Sometimes The Shortest Distance Between Two Points is NOT a Straight Line: GEODESICS by Parth G
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- Опубликовано: 31 май 2021
- What happens when the shortest distance between two points is NOT a straight line, and exactly what is a geodesic?
Hey everyone, in this video we'll be looking at how the surface we happen to be studying impacts the definition of the "shortest" distance between two points on that surface. A geodesic is exactly that, the shortest distance on a specific surface.
On a flat surface like a piece of paper or a computer screen, the shortest distance is always a straight line. This can be proved rigorously using calculus of variations, but is also quite intuitive. For example, we can try to imagine any path that isn't a straight line between two points, and then laying a piece of string along it. The string can then be straightened and compared to the straight line path - and the not-straight path will always be longer. This also applies in 3D space, assuming the space is "flat", or "Euclidean" as it's known.
However, if we now consider two points on the surface of a sphere, then the shortest distance between them (if we are restricted to move along the surface) is a curve. And yet we can imagine digging into the surface along a straight line to take an even shorter path. But this only makes sense if we consider a 2D sphere "embedded" in 3D space.
In the study of relativity, embedding is just a useful visualization tool - but it doesn't necessarily refer to anything physical. Using our sphere example, it's a 2D surface that NEED NOT be embedded in 3D space, and so it makes no physical sense to dig into the sphere as we only have access to the two dimensions of the surface.
Similarly, our universe can be described by 4D spacetime in relativity. And it need not be embedded in anything 5D. So when spacetime itself is curved, the concept of a straight line does not have any physical meaning. Two points in this curved spacetime may have a curved geodesic between them.
It's important to note that light travels along these geodesics, which is why it is important that we study them. And it's also worth nothing that spacetime curvature is caused by mass or energy found within the spacetime, as explained by Einstein's Field Equations.
So the point is that the shortest distance between two points need not be a straight line, especially if the surface that the points are on is curved in some way. And the shortest distance for a given surface is known as a geodesic.
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Minor quibble: At about 2:08 I think it would be better to say "circumference" rather than "diameter." That is, the length of a great circle on a sphere is the circumference of the sphere.
Whoops! Totally missed that, you're absolutely right!
@@ParthGChannel hello
I hate to be that guy, but another minor quibble: when visualizing warped space, space warps away from the mass rather than toward the mass.
@@ParthGChannel No Mistake my friend by describing With Great Circle That open way to different solution depending on viewer I'm a navigator and help me lot lolll.
Really hope to see you soon LIVE 3D in relief and natural size like you see you soon
7:20
"Even Wikipedia is a useful resource"
Don't let my teachers see this 😂😂😂
In general research should always start simple and Wiki for real is a good starting point. Not more but not less :)
Just cite what Wikipedia cites and your teachers will love you
@@dsdy1205 it's like that meme of the guy blocking a door:
Me: uses wikipedia
Teachers: "No"
Me: uses the sources wikipedia used
Teachers: "Yes"
@Komaru Naegi thats not really true. Most scientific articles are supervised regularly. But eitherway as a starting point it is quite ok, as u get an overview and will see possible mistakes when checking the citations in the wiki article
@Komaru Naegi I really hope no university would except that :D
I wouldn't use it as a source, just as a startibg point for the research. Then u get a good overview and conrinue with the citations given there. I mean when u dont have a clue about the topic at all.
Otherwise start with a review article, but therefore u should already know basic concepts of the topic.
Your explanation to difficult concepts is very encouraging for further exploration...keep it up!
Congratulations on the award Parth! Linking to the the textbook for a more complete explanation was a nice touch. These videos keep getting better and better. You truly are a G Parth
Hey Parth! I've been watching your videos regularly for a long time. Your easily explained concepts help me understand physics better. I wish that you would make more concept based videos(like time dilation, neutrino oscillation or the twin paradox) along with the equations made easy videos... You have our support
Was waiting for a video on higher dimensional geodesic for a long time! Thanks Parth! Love your vids! 🤩
The shortest path on the surface of the sphere is "kind of" a straight line. It appears straight to someone living on that surface. If the surface isn't embedded in 3d space, it is as straight as a line can get.
yeah, take a straight line on a road trip from texas to boston. Then, zoom far, far away and all of sudden that "straight line" becomes curved because you are able to see the line curving on the surface that you couldn't see when you were close to it. Now, picture space itself as flat. Or at least space around your room, then think of that "space" or everything occupying that area being warped by a larger object near it. I'm not sure how intuitively break down this idea into the metaphor. I guess, "space" isn't such a simple idea.
There are two Geodesic Arcs between any two points on the surface of a sphere , equidistant in length and, a mirror image of each other. Unless, they are 180 Degrees apart (Antipodes)(Poles) which would then be a great circle route ....!The old stretching string between two points on a sphere trick ....the arcs formed would work for two paths between the same two set of points .
that was totally wicked i never knew shortest distance could elaborated this way even knowing the concept of space-time warping thanks parth G !!!!
I just started studying general relativity because i am very passionate about physics, and i was having trouble comprehending geodesics and tensors, and here you are!!! I love your channel! Please make a video about tensors used in relativity please! That would be great
Loves your passion for physics.To learn tensors and Genaral Relativity you can checkout "Eigenchris " Channel.
@@imaginer04 thanks!
I saw that Andrew Dotson made some videos about those
@@Ultiminati Yep,he is awesome.
Watch Ashok Sen general relativity:
Best
few flaws:
Unclear what is written on greenboard
Accent may be trouble for you
Cons
Best content
He can even make a dog learn physics.
Amazing video, I am finished with high school and I have been feeling inactive with using my brain because I miss the physics and math lessons. This video made me enthusiastic and curious again, and also helped me appreciate I guess nature again.
A French humorist (early 20th century), Pierre Dac, once said: "The shortest way of a point to another is the straight line, provided that they are well one facing the other. "
Calculus of variation..... Here we go....just a suggestion, you can tell why a rope suspended from 2 points forms a parabola and exactly why a Catenary Curve minimizes the potential energy
A rope suspended from two points doesn't form a parabola. It forms a Catenary Curve (the graph of hyperbolic cosine).
Check out this video for explanation:
ruclips.net/video/EHKFbl3VwMo/видео.html
Wonderful Explanation!
I just love your accent😍 and how you beautifully explained the most complex topic👍
I do so enjoy your videos. Thank you
I learnt this in a Doraemon movie👍
which one
@@aadarsh_1303x I don't remember clearly, there are so many of them!! But he subtly explains the working of anywhere door👍
Hey Parth, I am also watching your video regularly since long time and your conceptions are very helpful for learning both maths & physics.i am interested in learning Tensor so i would like to see you with tensor,so pls make videos on tensor
You explained soooooo well!!!!
Loved it. Keep posting these nice videos
Great work!
you explained this very well!
Amazing video! Thanks for sharing!
Can you make a video on Dark matter and dark energy?
You are such a good guy.Very good explanation.Love from Bangladesh
You describe physics in a very very nice way.
Congratulations!!
Good info 👍
wow! what a explanation.
Hi Parth once again kudos to your content.....
please make a video on WKB approximation.
It's cool how a flat object on a curved space becomes curved itself. You don't imagine space being anything more than flat. My desk, the floor, my walls, are all based on something we assume is flat to us. But, when something massive enough is around what is first considered flat becomes rounded. Weird, fun concept. I can't wait to study this more.
I have a doubt in the very concept of electric field.
we have defined that field is produced by a charged particle or body.
But i often ponder that just like space-time fabric ,which bends in presence of a massive body, just similar to that what if there is some kind of different fabric which bends in presence of charged particles or charged bodies and is not affected by mass. This would mean that charges are not producing fields instead they are bending that other kind of fabric.
Then wouldn't this completely change the way we study about electric fields ?
Hoping for a positive and quick response
thank you.
can you please do a video on the Dirac delta function?
I found your channel yesterday, and has no doubt to subscribe it. By the way, it would be good if you share the video making process you did. I'm so curious to make one ☺️
If fabric of space time deforms or curves then does the object in that fabric also deforms or curves??
Can you please continue this and start a GR playlist?
I love ❤ your videos
Keep up the good work🙂👍
Thought u might speak about brachistochrone problem......
could you make a video on step potential?
Hello bhaiya , I always wanted to ask that can you please tell me the way to become an astrophysicist I have dreamt of it since my childhood but never got the mentor to tell the path.
Also your videos are a lot fun and physics.
Do well in school. Get into a uni that provides physics course or astrophysics specifically. If you choose the normal physics degree, depending on the uni you are attending either you can specialize astrophysics in your last year or go on to do astrophysics in masters or PhD.
There are various ways of being an astrophysicist. The most obvious is to get a PhD in the field, but that doesn't necessarily mean you would work as an astrophysicist. There are a remarkable number of people with physics backgrounds who wind up with jobs on high finance. (I used to know a cluster of them in London.
In practice people doing astrophysics sometimes start out in some other branch of theoretical physics, such as nuclear chemistry (because that's what stars do for a living). The term "astrophysics" is itself quite broad. Everything from classical celestial mechanics to cosmology to particle physics to planetology can be called astrophysics. Brian May of the rock group Queen got his PhD based on research on dust particles in the plane of ecliptic in our solar system and I've heard that referred to as astrophysics.
In terms of practical advice, it depends on your circumstances. Obviously you need to learn as much physics as you can. The easiest way to do that, and to proceed on to getting a PhD, is through the usual process of undergraduate and post-graduate education, learning as much and as broadly as possible. I used to date a physicist until she came to her senses, and she told me that in her final oral exam before being awarded her PhD in experimental particle physics, the first question she had to answer was the available chemical energy from burning a molecule of gasoline. (I assume she could pick which specific molecule.)
If for some reason you can't follow the usual well-trod path you can learn on your own. RUclips is positively infested with videos of university courses in physics and you can order new or used textbooks on line. Unfortunately math in particular is hard to learn without someone to ask questions of, preferably in person. So you at least need friends in the field. Basically, you probably need to live somewhere near a university even if you're not a student there. If you get good at physics and you develop some contacts you could very well work your way into physics from the side. it doesn't happen often, but that doesn't mean it never happens.
@@mairisberzins8677 thank you
@@DGaryGrady thank you too for helping me.
Hey parth, please make a video on holographic theory
congrats on the silver play button!!
Thank you! Could you make an explainer on geodesic vs geodetic?
There are two Geodesic Arcs between any two points on the surface of a sphere , equidistant in length and, a mirror image of each other. Unless, they are 180 Degrees apart (Antipodes)(Poles) which would then be a great circle route ....!The old stretching string between two points on a sphere trick ....the arcs formed would work for two paths between the same two set of points .
Sir please a video on electromagnetic induction
Please give us some references where we can study further about all these
Sir can you make vedio on
Continuum in fluid mechanics and no slip condition
Please parth reply....I really injoy ur content thanks so much....u said that there are vids on youtube that can go through General relativity can u please tell us the name of the channels if that's okay....and I'm a self taught peraon i didn't go to school...do u think i can make it?
Can I study general relativity using high school calculus xD? I have got two months before uni begins.
I would love to get notified on this as well if anyone does reply
I don't understand the concept of two events. They occur at times t1 and t2. But what clock is used to define t1 and t2?
There are two Geodesic Arcs between any two points on the surface of a sphere , equidistant in length and, a mirror image of each other. Unless, they are 180 Degrees apart (Antipodes)(Poles) which would then be a great circle route ....!The old stretching string between two points on a sphere trick ....the arcs formed would work for two paths between the same two set of points .
you're the best
Nice video and presentation.
The shortest distance between two pints (in 3D space) is a straight line.
The shortest distance between two point on a SOLID sphere is the core of the great circle.
Do a video on space-geometry
Hi Parth, I love your videos! Keep up the great work man! Are you on Twitter?
How much mathematical knowledge should one require in order to learn general relativity (beyond basic calculus)??
does ,the final statement meant that ''curved spacetime causes matter to curve''?
Matter causes space to curve, but that curvature of space tells matter how to move and flux about its density. The matter itself holds it's own intrinsic property and itself gains it shape via the stronger forces at the scale of individual atoms and below, that being electromagnetism and the strong+weak nuclear forces.
Great circle track. Aviation 101.
Given wo points in space then an
observer can always adjust his view to where
the points are aligned, i.e., the points appear
to be on top of each other, so no distance
between them!(from his view), so although
it is true that the shortest distance between
two points is depicted(measured) by a straight
line, you can actually go one step further and
state that the shortest straightline is zero!
Missed opportunity for "this is a hard idea to *warp* your head around" lmao
Lol
Why time is scalar quantity
To describe the shortest distance/path between two points on a sphere, we embed it in 3D space, which is more than the 2D space we're describing. Does that mean that when you are describing 4D space, you embed it in 5D (or higher) space?
It can definitely help to picture a 2-dimensional spherical surface as the surface of a sphere in 3-space. But it's not actually necessary to describe the geometry that way, any more than you have to make reference to higher dimensions to describe the geometry of the Euclidean plane.
In fact, it's not easy to picture a 2-d hyperbolic geometry as a surface in 3-space. Around any given point it looks like a saddle, but it's saddles everywhere, and that's hard to imagine. At least it is for me.
You don't have to picture the Euclidean plane as embedded in 3-space, you just have to know the rules of its geometry. For example, in Euclidean 2-space the ratio of a circle's circumference to its diameter is pi. In spherical geometry it's less than pi (with the ratio depending on the size of the circle). In hyperbolic geometry the ratio is greatrer than pi.
As I understand it, looking at the tiny variations in the cosmic microwave background suggests the circumference of the CMB (all the way around) is pi times the twice the distance to it, suggesting that on a very large scale the observable universe is Euclidean, or "flat." We don't have to step into a higher dimension to observe that (which is good!). But we wouldn't even if it we discovered that the circumference/radius ratio were larger or smaller than 2 pi.
I wish I could say this better since it's something I wrestled with for a long time myself, convinced that if spacetime is curved it had to be curved inside some higher dimensional space. But as far as I know that's not really true.It's just something that seems natural to us because that's how things are in our common experience of planes and spheres and what-nots.
Okay just a question what is happening in this channel? I mean how can someone be so good man😂😂😂 damn bro I love it. Also a physics undergrad here and somehow your videos makes me fall for physics even more. Lol feels like the next Richard Feynman (the way he explained difficult concepts).
Sir what are the prerequisites for learning General Relativity?
It depends on the course. In 1945 Lillian Lieber wrote a book called The Einstein Theory of Relativity that assumes only a knowledge of high school algebra and geometry (at least the Pythagorean theorem). But it doesn't just skip over the math, it teaches you what you need as you go, until by the end the reader is working with generalized curvilinear tensors. A reprint edition can be had at low cost both new and used. For a sample of the book see
www.google.com/books/edition/The_Einstein_Theory_of_Relativity/ltHktbOFgcgC?hl=en&gbpv=1&printsec=frontcover
For more on the remarkable author see en.wikipedia.org/wiki/Lillian_Rosanoff_Lieber
The theory is essentially unchanged since it was introduced, but the mathematical representation is a lot different from what it was in 1945, or for that matter when I was in college. (When I was an undergraduate astronauts were still visiting the Moon.)
Here's a much more modern approach that requires only a fairly basic level of calculus. There's a textbook but you can get by without it. Of course, the more you know going in, the easier it will be. If you've had a course in classical mechanics and can convert between coordinates in special relativity you might even find it easy. The professor, Alex Flournoy, is very popular with the students and has a sense of humor. This version of the course is from the spring 2021 semester so it's still warm:
ruclips.net/p/PLDlWMHnDwyljkfy3EBSMlM5D5KQiUSpsB
You'll also need stuff from his website here: inside.mines.edu/~aflourno/GR/418.shtml
You don't need to know what a tensor is going in and in fact you'll wind up understanding tensors better than some professional mathematicians and physicists. The first half of the course is the theoretical foundation and the second have deals with the obvious topics such as black holes and cosmology.
I 'm from Bangladesh .. I like u videos very much bro....
@@abcxyz9034 ok good
Nice, I learned something. On second thought though this video has quite some problems I would say. It's nonsensical to say the shortest distance between 2 points is not a straight line when straight lines are simply not allowed/non-existing. It is rather the opposite. The shortest distance between two points would always be a "straight line" with geodesics being the generalization of straight lines.
I think the title is a bit click-baity, let me explain:
I'm an undergaduate studying maths, I've had a Topology and Geometry class so I'm not coming from nowhere and I definitely don't want to be rude or discredit this great _introductory_ video, I even took my notes I made for the exam to fact check myself. Please correct me if I'm wrong about anything in a follow-up comment.
1. The discussion if it's a stright line or not:
"Sometimes The Shortest Distance Between Two Points is NOT a Straight Line", well it depends on how you look at the path that is the shortest path.
Like it was shown in the viedo the shortest path on a sphere is along a great circle, but if you're on the sphere and walking from point A to B on a great circle/geodesic, than you perceive the path as a straight line, since you never turn left or right (the path has a curvature of 0).
-> So the question becomes who's perspective should we value more and thus determine, if it's a straight line or not, someone walking along the geodesic or some obeserver watching them?
But also when we look down onto the sphere such that the geodesic from A to B is exactly between us and the centre of the sphere, the geodesic and the great circle as a whole looks just like a straight line.
But this also holds if we walk/travel through curved space-time since the gravity will affect us too, not just the path we take. So if we are near a black hole and follow a geodesic, from our point of view we follow a straight line, since we never turn left or right, not even in the slighest.
2. Some comments on the visualization of curved space-time:
The visuals shown starting at 6:29 are somewhat missleading. I know that this is a typical visualization of curved space-time. However, how it is shown the black hole would actually repel matter instead of attract matter since space-time is curving away from to black hole and not towards it.
Here's a link of how I imagine curved space-time and that actually makes sense when we think about how gravity would act: www.forbes.com/sites/startswithabang/2019/02/16/ask-ethan-how-can-we-measure-the-curvature-of-gravity/?sh=7521bdab134f
3. A remark about a certain phrase: "The shortest distance between two points is a straight line."
The shortest distance between two points is not a straight line, since distance is a number. The shortest distance between two points is the length of the geodesic which connects the two points. I state this nit-picky looking argument, since it is very crucial to be precise when talking about complex topics and concepts, to audiences who are not that familiar with the subject. I hear you say "Shut up, we can understand what he is trying to say.", you might still _understand this particular sentence_ but if the sentence or the concepts behind the statement were more complex, you would not _understand_ that he phrased it poorly or even wrong since you might not be familiar with the concepts discussed.
If anyone disagrees with anything I've stated, feel free to leave a comment explaining what I got wrong and maybe some source, that you would suggest to dig deeper into this subject.
Nice ,I hope parth will reply to your comment.
I haven't understood the grand circle part: It there were 2 point on tha same parallel, but not at the eqautor, the shortest path wouldn't be a piece of circle with the radius of the sphere
It would still be a great sphere; the geodesic wouldn’t be along the parallel but along some other arc length between the two points. Try this out if you have a globe lying around, it’s pretty cool
I think you're assuming that the shortest distance between two points on the same parallel (i.e., the same circle of constant latitude) would be along the parallel. That might seem intuitively reasonably, but it isn't true. This is why a flight between two cities of the same latitude curves toward the north or south pole.
In fact, consider traveling from London to a place the same distance north of the equator and on the 180th meridian, If you look at a globe it's obvious that the most direct flight would cross the North Pole.
2 days ago, wow!
Amazing! I suppose this is why Racing Paths are always curved... Is it so?
Curved parth, straight parth... I'd take them all!
I was convinced by your relativity explanation that the shortest distance in reality would not be what appears to be a straight line. However, I am not convinced that space is warped to the degree that the actual shortest distance is travelling along the Great Circle of the sphere.
Shortest distance cannot always be the displacement practically
2:09 it's actually the circumference?!
Please explain Euler Lagrange equation. I really want to intuitively understand Lagrangian mechanics
You have a thing. That thing moves. The thing has potential and kinetic energy.
Lagrangian = Kinetic - Potential
Solve Euler Lagrange and you will get a differential equation for each of the coordinates. Aka the path the "thing" takes along each of the coordinates.
Haven't studied it myself, but from what I understood it's based on principle of least action. But check out Andrew Dotson's video on using Lagrangian mechanics to solve projectile kinematics.
He shows how to do the same thing you were taught in highschool physics but with Lagrangian instead.
@@mairisberzins8677 I know the Euler Lagrange equation mathematically but is in lookout for a intuitive understanding of why it works(which may be obtained from a proof of the equation also which I am not able to find anywhere in simple words all are complicated 😅). Still thanks for your suggestion I will definitely check his video 😀
Yeah. I understand the argument from the math. I also understand the intuition behind the Hamiltonian (KE+PE). But what is the (physical) intuition behind the Lagrangian (KE-PE)?
@@mintakan003 I know that Lagrangian is mathematically significant it had no physical significance but why does it work is what is want to know
Parth said in his Lagrangian video that he will soon make a video on why Lagrangian is consistent with Newtonian mechanics. Hope it comes out soon.
What if you take a small Element of your curved path ,it would be a straight line
There are two Geodesic Arcs between any two points on the surface of a sphere , equidistant in length and, a mirror image of each other. Unless, they are 180 Degrees apart (Antipodes)(Poles) which would then be a great circle route ....!The old stretching string between two points on a sphere trick ....the arcs formed would work for two paths between the same two set of points .
Urm, I don't know what it is, but hey, Parth? Have you changed something in the way you record audio? I didn't appreciate the audio as much as the previous videos. I don't mean to be rude. Im sorry
Well I've learnt that shortest distance between 2 points in a plane is 0 when you fold the plane in such way that the 2 points coincide each other.
it is always a straight line, but what straight is depends on the dimension you are looking at
Fortunately that sometimes is out of syllabus
2:05 CIRCUMFERENCE. NOT DIAMETER.
BUT ALL IN ALL, GOOD VIDEO. SORRY I'LL STOP shouting now.
I hate these kinds of click-baity descriptions of science. But I get it. The psychology of advertising to humans, and all.
If one were to examine the actual arguments, though, they're just pedantic quibbles about the lack of verbal qualifiers in the original statement, without any new, actionable insights provided. It still holds true that the shortest distance between two points is a straight line, as long as the "straight" line is considered relative to the space it exists in. That is, if you removed the curvature of space-time, you'd still end up with a straight line, as originally described. It's not like you're playing with imaginary numbers to discover something new about how objects move in space. As soon as you learn about space-time curvature, the appropriate approach to short-distance discovery is a natural given.
This is entirely different, for example, than Fermilab's video on why e=/=mc^2, where the explanation is that e=mc^2 only holds true for objects at rest because momentum (p) is zero, masking the importance of other terms in the equation. In that case, the video isn't click-baity because new insights are gained about the relevance of other terms that are regularly significant (for one, objects are always moving in space relative to something else; for two, knowing about the caveat informs you about when you can simplify your math). So, that video is about how the common equation that people memorize is actually just a special case, and a more accurate equation should be known (one that doesn't intuitively follow from the original premise).
I didn’t believe in nominative determinism until I watched a Brit named “Parth” describing paths for 8 minutes.
- some bloke whose name starts with “math” and who watches YT videos explaining geodesics
very nice name
Just think more carefully for a moment.The shortest distance between two points will ALWAYS be a straight line. It's the law; the same way 1 plus 2 equals 3, and no amount of bullshit or wishful thinking will ever change that fact. Take a look around, because reality isn't what you think it is. Sometimes, the simplest explanation for how things work, really is the right one. Geodesy is an attempt to reconcile a different fact, that namely because it would entail the expenditure of vastly more significant amounts of energy to travel in a straight line between two points far enough away from each other on the surface of a sphere, than it would to move along the curved arc length of the portion of the sphere's total diameter represented by the distance between them, still does not mean that distance is ever shorter along the curve. Rather, the energy expenditure is so much the less, because it's magnitudes easier to walk on a slightly curved and therefore longer path through air than it is to drill through solid rock and thereby take the marginally more direct route, but the one with huge energy costs associated with it due to the impenetrability and resistance of solid rock to movement through it, versus the relative conductance and minimal resistance of air to motion by way of direct comparison.
just look at an international flight path on a world map that's been projected onto a flat surface. The path is curved for the same reason that geodesics are curved.
Why your voice change from low to deep
Hey Parth, Can I consult you for General relativity and stuff !! Hope you listen to this coment!
You are from india
G deshon key are paar ka hisab hai but definitely decimated geodesic hai
Baki sarey desh dasi hai Bharat key
Sabka guru hai Bharat
Hoh?
Hi bro
Please share ur linked in profile
Obligatory event horizon refrence
Shortest run possible not the path
Parth
😀😀😃😃😃😃👽👽😃😃😃😃😃😃😃
Shortest distance between two point is to fold the plane and connect the two point 😊
This is a bit misleading. It still is a straight line. It’s just that a straight line on a sphere is depicted as a curved line on a 2D plane, and vice versa
For anyone wanting to know the math behind, follow EigenChris
Ah yes... the paradox of wikipedia.
The more complex the subject, the more likely is it to be false.
Because writing something like fake page of relativity in Wikipedia requires at least basic knowledge of relativity to even sound plausible. Therefore such inaccuracies are easier to spot and correct.
The point is that the straight line should pass through the sphere and one cannot easily pass through the sphere.
Wait till you come to know about a triangle with the sum of angles > 180.
I'd say "straight line" is usually defined as a geodesic
slalom