The Story of (almost) All Numbers
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- Опубліковано 15 лип 2021
- Have you ever wondered how we came up with all these non sense numbers? Well now you can find out. Watch along and find out the history of all numbers. (mostly)
If you haven't subscribe already, do so here: / h0ser
#philosophy #mathhistory #SoME1
The Story of Western Philosophy, and numbers, math maths mathematics, maths history, math history, the history of numbers, number creations, numbers, entire history of
Gruk is the most underrated mathematicians of all time
Rip geuk
Just imagine that his name was actually "Two", and suddenly he's the most well known name in all of mathematics. Without a documented history of him, we can't really say his name wasn't Two.
Also the indians' and their contribution in the world have been underrated especially in ancient and middle ages later scholarly works declined during 750 years of foreign occupation(Turks, mughal, then british) time but still happy that some people are spreading the word now
Some of the Contributions of india to the world-
Mathematics, Astrology, Ayurveda, Yoga, Zero, Toilet( atleast 2500 BCE), Chess, Shampoo, Wireless Communication, Buttons, Cure of leprosy and lithiasis, Cataract surgery and cosmetic surgery (2000 BCE), Natural fibres that are used in clothes(since 5th millennium BCE) , Ink, Fiber optics, Heena, apart from these USB and Intel Chip were also invented under indians. I know other countries have also made a lot of contribution to world but just wanted to let people know about a country what some arrogant people in West termed at times as tribal, uncivilized land...So this is a tight slap on their face.
Sorry if someone is hurt but that is fact west has demeaned indian culture a lot without trying to understand except few unbiased indologists and orientalists.
@@gyanprakashrai9412 Indians have contributed way too much, but as told in the video, Arabs liked to tell that it was their discovery instead that of Indians. This tells a lot about how Arabs and the outside forces were in the Middle Ages and before that. They only wanted their own fulfilment and the idea that someone would do such a thing is absolutely disgusting and heart-wrenching…
As a maths student, I can say that this is equivalent to disrespecting someone’s grave after they have died…
Our ancestors keep fighting with their own people, so yeah not suprised if somone got big booty that kick eachother ass then stole and rewrite their history.
Well if you compare that shitty situation to these modern times, ya can see how the chinese are so advancing in technologies, heck even they built their own space station, but still most of our media are being controlled by the west so we're not paying attention to those chinese. It's a same situation but different approach. lmao, humans are stupid af
this man basically explained the math lore
A small glimpse into it
The gameplay is way harder than the lore.
@@jonathasantoz I still remember the days fondly in the library as our classroom while our other school was being [cleaned up]. learning the basics of how to the sum of matics and mathe works.
Skipping the most important numbers of all, invented by Cantor in the 1880s.
Pretty badly, but it was funny
You lost me after two rock
Same
He lost me after rock
4:00 for anyone wondering, this number is 69420.
4:07 is 1354
MMDCCLXIII
it's 34210 you are thinking about
@@WhizzKid2012It’s 69170
@@boston.0703Nope, CD is 400 and XX is 20
Also, Pythagoras didn’t discover that root 2 was irrational, but someone within the cult of Pythagoras did. As the story goes, Pythagorean principles centered around the belief that the world could be perfectly expressed through numbers and ratios, however a simple mathematical proof was discovered that contradicted that belief. It is also rumored that the man who discovered this was murdered by the cult of Pythagoras either to cover it up or for blasphemy as mathematics at the time was treated basically religiously.
I know different version of the story, slightly more "justified" - irrationality of sqrt(2) was kept as a secret in Pythagorean cult as it was hard to deal with that fact according to their beliefs, and someone blurted it out, so he got executed by them for telling secrets to outsiders rather than heresy.
It wasn't treated religiously. It was the religion of Croton during that time. It was inspirational to Plato, in helping develop his world of Forms. You see, the Pythagoreans believed that math was the fundamental building block of everything, and that math existed in a pure form. Plato took this and ran with it.
Thank math that Aristotle came around to set things straight. Good thing nothing will happen to all the work he's done. No one will willingly choose to believe in Platonic ideals when reality is so important, right? Aristotle isn't gonna be lost in the West for over 1000 years, right?
Some say he was exiled from publishing his findings, others say he was drowned
@@brutusthebear9050 It's still not wrong to say math is the building blocks of the world since they are able to describe the world
@@Vysair Math is descriptive of reality, that is true. But, that is not what Pythagoreans believed. They believed that math was the *real* reality.
1:00
For anyone wondering how you can count to 1024 on just your fingers, count in binary. Each finger can either represent a zero by being down, or a one by being up.
With ten fingers, you can count up to 2¹⁰ or 1024
isn't it 2^10 + 2^9 + ... + 2 + 1, since you can count upto 11111111111?
@@mrocto329 1111111111 would be 1+2+4+8+16+32+64+128+256+512 for a total of 1023. (you have 1024 possible combinations but 0000000000 is just zero)
@@connorwright7040 No clue what I was thinking when I wrote that tbh, I guess I was too lazy to write 10 digits of 1's and convert to base 10?
Not really simce you need both hands and its humanly impossible to raise ring finger without little finger or middle finger without helping with other hand. So you miss numbers like 8 for example lol. So just 2^8 is more realistic maximum value
It is said that if a binary number has _n_ ciphers, you can count _2^n_ numbers, from _0_ to _(2^n)-1._
Having 10 fingers, you can count from 0, up to 1023.
It is quite amazing that many mathematician from all around the world calculated the value of pi and they never met with each other or knowing each other's work.
Here is a more interesting fact: I once multiplied the two numbers 4116453213565341246357132542 and 11247498996654853558153551, and I'm absolutely sure that I'm the ONLY person who has ever done that until now.
@@Tommy_007 Not if I also do it!
@@Tommy_007using a calculator?
@@Tommy_007some random supercomputer did it in 1997
@@Me-mt9rq😭
10:09 WHY HE LOOK SO DEVIOUS??????
Faaaacts
Why does he looks like he has a evil idea
It's interesting how when we look back, we realize how inefficient other older number systems were, but ours seems so good. Imagine on the future our number system is looked at like we see the ancient Sumerian one
i thought the same things
Even if we invent new number system, it probably would be based on our system, at least because it was used everywhere and it will be too expensive to change it. But I want to see new digits for hexadecimal system instead of letters
hello checkmark
Base 12, here we come
Like Hexadecimal or binary
I knew accountants were epic but not this epic 😎
Pushin 🅿️
@@user-db2se3nm5d there are ✌️ P’s in your sentence
You know who's epic-er, some high Indian guy.
@@h0ser my family works so hard I used to then 3 weeks ago I break my leg been on pain killers. Man I see why lazy people are lazY now. Walking? Who needs it. Not me shie.
@@h0ser since being "enlightened" I have grown distrust for the banks. Inolden days the teller had a gun and put his life on the line. So we paid him more. Then we gave the risk to the guard pay him less and increase pay for the banker to do nothing. Further more back then black people where alot more likely to wear suits. What did you think i was gonna say.
Thanks for saving the best for last! e is such a powerful constant. It also ties into complex numbers since sine and cosine can be expressed as a form of e to the x, although in engineering, we say j instead of i. I'm also a big fan of Planc's constant.
Dig the humor and easy story telling style. Enjoyed, thanks dude
2:59 The square root of 2 is approximately 1.41421356237, and 577/408 is 1.41421568627. They're pretty close to each other and it's impressive to think how they could approximate the square root of 2 to such an extent.
Dayum. Our ancestors were dripping
@@MohitSingh-kl5pf We just aren't on the same grindset like our ancestors back in the days.
@@praneethmashetty591yup but our scientists are
Hmm, back then Indians even knew the distance of the moon to earth. Pythagoras theorem was also in Hindu spiritual texts.
The number system was invented by Indians. Otherwise Roman numbers were used.
@@princeroy1837 they even estimated radius of planets and that too with remarkable accuracy except Jupiter and venus
Timestamps:
0:00 - Introduction
0:40 - Counting Numbers
1:25 - The First Written Numbers
1:50 - Origins of the Fractions
2:37 - Rationals Numbers
3:40 - Roman Maths
4:19 - The Infinite Concept
5:03 - Negative Numbers?
5:40 - The Zero in India
6:27 - Numbers Systems
7:56 - Calculus, Calculus, Calculus...
8:42 - Complex Numbers
9:35 - PI Number
10:32 - E Number
11:07 - End
Btw, the result is LXIXCDXX (69420). Deciphered by "Owuraku Asare"
And the subtraction result should be MCCCLIV, or 1354.
3:14- Pythagoras
@@carlofrancisco1501 lol timestamp is at π
@@shivamchouhan5077 Imagine if the timestamp followed the pi decimal with infinite precision and we just don't know it
LXIXCDXX is not 69420 its believe it or not: 689
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMCCCCXX is 69420
I love you dude. Your sense of humor is spot on bro!!!
This is a channel we needed but didn't deserve
6:45 "Bengali numerals, eight for four and nine for seven, this is madness!"
as a bengali growing up learning english, I can confirm
Mfs confirming shit for no reason
As another bengali I am confused 😭
Learning 5 and 6 was the most difficult for me, also when i wrote 3 and 9 and mixed them up as the other letters
Same
In Assamese also.
Hey thanks for explaining the story of my great-grandfather gruk. Means a lot.
when you think about it how did he become his great grandfather
The man from earth
he is granpa of all people
or your great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-grandfather
Grukpa
Loved your video and I have to say you are an excellent narrator. Though the video was informative and engaging, you found a way to pepper the content with well placed sarcasm. The part about "...Brahmagupta wrote this book called.... called....It's not important" had me laughing out loud. Very funny.
Having Moldau as the background music , and having maths as the main topic, means that this video is going to be EPIC!!
Underratedness levels are really high. We need to make more people know h0ser for he is amazing.
@Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3 @Kagamine Rin loves oceania part of indonesia uwu:3
@@manavshah8335 yikes..
Not that amazing ... Roman math is unpredictable propablity state of action
goofy ahh google logo
Euler didn't actually name e after himself, he just liked to use vowels as variables and had already used a in his book
e is NOT a variable, i hope you mean a constant
@@aakashprasad114 a constant is a variable
Based euler
onion
@@voidz8389 how can a constant be a variable if it isn't variable
I dont think I ever knew just how complicated math really is until watching this video
Thanks to Gruk, I fail at least one exam a year ! Thanks mate 💪
I know Pi has probably been proven to definitely be irrational, but how hilarious would it be if the computers finding the digits of pi just stopped... like they reached the end and we come to find out pi isn't irrational.
That'd be an insane crisis.
It would not be a crisis, and it would not happen without fault in the code (it's a proof for that reason lol).
Oh my gosh XD Truly so
@@ffc1a28c7 whoooooosh
@@rupert_1491 It's a shit joke because it's proveably false.
i always wondered, how confusing were the big roman numbers to educated romans. is it confusing to us because we arent used to it? or was it actually that confusing. some people even today can read roman numbers just as easily.
Thats interesting
It also works a lot better in Latin than it does today. Just like how different base systems came naturally to the people who used them. Hell, no one really has trouble with time, even though it's base 60 (one of the best bases imho) and base 24 (eh it's okay).
@@brutusthebear9050 hell, the whole time thing gets more confusing. i say 90 seconds, you get me. i say one and a half minutes, you get me. but if i said 1 minute and 90 seconds you would punch me in the face
@@shafwandito4724 It's neither. That's not a valid combination of Roman numerals.
@@shafwandito4724 It's -4 lol
On of the few great videos being created on UA-cam today. So interesting and hilarious.
When I was watching this video around the 1:29 mark, I realized that the background music was none other than the orchestral piece "Themes of the Moldau!"
Besides the video being a goofy mix of humor and simplified mathematical history (along with some additional facts), I really appreciated the choice of background music here, as I performed an arrangement (specifically by Robert S. Frost) with my high school orchestra classmates just a week ago from the time of typing (12/16/2022).
Nonetheless, if I hadn't known the name of the background music, it would've been nice if the description had a "music used" list; frankly, I feel that plenty of other YT channels should adopt this same practice.
I saw something a while ago about how if an average person was sent back in time they'd be able to describe all this fantastic technology, but if they were asked to make some they'd have no idea how. Since then I've been trying to learn the basics of stuff, and knowing how pi was worked out is very useful
That's why I always had the idea to find the best mathematician in town and blow his tiny brain away by my advanced math
Basics of “stuff”?
@@yourdreams2440 It’s not that hard really
Like playing around with logic gates
Once you know that a basic computer can be achieved with some time
Or the fundamentals of engineering
Depends on how far back and what inventions would be unknown. The average dude could invent farming or the wheel or maybe even things like the plow. But if it’s like the 1700s then not much they’d be able to bring apart from vague ideas
I love your geography videos, but this one is absolute gold to me.
This was the BEST explanation of numbers I heard hilarious and informative 😂😂
So freaking happy I found your channel
Today I learned that Pythagoras was an absolute madman. He was crazy, or at least by today's standards. He constantly claimed to be Hermes' son and that his father gives him the ability to see all of his past lives. He also drowned one or more students for weird mathematical discoveries, like the existence of irrational numbers. He considered it punishment from the gods.
@DHRMP "did you just entered my math class with a bean soup and expect me not to skin you to death for your heresy?"
@DHRMP if I recall correctly it was the soybeans, rather than the beans itself bc that reminded him of the vulva in women
Complex numbers are actually when you have a number that combines imaginary and number line numbers, it’s not a different name for imaginary numbers
Yes true a complex is a number with a real part and an imaginary part
I swear every time I look up "imaginary numbers" on Google the results always say "complex numbers". Sigh.
@@falcon_arkaig yeah, it’s a common misconception. An example of a complex number would be 3+2i, where the number line number “3” is combined with the imaginary number “2i”.
@@falcon_arkaig All real and imaginary numbers are complex but this is not true the other way around. A complex number is not just real nor just imaginary, it is a mix of both.
Imaginary numbers are complex numbers when written in the form 0 + Ci
The music is Smetana - Moldau if anyone is interested. It's really a beautiful piece.
I made a number in high school. It’s in the base 11 system between 7 and 8. It’s called schmeight. Doing calculations with a new digit mixed into the middle was fun to show off.
Ive spent the last several hours binging your channel and honestly this video has been my favorite
4:53 "wtf were they smoking"
I wanna know
Meth 🗿
@@bananaita8690 Ganja aka Weed. Where so you think weed comes from?
Best thing ive watched all week
6:45
Wow you actually mentioned our Bengali numbers
You got my respect and also a new subscriber!❤
Me an Indian watching this on the day gave my Engineering Mathematics Exam :
ITS IN MY BLOOD
🔥
W
I love the work Indian people did for mathematics.
Do know Pingala gave meru prastara ( which is now known as Pascal's triangle) and the Fibonacci sequence way back in 3rd century BC.
Also,
The infinite series for pi is mostly today known as Leibniz formula for π. But many few people know that this series was already discovered in India by Madhava (c. 1340-1425 AD) of Sangamagrama, 300 years before Leibniz or Gregory.
You can check on the internet
no it isnt you pajeet lmao
Ah yes the process of smoking one ton of weed in order to find the hyper-negative-infinities. Classic Mathematics
This was delightful and hilarious. Much enjoy.
I’m actually a big fan of your channel
5:56 in Greek especially there's even more of a confusion. The word for zero, μηδέν, literally means nothing/not a single thing.
And “Βιβλιοθήκη” means book place “library” very descriptive
Thanks for putting Bředřich Smetana as a background music))
Wow props to you for using the Moldau in ur vid, it's a great piece
This is great man, cracked me up. Keep going and you'll be big in no time.
this inspired me to try harder in math, but i forgot i already graduated
That shouldn't stop you
i literally had this exact thought 😭
Do it anyway! Math is even cooler when you learn it without being compelled to do so for some assignment and without the pressures of getting a good grade.
Your delivery has real "You, Me, Gas Station" energy 😂
7:57 is the most underrated bit of comedy in this video 😂
just casually doing my commenting on underrated youtubers. (your the best!)
I was in a math competition my junior year of high school in which we had to learn how to do math with babylonian and ancient egyptian numbering systems. I had locked that memory away, but this video brought it back. It's amazing how much we take math for granted.
why in the name of miracle whip, do you need to learn math in babylonian and ANCIENT egyptian numeral??? i know it's a math competition but why though? couldn't they just think of something else like uhhh accounting
@@thea.f.k2979 the topic of the entire competition was ancient babylon and egypt. It was an intermural competition, I just was only on the math team.
Thank you. That was an amazing early morning bullet to the brain😅
I learned more about calculus than I did last year in my class, thanks
Fun fact - Aryabhatta is speculated to have known that pi is irrational 1300 years before lambert proved it. Its just that most of the works of Indian mathematicians did not survive 😔
P. S. - If you don't know who Aryabhatta was then just Google it. You'll be surprised to know about his contributions to mathematics and astronomy.
Edit : For those of you who think I'm claiming it without any proof just read this page : en.m.wikipedia.org/wiki/Aryabhata
nice
Yes bro
"speculated" there is no proof. I say this as an indian, please stop glorifying our history
@@MenacingPerson I never said there is any proof. In fact, there isn't any proof that's why I said it's speculated in the first place. It's speculated because in most of his works, Aryabhatta uses pi as an irrational quantity. He might even have proved it but the works did not survive that's what I am saying.
And there is no harm in glorifying our history as long as it's true and not some bullsh*t from the WhatsApp university.
If it's speculated, doesn't that mean it isn't a fact?
Love this video so much, truly need more content like this - both interesting and EXTREMELY funny ♥️
I'm no mathematician myself but this video kept me watching till the end
Thanks bro helped me out for my math finals tomorrow, I‘m going for my bachelore
It would be wonderful to hear you explain the Table of the Elements.
Mate this is gold, one of the most important history videos on UA-cam
I can't believe it.
I've been taught all of math and it was actually interesting...
Now that's an achievement
My reaction to this information: ua-cam.com/video/Vg3I4Ut9uXE/v-deo.html
These are just the celebrities of math
This is generously "some" of math. A lot of the details are incorrect and the chronology is fucked up bad.
Math is way more fun when you don't have to commit things to memory for a test.
This is the coolest video I’ve ever seen
Great video...YA HOSER!
4:06 On behalf of Julius its MCCCLIV
MCCCLIV = 1354
Glad to know there’s people as insane as me
can we get julius caesar to confirm this
@@microwave856I'll call him and see
When I was studying calculus, sometimes we needed to hospitalize a ratio when it was zero over zero.
L'Hopital
@@orkkojit Thanks. I couldn't recall the correct term but only what we called it.
Why didn't these guys just use calculators man. Think smart not think hard 🧠
Rip mathematicians
Nah, think hard not smart
7:24 i love you for telling this
Ancient sumerians counted on a base 60 system. They used their thumb to count on the other 4 fingers on each hand, which added up to 12 and everytime they reached 12, theyd stuck up a finger on the other hand, counting up to 5 sets of 12s
Isn't it 16 if you count that way totalling to 80
Ah, so that's how that works! Brilliant... Perhaps this could work just as equally well with Base 12.... hmmm...
Whether it's geography, politics or numbers, this guy just drops straight bangers.
I loved the lore of math.
Can't wait for the expanded universe!
this is the best video i've ever seen. ever.
6:38 bro why is 4 an anime eye
四
@@2ndch. 4
10
Love the Smetana piece!
10:43 e is also used for 10^x =ex (exponent)
5:00 wtf was they smoking?
They were smoking Ganja
5:42 No you're missing nothing there.
ba dum tss
Thank you, Gruk.
YOU FLIPPED US OFF
This was the most epic and theatrical video about math I’ve ever watched.
Roman architecture is way more impressive when you imagine somebody designing them with roman numerals
yeah that's why we have leaning tower of pisa
@@manjeet2698 that tower was made in medieval italy...
@@IkarimTheCreature oh. my bad
Brilliant video. The world is awesome !
I need to take a moment to express my appreciation for you using Smetana’s Die Moldau as the background music.
You are doing great. Have been here since day #1
I'll suggest you make videos on broader topics like these, you'll get views as well plus people will enjoy cause your tone of narrating jokes is hilarious!
Idk it kinda seemed like he was disrespecting Indians. like no one else was treated that badly when it came to discoveries :/
@@Robopi3.14 I'm Indian, it seemed fine to me
@@ovn_tamil yeah I'm indian too
Nah he should stop making videos if they're gonna have misinformation. Arabic numerals came from Arabia first and taught to the Indians. Modern day Arabic uses old Indian numerals, and India made new numerals. Now Arabic numerals are used in English. Had Arabs just kept the Arabic numerals both English and Arabic would have the same numbers and hindi would have something else. Teaching Indians these new numerals was a mistake by the Arabs, because now they lose all credit. These numbers have been engraved in stone long before they taught them to other groups.
Good video, thank you
Can you make a video on other number series, like base 20 or 9 in other cultures? Thanks a lot!
Amazing, keep it up brother.
The build up to the second rock killed me 😂
Vltava! Krásná skladba našeho českého skladatele Bedřicha Smetany. Je pěkné ji slyšet v tomto anglickém videu :D
You did a great job of explaining number theory, continuous fractions some graph theory, discrete mathematics.
Really love your channel! Never commented before but wanted to say ur stuff is great and always improving 👍 (btw, do u think ull ever accept volunteer artists? love ot contribute some art to ur content one day!!)
Roman numerals were actually super efficient for basic algebra. I’ve since forgotten how it works but I remember that much.
From what I understand, people wouldn't do calculations using roman numerals. Instead, they would do the calculations on a counting board and then write down the results in roman numerals.
The Moldau background music is awesome
Well done, Grunk
Fun fact: when you're enjoying video games, ur computer actually do geometric transformation so hard
Just like no one before "Pythogoras" knew how to use the Pythogorus theorem, no one knew how to use the number 0 before Brahmagupta introduced it in a formal way.
And all the other stuff credited to Greeks which no one Earth had the big brains to figure out but only the Greeks had the ability to do.
All ideas have an origin. They are difficult to discover but easy to learn. Isn't that one of the wonderful things about humanity?
How did pythagoras know how to use the pythagoras theorem before it existed? hmm really makes you think doesn't it
@@rlpn6710 there are some geometric proofs, most of which use rearranging various similar triangles to form negative space.
Elementary theorems of mathematics spanned throughout the ancient world, but were mostly stated without proof. The Greeks were the first to prove those same theorems because Ancient Greeks loved debates; as such Greek mathematicians made use of the elenctic method to give mathematics a rigorous and unassailable foundation. The axiomatic deductive system that we know today evolved from the Greeks. No other civilisation had come up with it because they were more conservative and reverent than the Greeks; stage debates were a foreign thing to them, especially in China.
The theorem is known today as the Pythagorean theorem because the Pythagoreans were the first to prove it.
@@alternateperson6600 Offcourse buddy and because you are saying this that means you have read all the proofs of theorems given by Greeks and other civilizations with conclusive evidence that Greeks were less conservative and had more open debates than others civilizations.
I would trust that you wouldn't just make shit up on the internet without definitive proofs for your claims about Greek supremacy
1:01 He flipped us off😂
Concept of Instantaneous rate of change in speed of planet was existed in works of Aryabhata and Brahamagupta in 5th and 6th century as 'Tatkalik gati'. And it's calculation involves some differential equations.
Your choice of music at the beginning is immaculate. Very nice.
What was it though I am searching for it when I listened to it in a game so please tell me the name of this music.
What is it called?
@@zllrussr8529 Vltava - Bedrich Smétana
@@carlosgloystein Vltava - Bedrich Smétana