I’m saying that the tangent of a straight line in Cartesian coordinates, projected into polar, does not have constant tangent. A line with a constant tangent in polar, would look like a circle in Cartesian.
We are interested in the lines tangent a given graph, regardless of whether that graph is produced by rectangular, parametric, or polar equations. In each of these contexts, the slope
of the tangent line is dydx. Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ. Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.
From the link above. I really don't understand why you seem to think a tangent line in polar coordinates would be a circle.
But arent the ones from the circle 90 degrees on the inside of the circle as well? The squares could've just as well been placed on the other side of the (circle) lines.
No, the two angles are not equal. Outside/inside angles add up to two π radians. A square has four interior angles of 1/2 π radians, and four exterior angles of 3/2 π radians.
This is what AI would give you after countless tries strating with a triangle and having gone up the Pentagon and down to two pairs of unconnected parallel lines.....but what if all equally sized lines were connected? Bam! This
I thought this couldn't be true, so using one of the newer models (4bit flux) I told it to make a 5 sided star, and then put lines around the outside
lol this is very weird, did they forbid it from looking at pentagons in the training data or something? it can't do The Pentagon either, it gives it 8-12 sides instead
I don't really know, but I think it's mostly to do with pentagons being under-represented in the world in general. That and the specific way that a pentagon breaks symmetry. But it's not completely impossible to get em to make one. After a lot of futzing around, o1 wrote this prompt, which seems to work 50% of the time with FLUX [pro]:
An illustration of a regular pentagon shape: a flat, two-dimensional geometric figure with five equal straight sides and five equal angles, drawn with black lines on a white background, centered in the image.
A square? A square?! Wake up sheeple! That things not even a rombus! Don't you see the lies? Look at the lines! Look! Not all rhombuses are squares, but all squares are rhombuses! All squares are rhombuses and look at this thing they try to call a square. Where are the parallel lines? There's got to be parallel lines, don't you see, or then it's not a rombus and all squares are rhombuses. Don't forget that, don't let them take that fact from you and perpetuate their geometric lies. Does no one even remember what a rombus is? This is, this is basic geometry here that you should have learned in middle school or elementary school, but then you just forget it, and let people trick you with these misleading definitions and fancy diagrams but you have to remember that a Square. Is. A. Rombus.
Pac-Man's & Sons Original Famous
two blocks away from
Pac-Man's Original
which is a block and a half away from
Pac-Man's Famous
across the street from
Pac-Man's & Sons Famous
etc.
Does this even meet the criteria for "a shape"? I'd have thought you need to be able to travel from any point within the shape to any other point, without crossing a line.
Huh? Of course it is. A star is, so long as you don’t draw it out of two interlocking triangles, or construct it from 5 straight lines, and leave the internal parts of those lines intact. A crescent just…is. Unless you’re trying to claim the stars that sometimes appear with a crescent (e.g. on some Islamic country’s flags) are a part of the crescent itself.
Wait, you don't mean the line has to be straight? If that's what you mean, I'm fairly sure the internal lines in the post are only there as construction. The section of the triangle that's inside the smaller circle is just there to show dimensions, so it's drawn (slightly) thinner than the external lines
If you're talking about straight lines, then yes, that's how you define a convex shape. If any uninterrupted path can be taken, then the OP shape does satisfy the condition.
Edit: just read the other comments and I see the problem was that you thought the internal angle shown for reference on how the shape was built is part of the shape. It's not, just the thicker lines define the shape shown. The little crossmarks that show equal sides are also not part of the shape.
Depends how you define a shape. I don't think it's a polygon because it doesn't have straight lines. Technically a circle also isn't a polygon by the same rules, but circles have their own special little clubhouse. Sure is a shape though. I think this... thing is also a shape. Just not a useful one.
As it was presented in the OP, I don’t think it is a shape. If I get two squares and stick them next to each other so one side of each is touching, have I suddenly got one rectangle? Or do I still have two squares with a border between them?
Someone else posted an amended version with the internal lines removed. The equivalent of taking those two squares and removing the border between them, so you would have just one rectangle.
I couldn't find any definition of geometric shape that uses that criterion, including Wikipedia which also has a 5-pointed star shown with 5 line segments labelled as a shape: https://en.m.wikipedia.org/wiki/Shape.
The meme is wrong because squares are polygons by definition, which by definition are made of line segments, but this thing has curved sections.
Uhh, no. A crescent is a classic concave shape, but you can travel from any point to any other in a crescent without crossing a line, because it’s a single enclosed shape.
No irony, I didn't say straight because I didn't mean straight. I meant exactly what I said: you can get from one point to another without crossing a line. Because if you have to cross a line, you've either moved into a different shape (in the case of two adjoining shapes) or moves into empty space.
The 90 degree angles are supposed to be on the inside. Which in this case would mean at least the same side. Otherwise the 360 degree rule is broken and it's not a rectangle, much less a square.
When you miss one important constraint in your CAD project.
Oh man I felt this.
Wouldn't the angles need to be interior?
They are all interior to the meme
This meme seems to be in a 16:9 ratio making it a rectangle.
also the sides must be straight
It's 2024 now... Not everyone has to be straight anymore!
If you want to claim you are a square, you need.
WOW! just wow, do you hear yourself?
It's actually illegal
Believe it or not, straight to jail.
Hi.
Polar coordinate straight
Define straight in a precise, mathematical way.
The tangent of all points along the line equal that line
Only true in Cartesian coordinates.
A straight line in polar coordinates with the same tangent would be a circle.
EDIT: it is still a “straight” line. But then the result of a square on a surface is not the same shape any more.
I'm not sure that's true. In non-euclidean geometry it might be, but aren't polar coordinates just an alternative way of expressing cartesian?
Looking at a libre textbook, it seems to be showing that a tangent line in polar coordinates is still a straight line, not a circle.
I’m saying that the tangent of a straight line in Cartesian coordinates, projected into polar, does not have constant tangent. A line with a constant tangent in polar, would look like a circle in Cartesian.
From the link above. I really don't understand why you seem to think a tangent line in polar coordinates would be a circle.
geodesic
I knew math was homophobic!
This is merely a projection of a square on the surface of a cone projected onto a plane.
This is also not a polygon. It has infinite and 2 sides at the same time.
This actually has six right angles if you include exterior ones.
Kinda forgot the sides being parallel part. Like missing a step in assembling IKEA furniture, its not gonna turn out right.
You don't normally need to specify that the sides are parallel if you specify four right angles.
Also pretty sure definition of a shape requires only one enclosed or contiguous area.
This one is enclosed and contiguous though, the lines of the triangle end where the circular line starts. (The rest is just a drafting residue.)
No, it is 2 contiguous regions. The line of separation is the bounding line of a "shape."
Otherwise, the entire whitespace outside of the region is also part of the shape, as is anything it touches.
OK, imagine the space outside of the shape is black, or see through or whatever.
Well then the line of separation means nothing and then you've lost two right angles to the contiguous void.
Why? Does a cube floating in the void not have angles?
Without a distinction of where the cube begins or ends it does not because there is no cube and there are no angles.
The angle of the triangle that protrudes into the circular part is not a right angle.
My apologies you're correct, you lose two right angles.
Those arc sides are parallel in polar coordinates.
Anarchy geometry
If anyone makes this community, let me know please.
i will make it, but i won’t tell you
NOOOOOoooo...!
Easy there Diogenes.
Out of 4 lines
A square has all right angles inside the structure. This thing has two inside and two outside.
If you add that to the definition, you could still have a “square” with a segment of a circle connecting the edges in the middle
Then that section would be of a shorter length.
Ah, got me
But arent the ones from the circle 90 degrees on the inside of the circle as well? The squares could've just as well been placed on the other side of the (circle) lines.
No, the two angles are not equal. Outside/inside angles add up to two π radians. A square has four interior angles of 1/2 π radians, and four exterior angles of 3/2 π radians.
This is true, however now it has 4 inside and two outside the structure, so it now has something a square doesn't has.
Parallelogram.
This has an infinite number of sides
This is what AI would give you after countless tries strating with a triangle and having gone up the Pentagon and down to two pairs of unconnected parallel lines.....but what if all equally sized lines were connected? Bam! This
Fun Fact: It is very difficult to get any of the image generators to make a pentagon.
I thought this couldn't be true, so using one of the newer models (4bit flux) I told it to make a 5 sided star, and then put lines around the outside
lol this is very weird, did they forbid it from looking at pentagons in the training data or something? it can't do The Pentagon either, it gives it 8-12 sides instead
I don't really know, but I think it's mostly to do with pentagons being under-represented in the world in general. That and the specific way that a pentagon breaks symmetry. But it's not completely impossible to get em to make one. After a lot of futzing around, o1 wrote this prompt, which seems to work 50% of the time with FLUX [pro]:
quick test, with that prompt and flux schnell gguf 4 bit again:
it seems a lot stupider than pro lol
thinking outside the square
A square? A square?! Wake up sheeple! That things not even a rombus! Don't you see the lies? Look at the lines! Look! Not all rhombuses are squares, but all squares are rhombuses! All squares are rhombuses and look at this thing they try to call a square. Where are the parallel lines? There's got to be parallel lines, don't you see, or then it's not a rombus and all squares are rhombuses. Don't forget that, don't let them take that fact from you and perpetuate their geometric lies. Does no one even remember what a rombus is? This is, this is basic geometry here that you should have learned in middle school or elementary school, but then you just forget it, and let people trick you with these misleading definitions and fancy diagrams but you have to remember that a Square. Is. A. Rombus.
And all rhombus are parallelograms. By definition opposing sides must be parallel.
YES. YES! A square is a rombus is a parallelogram! You see it too! There are no parallels in this diagram, only lies and trickery!
You have shown me the truth
270°≠90°
You could say a regular square has 4 270° exterior angles
Poor Pac-Man does not look quite okay... :-(
That's a Pac-lapse.
Now make a square out of squiggly yarn
String theorists claim this is the true shape of spacetime!
relevant xkcd
This is a square in polar coordinates
Take that, Euclid!
Squircle
Man I miss my Zune 80
of course there's a Wikipedia page for that
It's Pac-Man with a megaphone!
Pac-man eating a new york slice
Pac-Man's & Sons Original Famous
two blocks away from
Pac-Man's Original
which is a block and a half away from
Pac-Man's Famous
across the street from
Pac-Man's & Sons Famous
etc.
Meet you at Ray's.
Or a comically big joint.
Pac-Marley
Snoop Pac
you geometry people go too far stop personifying vertexes, planes, and points math shouldn't be fun
HOW ELMO, HOW?!?
Is a corner with an angle of 180 degrees a corner? If yes, then all shapes have infinite corners and infinite edges.
free real estate
tihi
Ik exactly what this means but every single time I read it it makes me do the Micheal Jackson thing...
TEE-HEE
"Thanks I hate it"
Aah, thanks. But I'll keep reading it properly, as TEE-HEE.
Where are the broad, flat fingernals tho?
Plato boutta flip the table.
You're testing me, yo. An I'm bout to fail.
Could be a square in a two dimensional space with different rules.
Does this even meet the criteria for "a shape"? I'd have thought you need to be able to travel from any point within the shape to any other point, without crossing a line.
The part showing the angle is not part of it. They should've made it a dotted line or something.
Though, two of the 90° angles are.actually 270.
The classic cartoon star shape isn't a shape with that rule. Same wth a crescent
I don't know what a french pastry has to do with this.
Are you sure about that?
Huh? Of course it is. A star is, so long as you don’t draw it out of two interlocking triangles, or construct it from 5 straight lines, and leave the internal parts of those lines intact. A crescent just…is. Unless you’re trying to claim the stars that sometimes appear with a crescent (e.g. on some Islamic country’s flags) are a part of the crescent itself.
Wait, you don't mean the line has to be straight? If that's what you mean, I'm fairly sure the internal lines in the post are only there as construction. The section of the triangle that's inside the smaller circle is just there to show dimensions, so it's drawn (slightly) thinner than the external lines
That sounds like the definition for convex shape, not the general definition for a shape
it doesn't have to be a straight line between points eh
Then this shape does meet the definition
yes i concur
You’re the second person to have made that suggestion to me, but no.
If you're talking about straight lines, then yes, that's how you define a convex shape. If any uninterrupted path can be taken, then the OP shape does satisfy the condition.
Edit: just read the other comments and I see the problem was that you thought the internal angle shown for reference on how the shape was built is part of the shape. It's not, just the thicker lines define the shape shown. The little crossmarks that show equal sides are also not part of the shape.
Depends how you define a shape. I don't think it's a polygon because it doesn't have straight lines. Technically a circle also isn't a polygon by the same rules, but circles have their own special little clubhouse. Sure is a shape though. I think this... thing is also a shape. Just not a useful one.
As it was presented in the OP, I don’t think it is a shape. If I get two squares and stick them next to each other so one side of each is touching, have I suddenly got one rectangle? Or do I still have two squares with a border between them?
Someone else posted an amended version with the internal lines removed. The equivalent of taking those two squares and removing the border between them, so you would have just one rectangle.
Idk seems very useful to me, like if I need a paperweight or doorstop
I couldn't find any definition of geometric shape that uses that criterion, including Wikipedia which also has a 5-pointed star shown with 5 line segments labelled as a shape: https://en.m.wikipedia.org/wiki/Shape.
The meme is wrong because squares are polygons by definition, which by definition are made of line segments, but this thing has curved sections.
Concave shape vs convex shape
Uhh, no. A crescent is a classic concave shape, but you can travel from any point to any other in a crescent without crossing a line, because it’s a single enclosed shape.
A crescent isn't a convex shape though, and ironically you left out the word 'straight' in your rule about convex.
No irony, I didn't say straight because I didn't mean straight. I meant exactly what I said: you can get from one point to another without crossing a line. Because if you have to cross a line, you've either moved into a different shape (in the case of two adjoining shapes) or moves into empty space.
That's path connectedness. Convex shapes are ones in which any two points can be joined by a straight line internal to the shape.
IDIC!
Wat. There are three sides my dudes. What am I missing?
The semi circle side
It makes me want to be angry and laugh at the same time
It's hip to be a...
That music is just too darn loud
Is that a raincoat?
The 90 degree angles are supposed to be on the inside. Which in this case would mean at least the same side. Otherwise the 360 degree rule is broken and it's not a rectangle, much less a square.
that is less than 45 degrees
source: eyeballs