These videos consistently distract me from my actual math homework because none of my teachers tell me WHY math works. They just want me to do the problems. I always want to know HOW mathematicians came up with this stuff and why it works!
Nofxthepirate Math is the subject of the physical. It allows us to understand the workings of this world. Calculus, invented by Isaac Newton (And Leibniz) was what aided him in the understanding of physical, such as his famous and often abused F = ma. A pretty complex equation in itself (isn’t it physics? Yes but math and physics are closely related. One cannot happen without the other), it allows us to understand how the world works and how things work to put it simply. Elementary math like these teaches us the fundamentals to understand the workings of the world. It may not make sense now when you don’t see the full picture, but it is essential. Enjoy!
His teaching methods are very simple but the main thing is that it all comes from his heart instead of simply his desire to earn money unlike most teachers today. We need more teachers like you, sir. We LOVE YOU!
How much do you think teachers earn... Not enough to do a hard and stressful job just to earn the money. What I do suspect though, is that some might do it out of a desire for a little bit of power over students.
I usually come across this guy's videos while studying for my exam so I watch the videos partly even if they aren't related to my study topic. This time, I was so excited to see one of his videos and my topic match so I watched the video. I can say that I had seriously entered flow and I was enjoying it so much that I could've gone on for hours without a sign of exhaustion. Eddie sir, I simply adore the way you teach and hats off to you☺️
I'm 35 today, have a Bachelor's in Mechanical Engineering from quite a reputable university, and I just discovered why "irrational numbers" are named as such😞
Love how you are not telling us to do this equation and to show us how to do it but actually describe it and let us know the why part of the question. This even as a year 10 student has cleared my head a bit.
Im in the middle maths class at my school because I transferred here at the beginning of the year and we aren't learning surds. That privilege is reserved for the top class. So I'm here to prove a point to my teacher that Im actually serious about my education and the things I learn even if she isn't.
A question for Mr Woo, I'd like to hear his way of explaining : How do they know it is actually irrational and doesn't reoccur after like a billion decimal places. How do you proove it's irrationality?
Look up on youtube "proving the square root of 2 is irrational" you can do it because you can prove that it can't be written as a fraction. Then you just assume the same for many other roots.
You write down sqrt(2)=p/q, you tell that there's a rational number p/q equal to sqrt(2) and this is the hypothesis. Then you proove it by absurd, the equivalence can't be resolved because of even and odd number rules. That's it
There are two parts to answering this; The first is that if a decimal does repeat, it can be fairly easily shown that it must be expressable as the ratio of two integers and vice versa. This is actually part of the school mathematics curriculum. The second part is showing that the square root of any integer that isn't a perfect square, can't be expressed as the ratio of two integers. The easiest way to see this by considering a possible lowest form ratio a/b and putting a and b in terms of their prime factors. For a/b to be in lowest form there are no common primes between a and b. Thus when a/b is squared there are still no common primes and the ratio can never cancel to an integer.
What about continued fractions representation of square roots? It might be interesting to show them that as a parallel of your ratio examples. (Someone might have already asked about it in a previous comment, I have read some but not found one about it so far)
Hello sir, I just browsing in order to get some knowledge over surds cause I have an exam😁😁😁. Well now I can right the exam and you're really an awesome teacher I've ever seen in my life.. You're friendly and making the concept getting on to the mind...
I'm so amused that he said it's not "irrational numbers" like "you crazy man" immediately after comparing irrational numbers to a crazy jazz musician lol.
@@elimgarak7090 absolutely. You can sort of think of a fraction as a ratio of two numbers, and an irrational number is one that cannot be expressed as a fraction.
One thing, you said ''not like 'you're being irrational you crazy man''' aren't irrational numbers the exact reason why we use the word irrational in that context?
I did not see this teacher reply to any comments, so I don't know is he reads them or not, but I would like to thank him for the way he interacts with his students to get them interested in the lesson. Good on you Sir.
@@flamephlegm I've noticed several differences in his notation compared to what I learned in Germany, e.g. in other videos he puts arrowheads on both sides of a coordinate system axis. I learned that you should always only mark the positive end of the axis. It's interesting that mathematics, which is often considered to be the universal language of science and engineering, can be written in sometimes ambiguous ways. Dot-above-something could also mean "derive with regards to time", dx(t) / dt.
Why not use the term transcendental number for when a square root does not result in an integer and always results in a transcendental number there are other transcendental numbers of course
My teachers have literally no idea how to teach this year. I'm failing extension maths because of their inability to explain anything! My maths teacher literally writes the rules and an example on the board while we copy them down in silence. At least this will be helpful when my school shuts down due to corona! Now that I found theses videos, maybe I won't fail!! Thanks!
Watched video, but still had to google what a surd is. The missing info was that a surd is a _type_ of irrational number formed from the square root of a rational number. It's not just Austrailian for "irrational number".
There is a way of doing square roots, that don't have perfect square roots, finding the nth tooth, which is like a long division way or the Babylonian method
Pi is irrational and can not be written as a fraction. 22÷7 is just an approximation :) (according to my calculator only accurate to the second decimal place, so not a very good approximation)
Surds involve square roots of integers in order to define this. Numbers like pi and e eare beyond this, in terms of how disconnected from ordinary numbers they are. Pi and e classify not only as irrational, but also as transcendental. Surds are part of a classification of irrational numbers called algebraic numbers. Transcendental numbers are numbers that are not algebraic, rational, or integers. Numbers that transcend algebra, as in go beyond algebra. Algebraic numbers are roots of polynomials with a finite number of terms. These are numbers that involve roots, whether square roots, cube roots, or even roots of higher orders. But the point is, there is a finite number of terms in identifying an algebraic number in terms of 4-function math and roots. It takes an infinite number of terms in the polynomial, for a transcendental number to be the root of the polynomial. It is common that these numbers are identified as an infinite series, that give a means of calculating them. That is, a pattern of numbers that when added up, will converge to this value.
Great video, as always....but remember that although all surds are irrational, not all irrational are surds. "pi" and "e" are irrational but not surds. To be a surd we have to be inside a root....
Different analogy for music :P spotify playlist. popsong is one song one, elevator music, is playlist on repeat on given order. Crazy jazz music is random playlist which also takes in spotify suggestions, it never goes to exactly same repeat...
5/1 is not the same thing as sqrt(5) though, the same as 2/1 is not the same as sqrt(2). Technically, 5/1 is sqrt(25), and 2/1 is sqrt(4).. kinda.. also have to remember our negatives can be squared. Sqrt(2) / 1 is not the same as 2/1.
Love your channel, but to be truly rounded, remember you can revert, but you can't revert back because back is already contained in the definition and to do so is a redundancy
But why it goes nonrecurring? What makes them go changing patterns? ...U can also answer by why in some got reoccurring pattern... that will explain it too I suppose. :)
You get the recurring pattern for rational numbers, because it is a ratio of integers. Eventually, every denominator that doesn't form an ending decimal, will be a factor of a number like 9, 99, 999, 9999, etc. In the case of 1/3 and 1/9, we can express them as fractions out of 9. In the case of 1/11, we can express it as fractions of 99. Less obvious, in the case of 7ths, we can express it as fractions of the number 999,999. The number of 9's that form this grand multiple of the denominator in question, tells us how many digits get to repeat. 1/3 equals three ninths, thus repeats the digit 3. 1/11 = nine ninety-ninths, thus repeats the digits "09". 1/7 = 142857 / 999999, thus repeats the digits "142857". For this reason, only rational numbers can have repeating patterns of digits in their decimal form. If there is a repeating pattern of digits, there exists a number made up of 9's from which it is a factor. If it is irrational, by definition, it cannot be a fraction of anything, so its digits must not form repeating patterns.
Sometimes it is irrational, sometimes it isn't. First look at integers (whole numbers): If you take the square root of a square number (1, 4, 9, 16,...), you get a rational number out. If you take the square root of a non-square number (2, 3, 5, 6,...), you get an irrational number. Now consider fractions: If you take the square root of a "square fraction", e.g. "1/4" or "4/9" you will get a rational number (for our examples the answers will be "1/2" and "2/3"). If you take the square root of a fraction with non-square numbers in it, e.g. "1/3" or "3/4," then you will get an irrational.
These videos consistently distract me from my actual math homework because none of my teachers tell me WHY math works. They just want me to do the problems. I always want to know HOW mathematicians came up with this stuff and why it works!
Nofxthepirate Math is the subject of the physical. It allows us to understand the workings of this world. Calculus, invented by Isaac Newton (And Leibniz) was what aided him in the understanding of physical, such as his famous and often abused F = ma. A pretty complex equation in itself (isn’t it physics? Yes but math and physics are closely related. One cannot happen without the other), it allows us to understand how the world works and how things work to put it simply.
Elementary math like these teaches us the fundamentals to understand the workings of the world. It may not make sense now when you don’t see the full picture, but it is essential. Enjoy!
@@billyleecw calculus was not invented by Isaac Newton
google it..
Same with me
@@billyleecwThankyou.
I love that his elevator music example was the girl from ipanema.
Why
I was checking the comments for this exact comment. Love it
His teaching methods are very simple but the main thing is that it all comes from his heart instead of simply his desire to earn money unlike most teachers today. We need more teachers like you, sir. We LOVE YOU!
Unlike most teachers today?? How do you know the intentions of 'most' teachers. You sound like an underachiever looking for somebody else to blame.
@@danm3213 you sound like a teacher
Desire to earn money?? Buddy I promise you no one is going into teaching for the sole burning desire of earning a ton of money lmao
How much do you think teachers earn...
Not enough to do a hard and stressful job just to earn the money. What I do suspect though, is that some might do it out of a desire for a little bit of power over students.
Are you nuts? Nobody is a teacher because of a desire to earn money. Teachers don't make anything.
I usually come across this guy's videos while studying for my exam so I watch the videos partly even if they aren't related to my study topic. This time, I was so excited to see one of his videos and my topic match so I watched the video. I can say that I had seriously entered flow and I was enjoying it so much that I could've gone on for hours without a sign of exhaustion. Eddie sir, I simply adore the way you teach and hats off to you☺️
0:52 " You get a weird f*cking number"
laughed my ass off at that part haha
yea....i was wondering like did i hear that right...???
😂
funky*
The teacher I wish I had, for sure for sure 😂
How did I not notice thissssss
I'm 35 today, have a Bachelor's in Mechanical Engineering from quite a reputable university, and I just discovered why "irrational numbers" are named as such😞
Same thing mate. 35 y.o. Bachelor Medical Science.
It seems to be an Australian thing
@@julianbell9161 No, he means the fact that "irrational" numbers mean numbers that cannot be written in a ratio
Thanks Eddie Woo. Your work inspires my teaching. You are saying facts that are thought provoking.
Love how you are not telling us to do this equation and to show us how to do it but actually describe it and let us know the why part of the question. This even as a year 10 student has cleared my head a bit.
Great work Eddie, Australia's children and virtue youtube, all your students are blessed off the stress of maths. God bless you.
Im in the middle maths class at my school because I transferred here at the beginning of the year and we aren't learning surds. That privilege is reserved for the top class. So I'm here to prove a point to my teacher that Im actually serious about my education and the things I learn even if she isn't.
A question for Mr Woo, I'd like to hear his way of explaining : How do they know it is actually irrational and doesn't reoccur after like a billion decimal places. How do you proove it's irrationality?
Look up on youtube "proving the square root of 2 is irrational" you can do it because you can prove that it can't be written as a fraction. Then you just assume the same for many other roots.
You write down sqrt(2)=p/q, you tell that there's a rational number p/q equal to sqrt(2) and this is the hypothesis. Then you proove it by absurd, the equivalence can't be resolved because of even and odd number rules. That's it
There are two parts to answering this; The first is that if a decimal does repeat, it can be fairly easily shown that it must be expressable as the ratio of two integers and vice versa. This is actually part of the school mathematics curriculum. The second part is showing that the square root of any integer that isn't a perfect square, can't be expressed as the ratio of two integers. The easiest way to see this by considering a possible lowest form ratio a/b and putting a and b in terms of their prime factors. For a/b to be in lowest form there are no common primes between a and b. Thus when a/b is squared there are still no common primes and the ratio can never cancel to an integer.
You are a legend Eddie!
Amazing..I never have imagine such a analogy..😄😄
This is fantastic! Thankyou for this quality content. You are doing the world a real service. Cheers
Ur a good teacher in fairness to you.. Greetings from Ireland
Wow! I knew they called "irrational numbers", but did't know why! Thank you Eddie!
Brilliant lesson!
Impressive explanation .... got it at once !
Might be a U.S. thing but I've never heard of the irrational numbers being called Surds.
He's from Australia I believe.
He’s Aussie
I studied surds in class 10th....lol
Never heard that term in school here in Canada. We just called them irrational
Chris Broome We call them Surds in the UK too
Why, I never heard something so ab"surd"! :-)
I studied surds in class 10th ....lol
Surd is there, that's how I was taught in high school, might be wondering where you came from
Oh my sides, please stop. No, please stop.
way better teacher than ive ever had in my life
Great too easy explained . Love. From india 🇮🇳
Omg your Videos are so gerate thank you for filming that:)
What about continued fractions representation of square roots? It might be interesting to show them that as a parallel of your ratio examples. (Someone might have already asked about it in a previous comment, I have read some but not found one about it so far)
06:31 - " _What kind of music would this be?_ "
Me: Vaporwave?
Hello sir, I just browsing in order to get some knowledge over surds cause I have an exam😁😁😁. Well now I can right the exam and you're really an awesome teacher I've ever seen in my life.. You're friendly and making the concept getting on to the mind...
About to go into honours in maths and these videos are still fun to watch
**This guy is the most charismatic man ever **🔥
Greatest maths teacher
Bro, the first time I heard "that's a weird f*cking number. I died
Crazy immortal jazz musician? Nice!
I'm 30 now I heard surds when I was 12 or 13,. now I know what surds are.....Truly u r a genius sir...
Poor kid's now been watched turning up late for school by 81K people!
mr woo you absolute legend
Numbers that "terminate" do in fact repeat the repeating sequence being a zero by itself.
good to know, but in mathematical notation that's just assumed. Same way how a blank '2' always means positive 2; we never write +2.
Thanks Eddie ( I have math yearly tomorrow and this is one of the topics) [I Also have science]
I'm so amused that he said it's not "irrational numbers" like "you crazy man" immediately after comparing irrational numbers to a crazy jazz musician lol.
I just now realized that irrational has the word ratio in it. Maybe, all this time, irrational means non-ratio :0
@@elimgarak7090 absolutely. You can sort of think of a fraction as a ratio of two numbers, and an irrational number is one that cannot be expressed as a fraction.
The Best teacher👌
the moment he said sax for saxophone, i looked around to make sure my mum didn't heard it😂
crazy immortal jazz musician I died
I wonder what would think the boy who came late to the class about his math teacher speaking about guitar when he came in
That kid coming in late is now on youTube for eternity!
Is the dot over the repeating decimal a regional thing? Because I always learned that it's a straight horizontal line over the number.
I've been told that you can use both, and they both mean and do the same thing
Can anyone tell me, this lecture is of what standard ( grade) ??
7:07 lol :D u missed half of the best maths lesson ever
One thing, you said ''not like 'you're being irrational you crazy man''' aren't irrational numbers the exact reason why we use the word irrational in that context?
“how many of you play an instrument?”
Me: *puts hand up*
I did not see this teacher reply to any comments, so I don't know is he reads them or not, but I would like to thank him for the way he interacts with his students to get them interested in the lesson. Good on you Sir.
I think in the U.S. we would put a line over 0.3 and refer to it as "point three replicant" or something.
Same in Germany. We also use the line notation, but call it "period".
@@papajulietromeo-650 That's cool! Thank you for sharing!
@@flamephlegm I've noticed several differences in his notation compared to what I learned in Germany, e.g. in other videos he puts arrowheads on both sides of a coordinate system axis. I learned that you should always only mark the positive end of the axis. It's interesting that mathematics, which is often considered to be the universal language of science and engineering, can be written in sometimes ambiguous ways. Dot-above-something could also mean "derive with regards to time", dx(t) / dt.
@@papajulietromeo-650 the commas in numbers in Mexico still throws me off in a big way.
Was the elevator music he was humming, The Girl from Ipenema?
Jack Mandu I thought so too!
Oh boy now you’ve done it... “Bass Guitar plays the same 4 notes throughout the song...”
*Enter Davie504 🤪
Thank you
Which camera you use ?
Your videos become my way of procrastination ..
6:37 i actually raised my hand
Why not use the term transcendental number for when a square root does not result in an integer and always results in a transcendental number there are other transcendental numbers of course
My teachers have literally no idea how to teach this year. I'm failing extension maths because of their inability to explain anything! My maths teacher literally writes the rules and an example on the board while we copy them down in silence. At least this will be helpful when my school shuts down due to corona! Now that I found theses videos, maybe I won't fail!! Thanks!
Check out Khan's Academy, he helped me back in the days
Watched video, but still had to google what a surd is.
The missing info was that a surd is a _type_ of irrational number formed from the square root of a rational number. It's not just Austrailian for "irrational number".
Wait did he sing "The Girl From Ipanema" as the "elevator" song?
There is a way of doing square roots, that don't have perfect square roots, finding the nth tooth, which is like a long division way or the Babylonian method
Could using the word 'square' rather than 'triangle' create some misconceptions similar to saying 'I saw the sunrise'?
7:09 being the most replayed is funny lol
What is this class? High school or college?
Is that a typical Aussie accent? Surds, that is?
I watched this video with popcorn lol
I wish this guy was my math teacher
So are Surds short for ABsurd?
Only if it's the square root of AB...
So is "pie" a surd as it can be written as 22÷7 but it's decimal places doesn't repeat in a certain pattern?
Pi is irrational and can not be written as a fraction. 22÷7 is just an approximation :) (according to my calculator only accurate to the second decimal place, so not a very good approximation)
Surds involve square roots of integers in order to define this. Numbers like pi and e eare beyond this, in terms of how disconnected from ordinary numbers they are.
Pi and e classify not only as irrational, but also as transcendental. Surds are part of a classification of irrational numbers called algebraic numbers. Transcendental numbers are numbers that are not algebraic, rational, or integers. Numbers that transcend algebra, as in go beyond algebra.
Algebraic numbers are roots of polynomials with a finite number of terms. These are numbers that involve roots, whether square roots, cube roots, or even roots of higher orders. But the point is, there is a finite number of terms in identifying an algebraic number in terms of 4-function math and roots.
It takes an infinite number of terms in the polynomial, for a transcendental number to be the root of the polynomial. It is common that these numbers are identified as an infinite series, that give a means of calculating them. That is, a pattern of numbers that when added up, will converge to this value.
@Davie504 Eddie Woo is a bass player confirmed? Please make a video about this
Not gonna lie, I had to rewind because I really misheard what you said at 0:53
The key take-away is that surds can never be an exact representation of a value. Writing sqrt(7) is as exact as you can get.
The same can be said of Pi
3:40 in Germany we use a line over the three instead of a dot🤔
We use a line too (actually both), but we usually use it when there are 2 or more numbers repeating like 0.65656565656565....
7:06 That Kid must be thinking, only if I came early that day
Hey Mr. Woo, I've a question for you: Why do irrational numbers exist?
that kid who couldn't find the class
hahaha
Not quite 'dot dot dot' after the calculator's final digit - the calculator has actually rounded to that last sig. fig.
this is good
So they're... ABSURD!!! LOL
Year 10 maths, J.T + Mitchell watched the video
Tall and tan and young and handsome
, the boy from South Australia goes mathing
Great video, as always....but remember that although all surds are irrational, not all irrational are surds. "pi" and "e" are irrational but not surds. To be a surd we have to be inside a root....
damn i didnt realize this was 8 years ago, or instead of the crazy immortal jazz musician analogy, he'd just call it ai.
Times change huh.
Different analogy for music :P spotify playlist. popsong is one song one, elevator music, is playlist on repeat on given order. Crazy jazz music is random playlist which also takes in spotify suggestions, it never goes to exactly same repeat...
"Crazy man" =irrational
"Crazy man" =Ab(surd)
Sir we can write 5 as 5/1 and this is rational then why √2 /1 is not rational
5/1 is not the same thing as sqrt(5) though, the same as 2/1 is not the same as sqrt(2). Technically, 5/1 is sqrt(25), and 2/1 is sqrt(4).. kinda.. also have to remember our negatives can be squared.
Sqrt(2) / 1 is not the same as 2/1.
❤❤❤❤❤❤❤❤❤
I hear a girl from ipanema.
Love your channel, but to be truly rounded, remember you can revert, but you can't revert back because back is already contained in the definition and to do so is a redundancy
can he be my math teacher 😭😭
7:09 that chad tho
But why it goes nonrecurring? What makes them go changing patterns? ...U can also answer by why in some got reoccurring pattern... that will explain it too I suppose. :)
You get the recurring pattern for rational numbers, because it is a ratio of integers. Eventually, every denominator that doesn't form an ending decimal, will be a factor of a number like 9, 99, 999, 9999, etc. In the case of 1/3 and 1/9, we can express them as fractions out of 9. In the case of 1/11, we can express it as fractions of 99. Less obvious, in the case of 7ths, we can express it as fractions of the number 999,999. The number of 9's that form this grand multiple of the denominator in question, tells us how many digits get to repeat. 1/3 equals three ninths, thus repeats the digit 3. 1/11 = nine ninety-ninths, thus repeats the digits "09". 1/7 = 142857 / 999999, thus repeats the digits "142857".
For this reason, only rational numbers can have repeating patterns of digits in their decimal form. If there is a repeating pattern of digits, there exists a number made up of 9's from which it is a factor. If it is irrational, by definition, it cannot be a fraction of anything, so its digits must not form repeating patterns.
logo os cara q faz musica pra sempre q são surdos
5:12 Is he going to say Jazz? I haven't watched to the end yet...
EDIT: There are no wrong notes in Jazz
Wow, there is a difference here in America. We use a bar over the number to represent repeating.
So is the square root of a rational number irrational? Confused !
Sometimes it is irrational, sometimes it isn't.
First look at integers (whole numbers): If you take the square root of a square number (1, 4, 9, 16,...), you get a rational number out. If you take the square root of a non-square number (2, 3, 5, 6,...), you get an irrational number.
Now consider fractions: If you take the square root of a "square fraction", e.g. "1/4" or "4/9" you will get a rational number (for our examples the answers will be "1/2" and "2/3"). If you take the square root of a fraction with non-square numbers in it, e.g. "1/3" or "3/4," then you will get an irrational.
💕💕💕💕💕💕✌🏽
For the surd, the Music might be likened to the music played by a wind chime.
0.50-0.55, he says 'fucking'? someone please confirm!
Funky
square roots of numbers that are not squares are all irrational as are all radicands that are not bases raised to radical indices.
7:40
YA LIKE JAZZ???
At 0:53 I swear I heard him say "weird fucking number"
Funky
@@roninnib6635 i know, mate, that's why I left a comment, because It sounded like it