How One Line in the Oldest Math Text Hinted at Hidden Universes

Can you do a video on what exactly it means for the universe to be flat--or at least further clarify. I don't think I can wrap my head around it entirely, and I'm also worried that a...certain conspiracy group might latch on to the idea in the wrong way if not described in a little more depth.

Derik you just know how to blow some ones mind!

Just a side note: Bolyai is pronounced as Boyai or Bo-ya-e. The "ly" is an old form of "j" in Hungarian which is pronounced similarly to the English "y". Cool video.

Some time ago, I came up with a geometry that's hyperbolic on certain scales, but on larger scales, it's Euclidean again. It's a compactified version of the hyperbolic one. (Compactification is a tool originally used to create spaces that have more dimensions on smaller scales than they appear to have on larger scales. For example, a cylinder has 2 dimensions, but if zoomed out, it appears to be a line, both inside and outside.) Here's my construction: Start with an (n+1)-dimensional Euclidean space with the regular grid (like in Minetest). Select tiles for which a certain coordinate is 0 and the product of the others is even. Take the boundary of their union. It consists of squares that meet up in 5 in the corners. Replace them with a hyperbolic quadrilateral with 72° angles

never heard of bolyai pronounced this way. no wonder i had no idea who he was lol

Very well done. Another masterpiece. Congrats.

it's weird to think that one of Euclid's postulates describes geometry on a curve, which is often called "non-Euclidean" geometry

I wish there was a way for all the great minds of the past to see all the wonders of today made possible by their works. Imagine Euclid seeing this video

Can you do a video about nothing, as in no one has ever seen nothing and therefore nothing is actually undefinable.

wait, isnt nature going to follow the easiest route or path? so isnt that a sphere?

6 non skippable ads of 20 seconds, 4 skippable ads and a baked in ad at the end... I'm kinda done

Over million views in just 14 hours! That's incredible!

Chad Gauss coming up with new principles of math decades before someone publishes them. Only because he was afraid of being ridiculed.

What a man.

Hearing him repeatedly say Boh-lee-i just hurts my ears :D It's pronounced Boh-yah-ee Yah-nosh

I love this video! I wrote a paper on Non-Euclidean geometry. Your videos sums it up perfectly <3 absolutely great video!

Yeah, but I don't understand where is the problem with the 5th postulate. It basically states that two non paralel lines will eventually met. This is 100% true in a regular flat geometry.

Did you just say that Universe is flat? I thought it was sphere expanding in all directions.

Very tastium 😋

Indian mathematics 😢😢 plz give them some recognition ❤❤ love india 🇮🇳

Veritasium's videos are generally great but the math ones are on another level

I have one question that I feel is unclear from this otherwise excellently put together video (again derek does wonders). Right at the end he asserts that our observations have indicated that the universe appears to have a flat geometry, with a graphic of a planar figure. How is that possible in a space that is 3 dimensionally traversible? Is it rather that 'flat' doesn't indicate a 2d plane, but rather indicates how a 'straight' line eventuates. i.e. a 'flat' 3d space will more or less extend infinitely in a standard fashion, rather than looping in on itself like a spherical geometry or diverge radically like in hyperbolic? Or is it that the universe is broadly planar and that our experience of 3 dimensionality is just an anomaly?

basically this clearly prooves flat earth hahahha

That dude named i-hatethem

Let's say you slice an apple into discs. Now, since the video stated there are no parallel lines in the spherical geometry, why are the lines you sliced through not parallel to each other?

As a hungarian, it is quite painful to hear the pronounciation of János Bolyai 😂 It is in fact something like Ya(h)-Nosh Bo-Ya(h)-Eee [ˈjaːnoʃ ˈboːjɒi]. Other than that, great video!

I've only watched upto around 3min 30sec when I paused the video and try to understand rule 5.

Here's my understanding of it after a few minutes of thinking: The internal 3 angles of a triangle add up to 180deg, this is fact based on a rectangle or parallelogram having 2 equal triangles which added up to 360deg.

So it stands to reason if 2 internal angles of a triangle add up to more than 180deg, means there won't be a 3rd angle, meaning no triangle, meaning the 2 lines never merge.

Am I missing something? Why is it so difficult to prove?

Ok, I unpaused the video now so maybe answer is in the video.

Love seeing Dr. Kontorovitch back on this channel!

Just SPEECHLESS

The fifth postulate demonstrates how axioms aren't something you just have to take on faith. They are the defining features of certain contexts. They are true or false by definition. If they describe some aspect of the real world, we can observe them. The number of parallels depends on geometric context just like whether the order of multiplication matters depends on whether you work with reals or matrices.

I'm failing to put into words how valuable this channel is to me personally and, I suspect, to humanity as a whole. Particularly as an academic aspirer who became a single father at a young age and couldn't afford the physics degree I always wanted, I cannot tell you how it feels to have somebody like Derek reach his hand out to bring me along on these beautifully concise and clearly communicated lectures about math and physics that make me feel like I can catch a glimpse of the information I couldn't afford to receive in a university setting. Thanks to the whole team at veritasium, there is so much more joy in learning and for so many more people than brick and mortar institutions can reach. The fact that this is free is such an act of faith and hope in humanity. Education should not be for the rich alone.

Hyperbolic geometry: This is the biggest square I've ever seen!!

He is making great videos on all subjects, but why the hell only the math videos are getting all the views God knows.

How could you prove these without knowing if the universe is finite or infinite?

"WE LIVE IN A FLAT UNIVERSE"
now I can die in peace.

Euclid was a homie fr fr. He has reinvigorated my love of mathematics again.

Why did I think this video was an SCP video because of the fact that Euclid was mentioned😂

...and thanks for that really helpful video presentation

NOW what would your reaction be when i tell you that half of all this theory is actually taught and is in the curricullum of nine graders in India

wut

I wish I could show this video to my younger self. This presentation makes so much sense, as someone who struggled with math throughout high school up until college. great video as always!

Great job man amazing 🫡

Amazing video. Thank you! Never stop, please!

How can we, 3 dimensional beings, exist in a flat universe?

I understand that as per all these theories flat does not mean 2D but I don't see how it doesn't.

I think that trying to call something that is infinite either flat or spherical does not make sense... Well, now that I think about it, shouldn't it be spherically shaped because of the big bang having pushed everything out evenly in all directions?

Feel free to enlighten me, I need it.