long when some French lads already have it it’s so weird ! It might come on my birthday that’s approaching very soon hehe
I think it was just the france side being completely incompetent. Stayed a week in the port of arrival if I understand the tracking correctly
November 16, 2024 at 6:11 PM
I think it was just the france side being completely incompetent. Stayed a week in the port of arrival if I understand the tracking correctly
I feel. Last year it wasn’t rare for me to do do 4 hours nap from 6 to 10 pm. I truly feel. You got this I am sure *pets*
Here is my cat resting :D
Here is my cat resting :D
November 8, 2024 at 4:23 PM
I feel. Last year it wasn’t rare for me to do do 4 hours nap from 6 to 10 pm. I truly feel. You got this I am sure *pets*
Here is my cat resting :D
Here is my cat resting :D
I dwon’t seeeeee what ywourrr twalking about uwu furry talk 👉👈
(Yes I am bad at it but shushhhhh)
(Yes I am bad at it but shushhhhh)
October 31, 2024 at 1:06 PM
I dwon’t seeeeee what ywourrr twalking about uwu furry talk 👉👈
(Yes I am bad at it but shushhhhh)
(Yes I am bad at it but shushhhhh)
Yesterday I saw a wild fox ! In the middle of the Pyrénées Mountains in France ! I know the pictures aren’t great but I was too busy yelling ‘Renard’ (Fox in French). They even sat for us for a few minutes. My life goal have been achieved !
October 29, 2024 at 9:04 AM
Yesterday I saw a wild fox ! In the middle of the Pyrénées Mountains in France ! I know the pictures aren’t great but I was too busy yelling ‘Renard’ (Fox in French). They even sat for us for a few minutes. My life goal have been achieved !
I saw two small kittens today that were found by an old man who posted an article to found them a new house. Sadly I couldn’t take one due to my personal situation but my sister’s friend did take one :D
Small thought of @bremeows.bsky.social who call themselves silly kitten… much love Bre :3c
Small thought of @bremeows.bsky.social who call themselves silly kitten… much love Bre :3c
October 28, 2024 at 8:35 PM
I saw two small kittens today that were found by an old man who posted an article to found them a new house. Sadly I couldn’t take one due to my personal situation but my sister’s friend did take one :D
Small thought of @bremeows.bsky.social who call themselves silly kitten… much love Bre :3c
Small thought of @bremeows.bsky.social who call themselves silly kitten… much love Bre :3c
The red function with rectangles, anthony-mansuy.fr/TP25-ECE.pdf
The subdivision x_0 to x_7, fsm.rnu.tn/useruploads/...
Math equation, me with TeXit on discord
That’s it. Thanks for reading ! Don’t hesitate to share !
The subdivision x_0 to x_7, fsm.rnu.tn/useruploads/...
Math equation, me with TeXit on discord
That’s it. Thanks for reading ! Don’t hesitate to share !
October 23, 2024 at 6:27 PM
The red function with rectangles, anthony-mansuy.fr/TP25-ECE.pdf
The subdivision x_0 to x_7, fsm.rnu.tn/useruploads/...
Math equation, me with TeXit on discord
That’s it. Thanks for reading ! Don’t hesitate to share !
The subdivision x_0 to x_7, fsm.rnu.tn/useruploads/...
Math equation, me with TeXit on discord
That’s it. Thanks for reading ! Don’t hesitate to share !
So there we go we built integral and even found a way to calculate it.
This was my favorite lesson last year and I hope you enjoyed reading this. If you have any questions don’t hesitate to reach out to me !
In the next post you will find credits and a more elaborate function and triangles !
Thanks!
This was my favorite lesson last year and I hope you enjoyed reading this. If you have any questions don’t hesitate to reach out to me !
In the next post you will find credits and a more elaborate function and triangles !
Thanks!
October 23, 2024 at 6:24 PM
So there we go we built integral and even found a way to calculate it.
This was my favorite lesson last year and I hope you enjoyed reading this. If you have any questions don’t hesitate to reach out to me !
In the next post you will find credits and a more elaborate function and triangles !
Thanks!
This was my favorite lesson last year and I hope you enjoyed reading this. If you have any questions don’t hesitate to reach out to me !
In the next post you will find credits and a more elaborate function and triangles !
Thanks!
We would get this formula. It’s called Riemann’s Sum.
But then comes the magic. If we take a n larger and larger we add more and more triangles so we approach the value of the integral more and more. And that’s the magic, the sum will rigorously converge to the integral of f from a to b.
But then comes the magic. If we take a n larger and larger we add more and more triangles so we approach the value of the integral more and more. And that’s the magic, the sum will rigorously converge to the integral of f from a to b.
October 23, 2024 at 6:20 PM
We would get this formula. It’s called Riemann’s Sum.
But then comes the magic. If we take a n larger and larger we add more and more triangles so we approach the value of the integral more and more. And that’s the magic, the sum will rigorously converge to the integral of f from a to b.
But then comes the magic. If we take a n larger and larger we add more and more triangles so we approach the value of the integral more and more. And that’s the magic, the sum will rigorously converge to the integral of f from a to b.
If we create a nice even subdivision of length n where the step between each point of it is exactly (b-a)/(n-1), we can try to plug it into our sum that I showed earlier. What would it makes ? See in the picture the value of the subdivision on its k-th point.
October 23, 2024 at 6:12 PM
If we create a nice even subdivision of length n where the step between each point of it is exactly (b-a)/(n-1), we can try to plug it into our sum that I showed earlier. What would it makes ? See in the picture the value of the subdivision on its k-th point.
What if now we take a subdivision finer and finer. If we make the distance between two subdivisions smaller and smaller won’t we approach the value of the integral more and more ? On the image below you can see how the triangles fits under the curve more and more.
October 23, 2024 at 6:04 PM
What if now we take a subdivision finer and finer. If we make the distance between two subdivisions smaller and smaller won’t we approach the value of the integral more and more ? On the image below you can see how the triangles fits under the curve more and more.
Then we simply add the area of each triangles in between every subdivision. Here we have the sum of every triangles area (the multiplication) and we take the value on the left of the subdivision. Try it yourself ! Draw a line and draw each triangles on a random subdivision you made.
October 23, 2024 at 6:00 PM
Then we simply add the area of each triangles in between every subdivision. Here we have the sum of every triangles area (the multiplication) and we take the value on the left of the subdivision. Try it yourself ! Draw a line and draw each triangles on a random subdivision you made.
Then how could we calculate it ?
Introducing the rectangle method !
We will use the subdivision to draw rectangles in between each subdivision that will approach the value of the area under the graph. Let’s go over the details.
Introducing the rectangle method !
We will use the subdivision to draw rectangles in between each subdivision that will approach the value of the area under the graph. Let’s go over the details.
October 23, 2024 at 5:45 PM
Then how could we calculate it ?
Introducing the rectangle method !
We will use the subdivision to draw rectangles in between each subdivision that will approach the value of the area under the graph. Let’s go over the details.
Introducing the rectangle method !
We will use the subdivision to draw rectangles in between each subdivision that will approach the value of the area under the graph. Let’s go over the details.
So now you might wonder what are integral ? They are quite simple actually ! It’s simply the area under the curve of a function. Recall our function earlier ? Well the part in grey under the curve is actually what the integral of the function between the point a and b would be.
October 23, 2024 at 5:35 PM
So now you might wonder what are integral ? They are quite simple actually ! It’s simply the area under the curve of a function. Recall our function earlier ? Well the part in grey under the curve is actually what the integral of the function between the point a and b would be.
Now what if we apply the subdivision to a function, maybe when we draw the graph of a function you have to lift your pen but only for a point, then what if we find a subdivision where the function is continuous on every point exact the one in the subdivision ? That’s called by part continuity !
![Here we have a function that’s obviously not continuous. Though it’s by part continuous on the segment [-3, 3] because you can find the subdivision (-3, -1, 1, 3) where the function is continuous on the segment [-3, -1[, ]-1, 1[ and ]1, 3]. This makes it by part continuous. Visually we can see this as having to lift the pen but only for the exact point.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:njnitc6hnhw3tqhiwhkhsyzf/bafkreihcg6hfjvc6j6d5ky57l4jrtmfe4cwlqjy5um33jtp22p3rm3dn4q@jpeg)
October 23, 2024 at 5:28 PM
Now what if we apply the subdivision to a function, maybe when we draw the graph of a function you have to lift your pen but only for a point, then what if we find a subdivision where the function is continuous on every point exact the one in the subdivision ? That’s called by part continuity !
We say that a subdivision delta = (a_1, a_2, …, a_n) is a subdivision if a_1 < a_2 < … < a_n where a_1 = a and a_n = b.
While this might seems complicated, what it actually says is that it only grows and the starting and end point is the start and end of your subdivision. See picture for reference.
While this might seems complicated, what it actually says is that it only grows and the starting and end point is the start and end of your subdivision. See picture for reference.
![Here (x_0, x_1, …, x_6, x_7) is a subdivision because the first, x_0 is a, the last one, x_7 is b and the x grows, aka x_0 < x_1 < x_2 < … < x_7. This makes the set of points a subdivision of the segment [a,b]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:njnitc6hnhw3tqhiwhkhsyzf/bafkreigqfwe6uoai2fn6mnjpdeqcymm5q7htvmiq5xym53ea24crpq3t6q@jpeg)
October 23, 2024 at 5:23 PM
We say that a subdivision delta = (a_1, a_2, …, a_n) is a subdivision if a_1 < a_2 < … < a_n where a_1 = a and a_n = b.
While this might seems complicated, what it actually says is that it only grows and the starting and end point is the start and end of your subdivision. See picture for reference.
While this might seems complicated, what it actually says is that it only grows and the starting and end point is the start and end of your subdivision. See picture for reference.
We will say a function is continuous when you can draw the graph of the function without lifting your pen. For example here is the graph of a continuous function between the point a and b. See how you can draw it without lifting the pen. For the curious you can characterize it using limits.
October 23, 2024 at 5:07 PM
We will say a function is continuous when you can draw the graph of the function without lifting your pen. For example here is the graph of a continuous function between the point a and b. See how you can draw it without lifting the pen. For the curious you can characterize it using limits.
@dynastylobster.bsky.social how would you get out of this sticky situation ?
Art by @projjonmo117.bsky.social all credit goes to them :3
Art by @projjonmo117.bsky.social all credit goes to them :3
October 21, 2024 at 3:10 PM
@dynastylobster.bsky.social how would you get out of this sticky situation ?
Art by @projjonmo117.bsky.social all credit goes to them :3
Art by @projjonmo117.bsky.social all credit goes to them :3