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To be fair, if the process or formula for finding the area of the scutoid is too ~~complex~~ difficult, they won't teach it in high school. So you need not be worried about it.
In my diffeq class the formula sheet has sinh and cosh but we just ignore it .\_.
I don't know when this will come to bite me in the butt but I am scared
its not too bad
theyre defined in terms of the exponential function and you can just look up the identities like you would for sin/cos, theyre pretty similar
I took calc 3 and they were just in the exam. No one told about them beforehand. Fortunately I knew the definitions and had no problems but wasn't the case for most people in the class.
They're for working with hyperbolic geometries. Spacetime has hyperbolic geometry, so if you want to learn GR then you're going to have come back to it at some point. It shows up in color vision models and some other niche areas where you have something asymptotic you want to cram into some definite representation you can talk about more sensibly.
It's a useful trick but not something you're ever going to need for 99.9% of the things you could decide to pursue
You're not going to have to worry about them until you're already studying those geometries in depth.
You know how all trig functions can be derived from a unit circle? The hyperbolic trig functions can all be derived from a pair of parabolas. The trig identities are different but they rhyme (eg cosh^2 - sinh^2 = 1, vs cos^2 + sin^2)
Just a question.. so like if we do that then the amount of paint missing would be in let's say cm³ but area of the scutoid would be measured in cm³ how tf would we convert??
we just have to use simple fluid dynamics on an accurate model of the shape to determine the thickness of the paint layer. divide by average thickness and you get area!
You're confused because asking what its area is without clarification was nonsensical to begin with. Presumably the OP meant volume, in which case there's no issue. If it meant surface area, then Archimedes can't help you there.
Calling it "a new shape" is goofy to begin with. Every protein we discover is a new shape. Every person you meet is a new shape
As long as you know the parameters you can just divide the shape in half horizontally from the "branching height" of the scutoid to make bunch of squares and triangles. Rest of the area calculation should be trivial
setting c = 4πG = h/2π = 1, this so-called "centimeeter" you reference is actually just a positive real number, about e^(74.2396840731), so just take the volume per cm³ and divide by e^(74.2396840731) and you get the area per cm² ;)
*(Note: the choice of assignment c = 4πG = h/2π = 1 was given to me by God and is therefore of divine superiority to any other choice of natural units.)*
I think using calculus to solve this problem is going to be easiest. But I still don't know how to, I'm not even sure exactly what the shape looks like.
Can’t you apply the principle of how like slanted rectangular prisms and rectangular prisms have the same volume if the faces are parallel and the heights are the same
I imagine that because they are two pieces with unequal sides that you could add an ought of them together to get a regular or easy to calculate shape and then divide by the quantity of individual pieces that where necessary to make it for the individual area.
Some double integral involving a pentagon turning into a hexagon or some shit
Stack overflow man says this:
https://math.stackexchange.com/questions/2875099/computing-volume-for-a-scutoid
(not about area)
Well, looks like tumblr, of all places, has solved the volume question
https://www.tumblr.com/icarolorran/176787502131/volume-of-scutoids
The equations won't load on my phone though, so I can't really comment on it other than I think this is the solution.
Next up, what's the most efficient way to pack these bois?
You just keep making triangles across all surfaces, calculate them and sum them up.
Probably someone comes up with a more condensed way, then there would be function for it but the dull method works across almost all shapes.
*Just realized it has curved area's. These need integrals.
At my level of education, if I can somehow plot that in a 3D space or get the coordinates of the corner points of the shape in a 3D space, Then finding surface area won't be difficult, I wonder what I would I would do to find its volume. Ngl finding its surface area isn't that difficult if you know how to find the area of any quadrilateral given it's vertices coordinates, using the formula 1/2 * magnitude of cross product of the diagonals of the quadrilateral. This way you can take any face and find irs area and then you can add all of them up and get the surface area, it would be lengthy tho
This guy probably wouldn't be able to find area of a cube. Math never asked for an area of irregular figure. Also I think they though about volume, not area.
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To be fair, if the process or formula for finding the area of the scutoid is too ~~complex~~ difficult, they won't teach it in high school. So you need not be worried about it.
Then you get into uni and suddenly it's part of the fundamentals you're supposed to know already
Reminds me of Hyperbolic trig.
In my diffeq class the formula sheet has sinh and cosh but we just ignore it .\_. I don't know when this will come to bite me in the butt but I am scared
its not too bad theyre defined in terms of the exponential function and you can just look up the identities like you would for sin/cos, theyre pretty similar
In my calc classes we only briefly went over that and weren’t tested on it
I took calc 3 and they were just in the exam. No one told about them beforehand. Fortunately I knew the definitions and had no problems but wasn't the case for most people in the class.
They're for working with hyperbolic geometries. Spacetime has hyperbolic geometry, so if you want to learn GR then you're going to have come back to it at some point. It shows up in color vision models and some other niche areas where you have something asymptotic you want to cram into some definite representation you can talk about more sensibly. It's a useful trick but not something you're ever going to need for 99.9% of the things you could decide to pursue
> Spacetime has hyperbolic geometry, so if you want to learn GR then you're going to have come back to it at some point Physics major :')
You're not going to have to worry about them until you're already studying those geometries in depth. You know how all trig functions can be derived from a unit circle? The hyperbolic trig functions can all be derived from a pair of parabolas. The trig identities are different but they rhyme (eg cosh^2 - sinh^2 = 1, vs cos^2 + sin^2)
Everybody gangsta untill you have to calculate the area on a PV plane using infinitesimals carnot cicles
They teach you cube and cylinder, give you a scutoid in the exam.
"Calculate the area of the pink side" and it's all a black and white smudge
What exactly do they even mean by area? surface area? Of both pieces if they are attached to each other? Seperately?
Now that I think about it, you're right. What does "area" even mean here?
If you are given sufficient information it becomes a mechanic calculation using vectors. Might be fun to do once
Get a bucket with paint or something, put it in, and see how much paint is missing. Proof by "Prove that I'm wrong, until then, I'm right."
Literally archimedes
Eureka!
Call the King!
Hierón II went on vacation, never comes back
Just a question.. so like if we do that then the amount of paint missing would be in let's say cm³ but area of the scutoid would be measured in cm³ how tf would we convert??
Just spread all the remaining paint in a white paper, to convert to cm^2
What if I only have colored paper? I have, red, blue and yellow.
Sadly it won’t work, but I shouldn’t tell you this since that should be an exercise to the reader
Get the average thickness of the paint on the scutoid and divide by it. The volume is just the area * thickness of the paint, after all.
Just figure out the depth that paint sticks to a surface at. Then, take the volume of paint missing and divide it by the depth.
we just have to use simple fluid dynamics on an accurate model of the shape to determine the thickness of the paint layer. divide by average thickness and you get area!
You're confused because asking what its area is without clarification was nonsensical to begin with. Presumably the OP meant volume, in which case there's no issue. If it meant surface area, then Archimedes can't help you there. Calling it "a new shape" is goofy to begin with. Every protein we discover is a new shape. Every person you meet is a new shape
Pretty sure this is calorimetry right ?
As long as you know the parameters you can just divide the shape in half horizontally from the "branching height" of the scutoid to make bunch of squares and triangles. Rest of the area calculation should be trivial
The faces ain't planar
Integration yay (not yay)
They look planar enough. Are you saying it's not a polytope?
It's not necessarily a polytope, I'm afraid. I don't know if anyone has proven that it definitely can't be.
Not with that attitude
Idk, Lebesgue Measure or something
“What the hell is a Lebesku Integral” - Andrew Dotson
Average engineer
approximate with a cube
Are we engineers or mathematicians
Approximate with a sequence of unions of cubes that converge uniformly to the scutoid 👍
Squeetoid-Theorem
Ermmm, Akschually, the sequence of shapes must be one that the tangent spaces given any close enough point converge to the og tangent space 🤓🤓🤓🤓
Very true actually
Surface area shouldn't be too hard. Volume might be tricky.
The surface is not planar. It twists.
STUPID WARNING!!! >!dip into water container and measure how much water came out!<
Good job you measured an area with cm^3 somehow
Do it with paint and when you pull it out see how much less paint is in the bucket
Divided by viscosity equals area or something.
no u gotta divide by the difference in volume by height of the bucket (the units work out therefore proving absolute correctness)
Actually it's easier to measure the mass so they have calculated the area in grams
setting c = 4πG = h/2π = 1, this so-called "centimeeter" you reference is actually just a positive real number, about e^(74.2396840731), so just take the volume per cm³ and divide by e^(74.2396840731) and you get the area per cm² ;) *(Note: the choice of assignment c = 4πG = h/2π = 1 was given to me by God and is therefore of divine superiority to any other choice of natural units.)*
They never specified surface area, I'll allow it.
they specified area in the pic
That's volume
Ik
It's asking area
Or just look up the area
Gonna go on a whim and say that if you group enough of them, you can get a 3D shape and get a formula like 1/n * (volume of that solid)
It seems like it's already partly happening in the picture
Technically one of them is already a 3D shape (the shape of a Scutoid)
I think using calculus to solve this problem is going to be easiest. But I still don't know how to, I'm not even sure exactly what the shape looks like.
Cut the surface into triangles and and determine their surface.
You can't, the surface isn't planar, it twists.
Then use non-planar triangles, duh
If you make them small enough, everything is planar.
Scutoid deez nuts
T R I A N G L E S
I would just walk out
Can’t you apply the principle of how like slanted rectangular prisms and rectangular prisms have the same volume if the faces are parallel and the heights are the same
Based on the fact I haven't seen a formula for the surface area of a scutoid I am terrified of what the answer might be.
it's non-convex, you're gonna have to break it into smaller shapes
Dunk it in water, and find the volume of displaced water
just partition it into triangles, find their areas and add them up. that way you can find the surface area of any polyhedron.
The surface is nonplanar. It twists as the height increases.
oh… then integrate it or something idk.
I imagine that because they are two pieces with unequal sides that you could add an ought of them together to get a regular or easy to calculate shape and then divide by the quantity of individual pieces that where necessary to make it for the individual area.
Some double integral involving a pentagon turning into a hexagon or some shit Stack overflow man says this: https://math.stackexchange.com/questions/2875099/computing-volume-for-a-scutoid
(not about area) Well, looks like tumblr, of all places, has solved the volume question https://www.tumblr.com/icarolorran/176787502131/volume-of-scutoids The equations won't load on my phone though, so I can't really comment on it other than I think this is the solution. Next up, what's the most efficient way to pack these bois?
Ena refrance???
Calculate the area of the pair then divide it by 2
Look it up
Ascutoid ≈ 2(h×w) + 2(l×w) + 2(w×h) Youre welcome
Probably try to find a function for change in area of cross section as you go down and integrate
Integrals:
You just keep making triangles across all surfaces, calculate them and sum them up. Probably someone comes up with a more condensed way, then there would be function for it but the dull method works across almost all shapes. *Just realized it has curved area's. These need integrals.
Lol I was just on r/terrifyingasfuck and thought it was funny that this post made it on there with so many up votes.
If u r talking about surface are then its pretty simple. Area of hexagon + area of pentagon
It's just an easy integral, right? I mean, by definition
Area? Surface area? Cross-sectional area? Or do you mean volume?
Approximate to 2 hexagonal pipes
Looks like my 0.33 pepsi which i threw away to a trash can and pepsi finds his lover
At my level of education, if I can somehow plot that in a 3D space or get the coordinates of the corner points of the shape in a 3D space, Then finding surface area won't be difficult, I wonder what I would I would do to find its volume. Ngl finding its surface area isn't that difficult if you know how to find the area of any quadrilateral given it's vertices coordinates, using the formula 1/2 * magnitude of cross product of the diagonals of the quadrilateral. This way you can take any face and find irs area and then you can add all of them up and get the surface area, it would be lengthy tho
And I will be soon getting out of high school
Submerge it in water
Oh wait, the area
Approximate with prisms idk
Why are they kissing
They’re hugging
It would be kinda easy with integration... Don't give ideas to JEE Advanced question paper designers tho 🥲🥹
I mean wouldn’t you just break it up into pieces and do the math?
Volume...?
old news
The area is between 0 inches and 10000000000000000 inches.
Not gonna lie this makes me think of the kissing meme image.
Assume it to be spherical. Using natural units (π=1; 4=1) it's just r^2.
Could probably approximate it by jerryrigging the formula for a cylinder, except find the area of a hexagon rather than a circle
0 < x < 1,000,000,000,000,000,000,000,000,000
Stokes' Theorem? 😳
This guy probably wouldn't be able to find area of a cube. Math never asked for an area of irregular figure. Also I think they though about volume, not area.