Euclid's puzzling parallel postulate - Jeff Dekofsky

[@Jdekofsky]

True. In the original script, I spoke about that very fact. Unfortunately, in the editing process, that omission got overlooked. Thank you for pointing it out :). He dealt with some very deep issues in number theory that are still relevant today, including the infinitude of primes. This is related to the newest chapter of the prime story, which is the headway recently made into proving the infinitude of "twin" primes - primes that differ by only 2 (such as 3&5 or 11&13, etc.). :)

[@uniqueusername_]

I know this is a "little" late, but I have a question: why does the parallel postulate even matter? what does it enable you to prove?

[@JohnJohnson-zt3bv]

@@uniqueusername_ this is a “little” late but Extra History has made a series on Non Euclidean geometry which sort of explains this question

[@piepieninja]

I like the little "fuck you" to the flat earth society at the end there

[@_vallee_5190]

It's in reference to how euclidean geometry only works on a 2d plain, or the 2nd dimension.

[@joshvir262]

@@_vallee_5190 I didn't even know flat earthers existed 7 years ago

[@philindeblanc]

Anyone with any discernment knows that the FlatEarthSociety is a disinformation front to discourage exploration of geography cartography and measures of where we stand.

[@philindeblanc]

@@joshvir262 Yes, Up until the 1920, even later, flat earth was actually taught in schools. In fact, there was a Little House On The Prairy episode highlighting, and shunning it. Upuntil the 1940's There are encyclopedias using that understanding. Its the more scientifically sound observational reality. Vs a mathematic perspective using unknown or fabricated axioms such as R value. This is why Euclid's geometry is proven correct using deductive reasoning. But this goes against academia, so it is not in any mainstream institutions.

[@rutgers182]

you can have complex life in a 2d plane. it would just be really big. imagine a 2d plane so large that our universe is the size of an atom on the 2d plane. the 2d plane could have organisms that eventually make a simulation of a universe that is 3d (us). we might actually be living on a flat plane lol.

[@satnamo]

Mathematics is not about following directions. Mathematics is about making new directions. Paul Lockhart A Mathematician's Lament

[@philindeblanc]

Its basically creative writing, as long as you understand its base is fiction.

[@philindeblanc]

That is at the conceptual imaginary state. If you want math to be accountable to reality, it must come from reality. Coming from reality take a following of axioms the math can start, and with "good math" end in.

[@AsBi1]

nice info, i was struggling to understand this controversy but now i do.

[@philindeblanc]

you really dont understand it based on this video, as it grossly misinforms. The 5th postulate is an independent and proven correct postulate based off reality. It only doesnt work with a copernican sphere model consept, but that theory is less and less stable today. Academia will likely never change what is given as fact, but it is all based on false axioms.

[@EverythingShakespeare]

The history of mathematics is truly fascinating :-)

[@purplepill2024]

3:11: Flat Earthers - Yes!!! 3:18: WTF Bro!!!

[@philindeblanc]

He left out the 180 degree of convergence! Euclid is proven correct. Someone above noted the other postulate supporting the 5th. Even the 2nd supports it, yet is a postulate as it is independently proven. Use deductive negation, and its correct. Science is not found in a text book. Science is a methodology and based on the scientific testing method. If math is not based on reality, then we have a problem! Oh...oops...we already have that problem!!!

[@gargeeprakash]

Mathematics never taught us how to add happiness or to substract sadness but taught us that every problem has a solution.👏👏👏👏👏👏👏👏👏👏 That's really true. And thnx for the video 📸 🙏🏻👍🏻

[@carloscolon9968]

That is not the view of modern mathematicians after Kurt Godel surprising results in mathematical logic around 1930 and its undecibility theorems.

[@fractalphysics8045]

Also, Abel showed the existence of unsolvable 5th degree polynomials almost 100 years earlier in 1824! Still, I agree with @Gargee Prakash's sentiment, even though math has added much happiness to my life :D .

[@brokenjewel25]

I'm 18 and proud to say I'm in love with Tededucation 3

[@vinifg12]

Beautiful! The Euclid is fantastic!

[@tuannguyenanh25]

1:57 I 'fully understand'

[@1LeiaPrincess]

Thanks! Please make more videos about mathematics!!

[@BarrM78]

I took Pre-Calculus with Mr. Dekofsky!

[@satnamo]

How was you pre-Calculus with Mr. Dekofsky Michael ?

[@BlakeytheG]

IM TAKING MATH ANALYSIS WITH HIM RN AHAHA

[@philindeblanc]

good luck!!

[@tonylee1667]

Take a shot whenever Gauss or Euler is mentioned in a field of mathematics and I'd die of liver failure in 2 months

[@samarkumarghosh1708]

Who's favorite subject is maths,??

[@alexanderwhittemore1491]

Mine favorite subject are English Grammar

[@samarkumarghosh1708]

@@alexanderwhittemore1491 Oh I see.... in which class you are?

[@debabrataroy1312]

Mine!

[@canadianbacon007]

1:48 Here come old flattop, he come grooving up slowly. The greatest possible generality is before all things to be sought.

[@awakenedintofreedom]

And btw you cant have a 90 degree angle on a ball so every train track and building that has one just proved we are on a flat surface that's why flat earth is in there it's not a slight it's a nod

[@Martin-pb7ts]

Actually you can have a 90degree angle on a ball. Put a line around the equator and one through the poles and if you measure the angles where the intersect you will find they are 90degrees. Trust me mate, it's a science video, it's a slight. I appreciate your optimism though.

[@philindeblanc]

@@Martin-pb7ts LOL....so the basis of math is not conceptual, it is based off our reality of things possible. Otherwise it is a false axiom. Your concept of a line through the earth is a concept and is a false one. It is a nod indeed, as his 5th postulate is proven correct. EVERY structure engineer uses this as a basis of relaity in every singal structure we have. There is no way around that, EXCEPT conceptually.

[@hemanthpattem9949]

0:30 is wrong. Euclid's elements are not just about geometry.

[@philindeblanc]

very true. its also about how we see and perspective, etc.

[@jesusthroughmary]

And number theory

[@furkanfidan2763]

Çeviride hata var! "Düzlemde verilen bir doğru üzerinde olmayan bir noktadan bu doğruya paralel olmayan sadece bir doğru çizilebilir" diye çevrilmiş ama "Düzlemde verilen bir doğru üzerinde olmayan bir noktadan bu doğruya paralel sadece bir doğru çizilebilir" şeklinde olması gerekirdi. Yani "olmayan" kelimesi fazla.

[@paulrevere2379]

Curvature and line are mutually exclusive. 'nuf said.

[@조각치즈]

Maybe we can measure the shape of the universe

[@philindeblanc]

We cant even get to the moon without a bunch of lies...how do you think we can do anything even further?

[@boobylinks]

@@philindeblanc Yes, O.J. Simpson tried to tell mankind the moon landings were faked in the documentary Capricorn One.

[@TheBelmontClan]

Hmm, true because it is subjective to ratio's law and thats why selfish has no option but to parallel that of selfless, otherwise neither could quantify either. Mastering one over the other is a delusion of the unparalleled. A system of measure must have that of an equal, yet opposite.

[@davidjimenezlopez]

Please, use fact checkers. Yes, the Elements has 13 books, but not all of them are about geometry, only the first 6. There is also number theory (books 7 to 9), algebra (book 10, kinda) and stereomety (books 11 to 13).

[@m.s.8522]

(cont'd) And the sum of the angles of a triangle being 180 degrees is Euclid's 32nd Proposition and it is equivalent to the fifth postulate.

[@philindeblanc]

And proves him correct! And this is based off of observed reality. Other geometries are based off false axioms, and imaginary.

[@Stuckinthepow]

thank you so much!!!! I'm reading Euclids Elements all by myself. I was getting so mad, I couldn't conceptualize his wording. I figured if Einstein was able to teach himself Euclidian Geometry before he got his first pubic hair- Why can't I at age 29 :)

[@philindeblanc]

because you are academically taught a lie about the reality you observe. Once you break out of the brainwashing, you will see that Euclid is correct and proven to be correct, might I add. And IS the math based off of the reality we observe.

[@ManhNguyen-wd3mz]

My brain is break

[@ethansstuff2988]

yo this man is my math teacher

[@brendaponce9281]

Ethan’s stuff what

[@ethansstuff2988]

dessi ponce jeff dekofsky is a math teach, he teaches at my school and is my pre-calculus teacher

[@karimspiano]

Wait a minute... Isn't the postulate:" If there is a point A not on a line d we can only draw one line c passing through it parallel to d" Proved. Let's say you drew the line c passing through A parallel to d. Draw another line parallel to c. If two lines are parallel then they don't share points. Then A which is on c can't be on any other line parallel to d. So " If there is a point A not on a line d we can only draw one line c passing through it parallel to d" .... I am told it was proved.

[@philindeblanc]

You are mostly correct, and it was and is proven. academia cannot accept it. Just like Theory of Relativity is proven false, yet still accepted as the going idea. Institutions are messed up and lie to fit their will. But in your first part I think you are describing his first Postulate. The 5th postulate is proven as the 2nd is proven. This video picks the "Parallel" explanation and doesnt show, but sort of explains how any converging lines, inner angles will always equal 180. This is proven correct. but since it is based on reality of how we observe and understand nature, it goes against the academic institutional definition of reality. Basically using false axioms, and you get non-Euclidian geometry.

[@jesusthroughmary]

@@philindeblanc What is a "false axiom"? That doesn't even have a logical meaning.

[@philindeblanc]

@@jesusthroughmary Its very simple. Math being a language, a human construct...If the math is not based on scientific observation experiment then the math can show to be correct only as a concept, and not based off of reality. Try not to say that false axiom has "no logical meaning", as this is a basic objective look at math.

[@pulse5863]

"prove the postulate from other 4" the thing you proved was a theorem since you used up previous theorems to even begin with parallel lines

[@HigherPlanes]

I get the feeling folks were a lot smarter back in those days

[@philindeblanc]

yes and no...We are a LOT "dummer", and think backwards to try and make conceptual math fit reality. It doesn't!! Good observation!

[@SeaTekMonstroso]

What's a Geometry?

[@AndrewKelley]

This was especially fun after just having completed Antichamber.

[@wisnaromdona4811]

Love this!

[@KieranGarland]

Excellent. Thanks.

[@BlakeytheG]

YEAH MR DEKOFSKY!

[@flewggle]

I still dont understand why the 5th postulate was so difficult to prove.

[@philindeblanc]

Its not. Its because many academia didnt want it to be proven because it went against the copernican theory. But at the end it is proven and correct. And is based off reality. It is still the basis of EVERY building or structure ENGINEERING on the face of the earth.

[@jesusthroughmary]

It's not provable, it has to be taken as given in order for Euclidean geometry to work. That's why it's a postulate.

[@philindeblanc]

@@jesusthroughmary All true axioms are taken as given as long as they are taken from reality. Thats what separates true and false axioms. Axiom is provable by using it in reality.

[@jesusthroughmary]

@@philindeblanc I guess the earth is flat then

[@philindeblanc]

@@jesusthroughmary We use it as if it is flat. Every engineer on the earth to this day uses this basis. I dont know the shape of earth as a 3D object, but the surface is flat based on math, measure, and all observations, and scientific methods. but it doesn't mean the shape is flat. Mathematically it is at least 37x larger than we claim.

[@anticorncob6]

Actually, they aren't all about geometry. There's some number theory too and some talk about perfect numbers. There are lots of equivalences to the standard parallel postulate, and my favorite and standard one is that if two parallel lines are cut by a transversal, the corresponding angles are congruent.

[@philindeblanc]

yes, and always two inner angles equal 180degree.

[@paulrevere2379]

Curvometry is ok, but it does not disprove geometry.

[@jesusthroughmary]

If the parallel postulate could be proven, it would have been a proposition, not a postulate.

[@Name-jw4sj]

Euclid didn't know that at the time. He himself also didn't feel absolutely sure it was a postulate since he didn't use it much to prove his other propositions. And many others after Euclid also believed it can be proven since the postulate wasn't self evident.

[@philindeblanc]

It IS a postulate as it stands on its own. You can prove it by deductive reasoning. There are a few videos on it that explain it well. This video only demonstraights the Parallel postulate. But notice in the start of the video he reduces the context to JUST the parallel, and not including the intersecting lines that will always have a 180degree sum of 2 inner angles. There are much better and more openly honest videos on this. there is a reason this is top trending and 1st video that pops up. As it aligns with academia and what is taught. Not what is true factual reality..

[@jesusthroughmary]

@@philindeblanc If it is a postulate then you can't prove it by deductive reasoning

[@philindeblanc]

@@jesusthroughmary If we mean postulate as a axiom, which is how I have seen it used, then sure, you can prove it, and is proven daily as it is used in reality.

[@Stuckinthepow]

Why does Euclid not make note of a plane in his wordings? Same with all his Postulates. Once you conceptualize points and lines on a plane, it makes it so much easier.

[@RichardAlsenz]

Euclid plays a magic trick of distraction . This is a fundamental problem for all geometries. A picture of a point is never, by Euclid's incorrect first obvious assumption, a point. A point.can not be observed, only a picture of a point can be observed.

[@philindeblanc]

@@RichardAlsenz This claim is fundementally wrong. ALL each and every single engineer constructs based on Euclidian geometry and is based in reality. this is why it is so key. Academia cannot accept this, and therfore you have "nonEuclidian geo". Not the other way around. Its the point NOT to conceptualize it, as that would be based off false axiom.

[@RichardAlsenz]

Euclid summarised these statements as definitions. He began his exposition by listing 23 definitions in Book 1 of the 'Elements'. The first assumption assumes it is obvious that : 1. A point is that which has no part. Is this assumption true? If it is, there is only a picture of a point because a point is not observable. The Point is not observable if it has no part:?) Which disqualifies it as being consistent with the scientific method. See Margitte's "this is not an apple" Gauss to Bessel Goettingen 9 April 1830 …The ease with which you delved into my views on geometry gives me real joy, given that so few have an open mind for such. My innermost conviction is that the study of space is a priori completely different than the study of magnitudes; our knowledge of the former is missing that complete conviction of necessity (thus of absolute truth) that is characteristic of the latter; we must in humility admit that if number is merely a product of our minds, space has a reality outside our minds whose laws we cannot a priori state …

[@RichardAlsenz]

@@philindeblanc The use of space for mathematical operations is a problem for any theory. Gauss pointed this out in 1929 and it was 40 years old in his mind. See the last paragraph for his conclusion on where it would lead. I call his problem with Geometry "Gauss's Gordian Space Knot". He searched his life for its resolution. See his friends and former student Weber's attempt to resolve the issue. 14. Gauss to Bessel Goettingen 27 January 1829 …There is another topic, one which for me is almost 40 years old, that I have thought about from time to time in isolated free hours, I mean the first principles of geometry; I don’t know if I have ever spoken to you about this. Also in this I have further consolidated many things, and my conviction that we cannot completely establish geometry a prioir has become stronger. In the meantime it will likely be quite a while before I get around to preparing my very extensive investigations on this for publication; perhaps this will never happen in my lifetime since I fear the cry of the Boetians if I were to voice my views. It is strange, however, that except for the well known gaps in Euclid’s geometry which till now one has tried in vain to fill, and never will fill, there are other defects in the subject that to my knowledge no one has touched, and to resolve these is by no means easy (but possible). Such is the definition of a plane as a surface for which the line joining any two of its points lies wholly in it. This definition contains more than is necessary for the description of the surface, and tacitly involves a theorem which must be proved first …. Reconstructing the geometrical theory is necessary for any progress on this subject. Points and lines and their use of them are delusional endures. If you are interested I can disclose this to you. [e-mail]. Your approach may have possibilities. Good lucK in an area which Gauss was upon. "According to his frequently expressed view, Gauss considered the three dimensions of space as specific peculiarities of the human soul; people, which are unable to comprehend this, he designated in his humorous mood by the name Bœotians. We could imagine ourselves, he said, as beings which are conscious of but two dimensions; higher beings might look at us in a like manner, and continuing jokingly, he said that he had laid aside certain problems which, when in a higher state of being, he hoped to investigate geometrically.:?)

[@philindeblanc]

@@RichardAlsenz I'm gonna read that again. DO you have a good refrence for Euclid Elements or really important one that gets forgotten, is the book OPtics. Would love to get these, but so hard to know which versions are badly edited taking things out or "explaining them waya" vs a honest translation. Thanks for your comments

[@leewilliam3417]

Great😊

[@rianhasiando]

Well Explained. Thank You.

[@DrEMichaelJones]

Euclid didn't call it "The Parallel Postulate" If you call it the triangle postulate you'll be less confused.

[@philindeblanc]

Euclid's geometry is the only geometery based from how we observe the earth and most scientifically sound and based off reality. Those diverging from these axioms are imaginary space geometry.

[@RichardAlsenz]

Gauss to Bessel Goettingen 9 April 1830 …The ease with which you delved into my views on geometry gives me real joy, given that so few have an open mind for such. My innermost conviction is that the study of space is a priori completely different than the study of magnitudes; our knowledge of the former is missing that complete conviction of necessity (thus of absolute truth) that is characteristic of the latter; we must in humility admit that if number is merely a product of our minds, space has a reality outside our minds whose laws we cannot a priori state …

[@adiaphoros6842]

Found the flat earther.

[@philindeblanc]

@@adiaphoros6842 Its simple

[@adiaphoros6842]

@@philindeblanc And you're a simpleton with a cracked pate.

[@Maria___2i]

Things are looking up-vital refund info

[@dakiddstay23]

take that flat earthers!

[@philindeblanc]

this actually helps the flat earth crowd, in case you didnt notice. This teacher adapts it to his belief, not stand alone on proven geometry. Euclids 5th postulate is prove correct time and time again. I dont know the shape of earth.

[@carloscolon9968]

We have to think that Euclid did not have the believe of geometries consistent with the negation of the fifth axiom. It was not and idea of his times. The mathematical community had to wait two thousands years to develop into that directions. Even the famous mathematician Gauss had doubts of publishing his results on non euclidean geometry.

[@endo9902]

I don't understand. postulates are definitions that cannot be proven.. so why the fuzz about trying to prove them?

[@Nothing_serious]

That's exactly why it's controversial. Euclid just turned it into a postulate because he cannot prove it.

[@philindeblanc]

What?? They are all proven. The 5th was contested, yet also proven. Postulates are axioms based on our reality. Every SINGLE engineer uses them to contruct ANYTHING and EVERYTHING that is real.

[@notrhythm]

ig we want to minimize our axioms/postulates

[@thatomofolo452]

Wow 😮

[@spyrmac]

Could you have 3D shapes in non Euclid geometry? We can draw a sphere in Euclidean space. Can we do it in a non Euclid space ?

[@carloscolon9968]

Yes, only that they dont agree with our formulas for most used geometries. The distortions sometimes are shown in big distances and not in small space.

[@illusion887]

i have no idea whats going on in this video

[@TheBelmontClan]

Huh, that's the quantitative postulate of double slit theory, is it not? Are the particles and waves a mathematical hybrid of introverted and extroverted parallels? That of perceptions merely complimenting that to which is one another as basis of tandem atomized realities. A system of measure that has no way to be measured upon that of observation, that is the mystery of value, is it not?

[@sarahbell180]

?

[@alexwang982]

Lol, it’s a troll

[@thaigo972]

Did you just have a stroke?

[@HigherPlanes]

To this day, IMO, this is the best TED talk: /watch?v=SHbkEs_hSec&list=PLC936A50CA3F9DA63&index=30

[@madupaduvlogs88]

this is an easy postulate but the only thing that complicates it ,is that it is a bit big than other postulates

[@Stuckinthepow]

oopsy, never mind. I didn't finish the entire video before asking my question about the non usage of a plane. haha that whole space fabric time dimension thingy came after! ha, thanks Einstein

[@chrisg3030]

"All right angles are equal", the 4th postulate, has like the others including the 5th, a practical import even if surrenders some truth as a trade-off. You're erecting an astronomical sighting post on a hill which looks pretty perpendicular from where you're looking, but turns out to be leaning drunkenly when you walk round it, so some more righting needs to be done to make all the angles equal. Fair enough. But what about when this situation is transposed to a 2D diagram on the page in which a straight line is drawn to the centre of a circle from beyond the perimeter? The two outer right angles are clearly bigger than the two inner ones. The 4th postulate demands we ignore this obvious fact and measure the angles as if they've been formed between the straight line and the straight tangent to the perimeter. Only then do they all become equal. The 4th seems a particularly questionable postulate.

[@alastairbateman6365]

+Chris G 'surrenders some truth as a trade-off. You're erecting an astronomical sighting post on a hill which looks pretty perpendicular from where you're looking, but turns out to be leaning drunkenly when you walk round it' ................. (1) There has been absolutely no truth surrendered as a trade off. NONE! (2) Like driving, drink and surveying do not mix. So sign the pledge, go on the wagon and eventually you will find those parallels are parallel. (3) If my understanding is correct it was the development of hyperbolic geometry where parallel lines meet at infinity that brings the 5th postulate into question. Funnily enough it is a hyperbolic curve that confirms the 5th postulate.

[@chrisg3030]

+Alastair Bateman Your point (1): I was trying to suggest that the truth Euclid surrendered for doubtlessly good reasons was that clearly not all right angles are equal, at least if you allow that four right angles can be formed by the intersection with the arc of a circle of a straight line drawn from its centre. (2) I think you're referring to my other post about the 5th Postulate. I was assuming two lines known to be not parallel, though maybe very close to it, which must therefore meet and intersect at some far off point in one of two directions you look but you can't see which from where you are now. The 5th postulate is a quick and simple way of getting an answer. (If that's a correct interpretation, then calling it the "parallel postulate" as many do is rather misleading since it isn't meant to say anything about parallel lines at all.) (3) I think the 2nd and 3rd postulates may be Euclid's way of saying straight lines and curves are forever different and can't morph into each other, which I'd love to discuss later if you will.

[@alastairbateman6365]

+Chris G ..... 'clearly not all right angles are equal' ......... (1) Things which are equal to the same are equal to one another. (2) When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle and the straight line which stands on the other is called a perpendicular to it. (Both straight out of Elements ). Do we have an error of observation. When I wear my varifocals the computer keyboard rocks from side to side! Astigmatism can also cause pin cushion effects distorting regular figures. As for the rest beyond my comprehension!

[@chrisg3030]

+Alastair Bateman Yes, I realise I have the cheek to argue that not all right angles are equal, despite what Euclid has to say in Elements. My example is of a straight line intersecting the arc of a circle and proceeding to the centre. The adjacent right angles thus formed just outside the circle are equal to each other, (just as the adjacent right angles described by Euclid in the definition you quote), and the adjacent right angles just inside the circle are equal to each other, but the outer and the inner aren't. The latter are visibly smaller. I suggest the reason why we aren't permitted to recognise this is in order to maintain the firm distinction between curves and straight lines laid down by the second and third postulates. The only condition under which we're normally allowed to speak of right angles in my example is if they are considered to be formed not by the arc and the incident straight line but between that line and a straight line tangent to the arc - only then are indeed all equal.

[@alastairbateman6365]

+Chris G Ahhh...... ummm... I've got it, by jove I've got it! Well I think I have. In my little 'bubble of normality' I am standing at the point that 'hath no part' where the extended radius of the circle cuts the periphery and the tangent to the circle at the point that 'hath no part'. Being outside the circle I can only walk along the tangent line towards either of the two infinities. You on the other hand in your 'through the looking glass bubble' and therefore inside the circle can only walk the curved path on the inside of the circle. Now your path like mine must be infinite which means that the radius and therefore the periphery of the circle are also infinite. But our infinities must be at the same point that 'hath no part' so I am propelled along the tangent in one direction or the other to an infinite distance away from the point that 'hath no part'. You on the other hand are propelled to the circles centre that 'hath no part' around which you can only walk in a curved path. Now not only you but every other material object in your 'through the looking glass bubble' world resides in the centre that 'hath no part' so it is a singularity of infinite density, either a super massive black hole or the origin of a 'Big Bang' for some universe. ........... So am I to understand that had Euclid not made the blunder that he did with the 'Fifth Postulate' he could possibly have conjectured the existence of black holes or the 'Big Bang'. Now that is truly, truly amazing and I must thank you for the enlightenment that you have brought me. ............ Unfortunately I still cannot get parallel lines to meet at infinity in my 'Euclidean bubble of normality'.

[@jakeruttenbur5742]

Woww! Mind blowing!

[@philindeblanc]

its science fiction...its always mind blowing! :-)

[@anaradlar]

awesome!

[@SophiaCookie]

Good job your first comment :D

[@tombweisner]

great!

[@adityakaundilya9975]

That's why 13 is considered unlucky number ! :)

[@anticorncob6]

You unconciously assumed two things: a) that there exists at least one line passing through A parallel to d b) that the transitive property applies to parallel lines, that if d is parallel to c and c is parallel to f (I'll just call if f since you didn't give a name for it), then d is parallel to f. You lose, sorry.

[@BoundInChains]

mr. uploader, have you ever gone outside what you have been taught yourself?

[@Jdekofsky]

That is not proven. That IS the Parallel Postulate at work. Without The Parallel Postulate that does not necessarily HAVE to be true. That is the entire issue :)

[@patod4]

it is clear you are reading, so you should go slower. Thanks anyway

[@j0nnyb0y54]

Wait...what?

[@messiahblack4816]

Euclid had teachers, please stop the alluding....

[@GabrielKnightz]

Thats really cool about that mmhmm...aanha... (i wonder what my super power would be, maybe ill use it for good or maybe rob a bank....i wonder whats for dinner...cats)

[@TheDaikashido]

the second definition is only good if you're dealing with a plane

[@philindeblanc]

No, it is true and good in EVERY engineering structure made to this day. Therefore it is based on reality, not academia. Not a single bridge of any size, even over 20 miles accounts for a curve. not a single right angle. That is reality. We just dont academically accept it. Pretty crazy eh?!

[@AnantMall]

well i read it different .... the last word being different !

[@TheBelmontClan]

Hmm, thats funny like the definition of marriage, as if it postulates the parallels like the oars of direction with each row being a system of measure, yet the fears are oddly the same. It's basic math

[@ahamzah12]

Calculus!!!!!!!!

[@AdityaKumar-ij5ok]

The narrator is bad at speaking at the correct pace in which everyone can absorb completely what he's said

[@MegaShitou]

:( MY ENGLİSH NOT Perfect for understanding...

[@IRON9LORD]

Wow, showing Arabs as knowledgeable people is great, the were so diffrend than Arabs of today, Thanks TED

[@philindeblanc]

Dont thank TED, TED is academia, and wants you to think Euclid was wrong. He is proven correct and in a reality based axiom.

[@sudeshrani4327]

Worst narration ever

[@philindeblanc]

yeah, misleading and incomplete.

[@IRON9LORD]

why am I , I'm Arabic, I know that current Arabs are ignorant, Unlike IbnAlhytham and AlKhwarizmy and Jaber bn hyyan , Why are you so pessimist ?

[@justsaying605]

flat earth