The Magical Disappearing Square
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- Опубліковано 30 лис 2014
- I’m a high school mathematics teacher from Sydney, Australia and I recorded this video in my regular classroom. Find out more here: • UA-cam Stories: Learn...
I really love using geometry to teach mathematical ideas - here’s my demonstration of Pythagoras’ Theorem: • Visual Proof of Pythag...
You might enjoy my TED talk: • Mathematics is the sen...
Other learning resources here: www.misterwootube.com
Let us not forget though: What makes this whole video so relatable to everyone is the school-projector just randomly peacing out in the middle of class.
I think it was just his computer went to sleep bc he'd been away from inputting for an amount of time, but even that is really relatable
On the other hand its a beamer which makes it really unreal at least for my country lol
Omg i was at school today with a sub and the same thing
happened while we were watching a video😂
yes
I’m pretty sure the projection was the magical disappearing square
Everyone talking about the projector going out but the most memorable/relatable part was the one kid feeding all the answers when a question is asked. There's always one.
All hail the answering kid!
That kid who can’t stand the awkward silence when a class ignores a teacher’s questions, unfortunately seals their own fate by reassuring the rest of the class that they never need to answer.
Because if no one raises their hand it halts the lecture and I know the answer so imma put my hat in the ring.... All 16 times a question is asked xD
She sits next to me :)
@@diggoran ohh nahh, that kid is hella happy if he can go with his teacher like that
I asked a teacher how this is possible in 11th grade and she pretty much just said 'it is what it is'
Thank you for actually explaining how this works!!! Appreciate you
Agree. I propose another way to understand this math problem:
- A lot of people apply the triangle area fomula for the two shapes (the two big shapes that contain smaller ones). As a result, they have the same area because ostensibly both are right triangles with equal sides.
- This is the main reason why this is such a paradox: they seem equal but different at the same time. If you look closely, only the upper shape ( the shape that contains other 4 smaller ones) is really a triangle. The lower one is not a triangle so you can not apply triangle area formula for it.
- To calculate the lower one's area, you should combine all 4 smaller ones' areas plus 1 square. There you go, it is solved.
This is a pretty elementary problem with a verysimple explanation, and you asked your teacher-maths teacher I presume with at least a degree in mathematics-and they didn't even attempt to explain it to you? Are you sure you're not making that up?
@@thekaratekidpartii2169 depends on the country. Not every teacher is like a teacher from first worls country
@@thekaratekidpartii2169 different teachers have different limits on what they want to explain, I think, when I asked my English teacher if overture and aperture had similar etymology she just brushed me off, but whenever I asked my history teacher a question (ie "was being gay illegal?" "Didn't Ronald Reagan release some acts about immigrants? " "isn't this the reason exterior doors open outwards?") He always answered and explained them
@@thekaratekidpartii2169Answer = you like the smell of your own farts.
I would have DIED to have had a teacher like you back in High School, maths was always something I struggled with, and disinterested me massively, THIS would have just given me a spark to focus, thank you for doing this for younger generations man honestly.
But then you would be dead and reborn to a class where there aint one. Maybe this even is the reason for not having one because you already did so.
Math
How would you have studied further then?....Dead man can do nothing ...😂...
Just for fun...
@@DeltaAssaultGamingthere’s multiple forms of math. Maths
Same.
it's not even the optical illusion that fascinates me, it's more the pure excitement and dedication this teacher has while trying to explain something to his students. 10/10 for this teacher :)
Yes he was most excellent, was he not?
Very passionate!
The best two math teachers I ever had were passionate in this exact demeanor during my sophomore (Geometry) and junior (?) yrs.
Interestingly, I had the polar opposite experience freshman and Senior year with two old farts.
Freshman yr was Algebra II taught buy a Vietnam veteran who had flashbacks.
I think Senior Year may have been Trig but I failed both Algebra 2 and trig pretty miserably if the requirement was actually retaining any mathematical information from those years. I maybe earned a "D"or "C" at best.
Anyways I'm pretty pathetic at math, takes me a while to pick it up. Made A's in every other class and graduated with a 3.6.
So this is basically an optical illusion because the angle of one of these triangles does not make it a true (right angle) triangle?
Which one is not the real triangle..the top?
Agreed. This kind of teaching is what makes learning subjects that are fairly seen as a complex topic by many, not feel boring and confusing. The back and forth interaction also matters.
I personally preferred this method as I struggled so much if I learn with only one of the methods. I really can't if I only have to choose between visual or audio. I need both of them.
He’s teaches with so much energy unlike most my teachers I ever had
Bro, it fascinates me that this was 7 years ago
@@fishboyboby4281 why?
That was a REALLY good explanation of the disappearing square. lol.
it’s easy
@@404Tired sad moment
Yes this is really confusing one, because all the part in the triangle above are in the same size as they are in the triangle below and so its really confusing, that one part is missing, while they are in the same sizes as they were in the one above and so it should be impossible.
@@jout738 how should it be impossible? Compare the top grids above both triangles top lines and they don’t match at all. Obvious differences. This trick was done on a chocolate bar too to better visualize.
@@danielvelkovski3156 I think the chocolate bar one actually did result in a different shape to produce the illusion. Here all of the points of each triangle are precisely on the grid and the grid is the same. It's clever because it makes us assume the large shape is a triangle when it isn't, but the shapes still do land on each regular grid line. At least that's how I understand this illusion.
I’ve never actually heard the explanation behind this problem before. This is actually so fascinating and I love how excited math teachers get when they talk about problems like this!!! It’s so wholesome
Smash?
This explanation is pretty complicated tho here's my version
The hypotenuse of blue triangle is √(5²+2²) which is ≈5.3851
Now the hypotenuse of red triangle is √(8²+3²) which is ≈8.5440
Adding both we get ≈13.9291
Now, onto the hypotenuse of the big 'triangle' which is ≈13.9283
Meaning the hypotenuses of the smaller triangles don't add up to the hypotenuse of the big 'triangle' meaning something is wrong here
And because both small triangles are not similar meaning both of them combined wouldn't make a triangle hence the big 'triangle is a fake
Simpler: 2/5 not equal 5/13
If all math teachers had half of this man's energy, the world would be filled with geniuses
He’s an engaged teacher, and he has a responsive class. That’s how good stuff happens in a classroom.
Yep.
If you have a bad teacher, or unresponsive classroom, the magic just disappears.
I know I was rather uncaring as a student. XD
@@XFizzlepop-Berrytwist Tbh if a teacher is motivated and good the class will be aswell in 99% of the cases. But who can be bothered if the teacher is just boring and cant explain.
@@artic8516
I dont really think thats necessarily true, there are some kids, that absolutely do not care, I’ve met a few.
Same could probably be said for teachers as well.
@@XFizzlepop-Berrytwist yeah some kids always, but having a whole class thats trying its best is impossible with a bad teacher
@@artic8516
Sure, I can agree to that.
This actually makes so much sense. Idek why I clicked this video either. Love how he kept going and barely called attention to the signal loss. I know so many teachers that would've stopped and tried to figure that out before completing that bit of the lesson, or even their sentence
he actually knows his shit through and through
@@samjohnson609 definitely. He is a good teacher for sure
Yup. I've even had college professors waste an entire lecture trying to fix a sudden technical issue that didn't matter at all.
Just wiggle the mouse. It was the screen blanker.
@@ArchIVEDCinema I had a college professor waste half of class every day telling us we were behind her other class (I wonder why /s)
This makes me miss school. Sometimes I would have class where the instructor would be this enthusiastic and entertaining, with a bright and attention grabbing voice and style of taking.
Having a teacher or two like this guy would've made a huge difference in my education.
I wish any of my teachers had this level of enthusiasm. Most either felt like dying or complain about not getting paid enough
@@GalaxyStandard77You have to remember that does come with years of eroding stress and malcontent. If they’re being paid way low (lower than some menial jobs), and have to deal with cheeky little gremlins for significant amounts of time, you can start to see how years claw away at their enthusiasm. This teacher is pretty young, he still has his career ahead of him, and plenty of energy to spare.
That is not to say there aren’t shitty teachers either. My love for science disappeared with the worst science teacher who not only had just a tiny sliver of interest on the subject, but also tried to touch me up.
My math teacher actually was like this, amazing guy! Tho my grades weren't amazing in Math. But at least I could enjoy.
The projector timing out was too relatable. That happened every time my teachers would present. Love it.
Projector didn't time out. He just has his computer set(by default) to go to sleep after x minutes without input. Hence why it says no signal and to provide input from the source because the computer went to sleep and thus stopped sending a signal to conserve power. It is simple to disable but most teachers never do it for some reason and this is the result.
Ave, true to Caesar!
You guys have projectors. In India we write in green old boards with pieces of chalk
@@KaoruSugimura Well, that IS effectively a time out.
The irony is that the sudden timeout was actually fortunate, because it freed up some space on the whiteboard for the teacher to draw the exaggerated triangles.
You can really see that this guy has a genuine passions for teaching this subject. Teachers don’t get enough credit these days and it is really nice to see someone so passionate about this.
Betcha he works at a private school. If he's at a public then they lucked out!
Some teachers get too much credit. Some don't get enough. But what's the correct amount of credit, and how do we empirically judge?
@@noblephoenix6151 Yeah, we'd better quantify everything
If I had him as a teacher, I'd be the next Einstein and Tesla combined no 🧢.
My gosh you people got this vid into my recommended
If I remember correctly this is essentially the same as the extra chocolate piece trick, only in reverse. You lose a bit of material (or in this case, shape) somehow in the different arrangement, that just so happens to be big enough for a square to fit in.
Obviously the chocolate bar one works because the cuts in the bar create enough area for an excess piece, but I'm not sure where that is gained here, except I remember hearing something about the big triangle.
Neat trick. 👍
I've been out of school for 5 years and I am genuinely fascinated by this.
This is a similar principle to the "infinite chocolate" paradox that's been floating around the internet for years - the "extra" piece is hiding in the angled cut. Because its area is made very thin and spread out over a long distance (and if you're using real chocolate the cut is probably a bit messy) it's hard to notice with the human eye. It's all an optical illusion!
Awaya🥞🕎♾️⚛️⚛️🚺
Actually no.. In that chocolate paradox.. The height of both the chocolate changes.. That's why the problem..
@@mystyx5528 he is talking about the actual physical choclate paradox which is when you look at the pieces it looks like it is uneffected but if you calculate the mass or the weight it is different. However in the internet there is an animation that is just made to trick people and that is not illusion or anything it is just an animation trick.
The chocolate bar just gets slightly smaller hahaha
Was looking for this comment
When I was younger I tried this over and over on the same chocolate because I thought that I found a glitch in the matrix, but I analized it enough and came to the conclusion that I was stupid.
This is an amazing teacher. I love how interactive he is with his students. He is stimulating their curiosity and encouraging them to figure it out, while guiding them to it.
Mad respect for this guy! It's been years since I needed to study math, yet occasionally his videos come up and I can't help but watch one. Makes me want to be a student in his classroom.
That exaggerated example is the best way to explain stuff. I am not a teacher but I always use such exaggerated examples to explain things to family, friends or colleagues. It's very effective.
This is how I manage to understand all mathematical concepts. Using the same logic and applying it to either exaggerated or simplified versions of the situation, this often helps me confirm that I'm on the right track or that I'm learning things right.
@@KatherynneF YUUUP cannot agree with y’all more
If you understand the extremes the stuff in between starts to look pretty simple
Exact same for me, my example being how to explain that you are slower on average doing laps when there is wind vs when there isnt. If there was 150mph of wind you couldn't do laps at all.
Me too I was thinking I was the onliest one to do that but exaggerate thing is amazing to compare/explain things
These students are so lucky to have him as a professor.
That’s like grade 9 math. It’s a high school.
@@AKun07 doesn't matter, he makes math interesting. I mean I like math already
I know right? My Geometry teacher just left a cupcake out for half a year to emphasize that “if the cockroaches don’t eat it neither should you” -_-
@@AKun07 You don't know he could be a professor. My geometry teacher in 10th grade was also a respected professor that taught workshops for other college professors. He just wanted a simpler life so he didn't teach at the University level.
Im about to take calc 3 and I still find this interesting. Beauty of math will be degrade by its level, but shines whenever there’s something unknown to you and you can make it know using math.
Great teacher! Energetic, likable, makes something really boring and complex into something fun. We need more people like this in our universities.
I'm not one for randomly watching school videos of a short fragment of a subject lesson, but when I saw this, I just couldn't wrap my head around it. I just *had* to watch, and this guy, he has really has the fast-paced energy to keep your attention on him, and he doesn't drag on. He really does a fantastic job, props to this guy.
what an upbeat teacher, if everyone had his energy we’d all be engaged in studying all the time
Pay teachers a decent salary, and finance public schools adequately...
@@j.calvert3361 i’m not in control of that bro
He's since become a course director so teaches less.
@@j.calvert3361 I dont think the pay is the problem
And have a decent class who doesn't disturb the teacher
This is such an awesome teacher. He’s not teaching at his students. He’s involving his students
He is teaching his students, not lecturing them. That’s just in my words
I'm shook that America seems to have so bad teacher standards
@@Urk3X most teachers care about their paychecks rather than helping young minds. Their are some teachers like this guy who truly care but they are a dime a dozen.
@@nevaray9413 'dime a dozen' means plentiful not rare
@@theflippingflip lmao! mb... you get what I was saying tho
Love all the comments about how you would've changed people's lives having you! Couldn't have paid me to listen in school, but a youtube recommendation was all needed for me to listen 😂 You seem like an awesome teacher.
His lectures are so awesome! I discovered him while trying to understand primary and foreign keys in CS. Very engaging and easy to follow.
I got another proof to tell my students how important a 1° angle is. Thank you.
random thought, load up Universe sandbox and rotate Jupiters momentum by 1°
(not actually sure what would happen)
@@busTedOaS instructions unclear, cows are on Mars now
@@iamalolz lol
@@iamalolz Aw, man.
Not again...
@@busTedOaS i guess it now takes an egg like route around the sun
This guy has passion! That's what makes a real memorable and effective teacher. Especially of things that can easily be so dull.
We need more people like him!
He is what a teacher should be! Teaching shouldn’t be dull and neither should learning
youre gay
@@ramenveins9215 youre fatherless
@@gettokyoko whats wrong with people not having a dad
@@nam3ey cause they start acting like the comment above his
I'm loving the enthusiasm of this man right here. That's how you get students to be more involved and care more about mathematics. Good stuff!
This is a great lesson for mathematics, had me stumped for a second. I'm trying to get into teaching specifically mathematics, this gives great information.
Math teachers all have one thing in common: they get very excited about what they teach and the more they get excited, the more their writing starts to turn into geroglyphs.
But, Siara! There's a ~1º mismatch! That changes everything! 〽〽#〽
Nope
Definitely not. Mine are all dead inside I'd love a math teacher like him
@@potatosirmeow3972 fr all my maths teachers in my school are all sad and miserable
I wish ALL of them would have it
I was completely lost for like 90% of the video, but he managed to make me understand at the very end. I'm impressed
Why did you have 10 likes
Dude no one cares. Stop commenting on trending videos it won’t make your channel bigger. Loser
@@tie7626 well thats offensive
you were completely for 90% of the video
Forgot a word there.
Absolute A+ to this man.....not sure where you are in the world but I sure hope you are well compensated. You are who I want teaching our children...BRAVO!!
No body beats Eddie Woo in sympathy !!!! His humbleness is also what makes him the BEST !!! I watch his videos weekly !!! Thank you Eddie for being around us. You are one of the best 5 teachers in the World !!! Watching your videos makes me fell so happy !!! 🙏🙏🙏
I literally haven’t studied math in 18 years and This guy was able to keep me following along with no issues
Why you havent studied math for 18 years? Your math teacher would be very angry 😠😠😠
L I T E R A L L Y
You've disappointed not only your math teacher, but your English teacher as well.
18 years?
guys he probably got graduated a long time ago and u dont have to study after graduating...
@@juliebraden6911 they spelt it correctly though?
When people say that “math is boring” I always tend to think “no, your math teacher was boring”. This teacher is a testament to how much fun math can be. Oh what a different world we would live in if they were all like him.
Nah math is boring lmao. This was just a kinda cool illusion
@@iGaveLiaHIV for you ;) I love math, but I’ve been lucky to have had some awesome instructors.
@@iGaveLiaHIV well considering ur name is "I gave lia HIV" your opinion is invalid
@@BeauTylerMakesMusic I've been lucky to never have to use anything but basic math since high school
Indeed it is , you know its late to say , but i gotta learn math through internet myself because my teacher back then was bad , he just leave us a questionnaire and take it when his class end , everytime
Teachers like you are why I will always LOVE math. Thank you for being such a good teacher, and have an amazing day!
This is one of the best, most excited and enjoyable to watch teachers I have ever seen!
I love how he says at the beginning "what *appears* to be a triangle"... I think that many people presenting this "puzzle" would just say "here we have a triangle" and therefore making it unsolvable. I like people that think before they talk :)
It is a trick, saying it appears to be a triangle only helps explain the solution.
@@Zapscallion Of course, i get it, but i'm a little pedantic. If he said that it was a triangle, it would therefore make it unsolavable, since the "puzzle" wouldn't make sense anymore.
That's why he used the word "appears" and i like him for thinking about details like that.
@@chrisakaschulbus4903 I agree. It would be unfair if he said "this is a triangle" because he would be lying about the parameters of the puzzle and as his students they would believe him
I can tell by looking it isn’t a triangle. I’m thinking about making an even more deceptive puzzle by picking even closer pair of ratios.
@@marshallsweatherhiking1820 "I can tell by looking it isn’t a triangle" For me it's just on the edge between noticable and "maybe i'm imagining things because of the different colors"
I had a math teacher like him when I was in high school. Extremely enthusiastic and enjoyed the experience of teaching us over passing standardized tests. Needless to say, Math was my favorite subject
Teachers like that are the best
He's still young, plus this isn't in the US
Good for you my math teacher doesn't even try to convince the students that it is useful in any way
Lucky!
@@Living_Happily same
What a wonderful and dedicated teacher! We need more teachers like this 😊
I used to have a teacher that has as much enthusiasm you do in his work. He was on of the best I ever had, It is teachers like you that makes education actually fun and desirable!
Can you imagine if every teacher what this interactive and enthusiastic about teaching a subject like Math? So many kids in my school would've benefited GREATLY from someone like this.
I had one. Super lucky to have had him for calculus. You were even one of the cool kids if you took AP Calc. Made it fun for sure.
Yep it would be great! Unfortunately not many places actually reward exemplary teachers above the really damn awful ones.
Many, many of them are.
You kids just choose the wrong subjects in college.
@@adameves5970 this is fairly obviously primary school or high school level. Based off the amount of funding and the broken projector.
Why the need to take an antagonist tone on a feel good comment.
“You just took the wrong classes in college. 😤 “ sounds like you took the wrong amount of ego out on loan.
Just let other people have a good moment and don’t be a cunt about it.
Let me rephrase your comment to not be toxic.
“From my personal experience, I found a large amount of my college professors were like this, particularly in the STEM fields.”
Thats it. I said the exact same thing you did, possibly even MORE detailed, AND I added something to the conversation.
What did you do? Just try to make a stranger feel bad because you have nothing better to do with your brain cells.
Seems those college courses were a waste.
@@Brianlikescars Roasted, burned, and then corrected. Masterfully done.
We need more teachers like this. He reminds me of my high school math teacher. Patient but works with great energy; focused but stops everything to engage with a student that wants to participate; encouraging and confident. I’m an old man now and this brought me right back to the classroom in the best way possible. Bravo sir.
Well said
Yes! We need teachers (especially math teachers) that love TEACHING, not just their subject.
This is Hope for the new generation !
Inspiring many vocations it can be, at least to be wished it has.
For one moment imagine, if becoming you are the teacher you never had in your past lifetime, and so give this present to the world.
how great you feel. Seeing smiles of interest and curiosity and changing secretly their path of life in a way better.
Off course, apply to other works/ and vocations building future improvements it could be thought.
Well well well, I repeat..
This brings Hope about the new generation !
I had a world history teacher in HS. I never liked history cuz i thought it was boring, but when HE taught the subject, he MADE it interesting. Inversely, I once had an Art teacher who taught art (which i like) but was boring in teaching it (i slept through every class)
I would have loved to gone to school if I had just 1….JUST ONE teacher like this….it’s so imperative that we filter job applicants and make this a must for every student! It was refreshing to see
I've seen this puzzle explained a couple of times, but this is the clearest way I've seen it described
Thank you for teaching! The energy here is unreal. Great video
This guy’s enthusiasm makes me miss school, why couldn’t every teacher be this good 😩
@Billy Mack, Texas Detective sad
I feel like it'd be hard to have this kind of energy every day, especially when half your students don't care. "When are we going to need this" etc.
Because the school system we use pretty much everywhere is fundamentally broken and not conducive to encouraging curiosity and independent learning of topics which interest the students, thus crushing the spirits of teachers and students alike.
@@Soumein i feel like it's esp hard in math too. in science or history if you teach interestingly you can get your students to care, but a lot of kids won't care abt math no matter what
It's due to them following a system. Teachers can actually do their best to educate their students, it's just they gotta have to follow the school systems which I find sad. Most fun teachers usually implement themselves and their personality to their subject which makes it interesting, but sometimes the system prevents them from doing things which actually would make the subject more interesting.
I think it's always so very important to understand why things are the way they are in mathematics. I hate in college where they don't explain much of why like this. When you have a firm understanding of the nature of the problem, the equation becomes arithmetic.
College?.... In my country thind level of math is taught in the elementary schools...
@@idonothing7557 really? You compare college level math to grade school math?
@@idonothing7557 He said math in context of in general, he never mentioned the geometry in this video specifically. That was not even the point of his comment
iN mY CoUNtRY We hAd tO SoLvE CaLCuluS wHeN We WeRe FiVe yEaRs oLd
@@HimaruXx legend 😂
I love all your content. Wish a math teacher like this.. Even though I don't have anything to gain from these videos, I love that it's helping any future generations
It's really fascinating that you can see the issue better when the projector goes out
This man had my full attention for the entire video and it only took him about 5 minutes to give a very good explanation for this thing. One of the best teachers I’ve seen. Some teachers I’ve had would have taken an hour to explain this in a very boring, confusing way, and then be like:
“Don’t be afraid to ask questions.”
*Proceeds to ask question*
“Why didn’t you pay attention???”
DUUDDEE EXACTLY
I SPEND LIKE HALF AN HOUR JUST WAITING FOR OUR TEACHER WAITING FOR US TO QUESTION LIKE WHATT
You know, he first made a vid for a sick student in like 2017, then he made more when COVID came and now he's really popular. We actually watch his videos as part of the curriculum in Australia
@@caveboy5677 damn that's interesting
Wow it’s almost like Ull pay attention to your phone but not ur teacher, yep, learnings fault
I've pondered this "missing square" for years. Never really figured out why this happens. Thank you for the explanation.
😵
+1
We can now apply this to stealing a square from a friend's large 13 by 5 chocolate bar
i wish my teachers were this energetic
Slopes of blue triangle vs orange are not the same, 2/5 is not 3/8, there for the total shape (the top one) is "not" a triangle, but a quadrilateral instead. Hence that's how the empty small square is there.
Yep. It was obvious. I also noticed it at the first second :D
did i just enjoy a math lesson??? public schools need more teachers like this guy. absolute legend
No. You enjoyed a short youtube video. You had classes before and you know it's not like this.
Not all math chapters are beautiful, interesting, easy to visualize, fun to learn, etc. Believe me, I'm an inter second year student from India. I've solved a lot of problems from various chapters. you need to dedicate hours, and hours on a chapter to fully grasp it, and it's nowhere as fun as watching a youtube video for passing time..
@@azysgaming8410 oh it's an absolute joy with the right teacher
private school teachers are just as dead inside
IDK where you live, but in most US states public schools have better teachers on average because they pay better than the average private school. (Source: I'm a teacher from a whole family of educators.) The idea that private schools are "better" is mostly down to the fact that they can more easily expel students.
It's been over 20 years since I graduated highschool. Never had a math teacher this excited about explaining math. Almost makes me want to go back to school and learn more 😄
you LIKE school?
@@pidgey3734 with a teacher like that maybe
Currently a high school senior and these teachers are rare and need to be protected at all costs. MOST are not as passionate as this teacher.
really hoping to get a teacher like this next year
Well the video doesn't play the part where he gives gives them an extensive homework assignment right after this
God if I only had a math teacher like this man. How much different and more confident I would be in math.
As a teacher I really enjoyed watching the excitement displayed by this teacher!
Literally barely passed math in highschool and this guy just taught me a little bit of trigonometry without making me feel dumb or bored LOL we need more people like him in school 👌🏾
I'm sure most teachers start out like this guy. He looks pretty young. It's the downsides of the job that add up over years and the teaching profession isn't exactly overflowing with applicants. There's way to fix that and I hope it gets better some day.
Edit: you can stop disagreeing with me and get your reading comprehension up, I said "most" which means it's not true for 100% of teachers.
@@anonymoususer4706 Meh, disagree. My college algebra instructor was about this guy's age and he was the worst math instructor I ever had. Seldom explained how/why we used certain functions, operations, etc, and anytime I asked, "why is it done that way?," my questions were typically either dismissed out of hand or I was told to "research it on my own time."
Most of my "instruction" in college algebra was myself, poring over my textbook weeknights at my kitchen table in my apartment. I basically had to read and re-read lessons, do textbook examples, quizzes, etc and then check my work against the answers in the back of the book to teach myself college algebra. It was the only class in college I had to that in, and I had numerous programming classes.
My physical science teacher in high school was the complete opposite though -- he was also the head football coach, and no matter what area of physics we were studying, he could make football analogous in his explanations. I aced that class so easy it should be illegal. LOL
My college math teacher didnt speak english. But they still took my money.
@@anonymoususer4706 disagree, most of the funnies teachers in my school were the old folks.
It's not concrete, but very often does matter.
My only question is how did he make a perfect straight line at the start.
isn't that a special ability of every math teacher
Don't show him circles
lol
@ZeroKung2309 what are you doing here
Lamo
Love the enthusiasm and energy with this teacher. Need more like him, and less senile old teachers surviving off tenure
Wow I’m really happy right now. You’re the type of teacher the world needs. You’re really want us to teach something and not doing it because it’s only your job. Man we love you
The amount of energy this guy puts into his class might not seem much by just watching this video, but imagine him doing that for one entire class and other classes during an entire year... That's incredible! Teaching is exhausting, but it's really rewarding in the end to see your students learning something.
A good teacher is not a person who knows it all, but a person who knows HOW to pass information forward. And those are two completely different things.
Amazing teacher!
An especially good teacher instills a love of learning in their students, this guy has that down too.
Passion goes a long way
I'm 30 and haven't been to class for a while. Sat down and watched this whole thing with fascination. Taught me something new today
Too many know it all- teachers and very few talented communicators and passionate teachers. Teaching should be made very hard to get into for people that don’t care/aren’t passionate about it and that have no talent at teaching. Too many have 0 talent at teaching and only spill words at you. Like they should ask themselves “Am I good communicator? Can I properly teach and explain stuff passionately? Will I do this for many many years or will I get bored of it?” Most of them only treat it as a job and that’s sad and disastrous for the future generations.
@@HyperionFive All true. However, if you consider how much teachers are paid, it's no surprise. Where I live, the average wage of a teacher in a public school is a bit less than that of a cashier. Would you expect someone getting this little money to dedicate themselves that much? Yes, something could be said about dedication not being about money. But good money would attract more people, out of those more would turn out to be dedicated and good teachers. Plus, a good salary makes many day-to-day worries go away, allowing you to focus more on what you love (i.e. teaching). We seem to be paying very little to teachers in many countries while it is indeed true that much of our children's future depends not only on if, but how they are educated. A lot is also expected from this profession and it's not proportional to the salary. I understand why that is (i.e. teachers where I live can be pushed around more than doctors or miners even when they go on strike, so the government will not pay them more than it absolutely has to), but it's not a pretty picture.
This man is the best teacher, taught me something in 5 minutes, and not an entire hour.
I feel like so much of my time in school has been wasted because teachers spend 2 hours teaching something that I learnt within the first 10 minutes of them talking.
@@rachelcookie321 Hey, sounds like you are academically gifted, and learn way faster than your teachers teach! It was the same for me when I was in school, and most of us who are academically gifted have experienced the same boredom you mentioned. But I just wanted to encourage you to be understanding that your teachers have to teach at a rate everyone can learn the material at, and to try to be grateful that you are one of the lucky people who learn way faster than average. Also if you go to university and have a major you're interested in a lot of the classes will be quite enjoyable, so you can look forward to that if you choose to pursue higher education!
@@Issac117 they could teach individually instead of wasting our time
@@rafasilva1265 my guy there aren’t enough teachers to have 1 for each student
@@misterfox8061 literally just let the students leave class whenever. that would make it an individual choice to leave
If I had a math teacher that taught with your sort of enthusiasm and energy I might have actually cared about mathematics. Really fun and interesting to learn about this.
He obviously loves teaching, loves math, and loves teaching math. The excitement in his voice when he gets to show his students how fun and interesting math can be.
I’m a Fine Arts student who had completely given up on ever understanding maths but the way this is explained and presented made me able to follow and understand it! Everyone deserves a teacher like this!!
Hmm. I disagree. This problem gives the illusion of trigonometry being inaccessible. It makes the hurdle seem much higher. Honestly this is an unfair problem. Normally you should be told which bits are the same length and if the angles are 90 degrees if you want to pull a trick like this. The reason they didn’t is because the answer becomes obvious to those who understand the notation (which is pretty simple to learn). That’s just a way to make people feel silly or stupid and I don’t think that encourages people to learn. 😣
@@Amaranthyne Shut up
@@FF-36 I _can_ type without vocalizing. Would that be sufficient?
@@FF-36 I’m sorry that’s how it came across 😅 The teacher took something easy and made it look more difficult than it was before solving it. I don’t think that’s what makes someone a good teacher. Does that sound less douchey?
I don’t know what happened to your second comment, or your third calling me a smart a&$, but…
Yeah, I’m smart. I wasn’t being condescending though. I wasn’t offended either, but I’m pretty sure you are. I’m not really sure why.
He reminds me of some of the enthusiastic math teachers I had growing up. I even had one whose absolute favorite thing to hear was the “OHHHH” of a student finally understanding a math concept. She got the biggest grin every time and it always lit up the classroom.
As a math teacher myself I can testify that it's absolutely a wonderful feeling to actually see a concept making sense for a student.
True.. if you teach and even few students understand it and revert back , its very rewarding.. cant force everyone to learn..
Good for you guys. The math teachers i had just mostly wanted to get over it and finish class. I had a really boring science teacher though, I'd feel sleepy the entire class but i would still get his lessons, made me love the subject.
You're such a great teacher! Keep it up! Young minds needs your inspiration!
I loved trigonometry!! It was so satisfying finding out the difference between the two angles… this was very fun to watch
Wait until you get to the part of trigonometry where you're calculating areas under curves and using differentials.
THAT took away my love of trigonometry.
Great example of "Trust but verify."
Mathematically verifying the angles of the two triangles is the key to solving this problem.
Look at the angles again. He is lying, they are exactly the same.
@@tsriftsal9718 You are incorrect.
Angle (a) of the 8 x 3 triangle is 20.556 degrees
Angle (a) of the 5 x 2 triangle is 21.801 degrees.
@@tsriftsal9718 even if you weren't able to figure out the exact degrees (like MaxCruise did above), knowing that tan^-1(x) is always an increasing function means that the two angles cannot be the same, since 3 / 8 ≠ 2 / 5
@@absoluteaquarian they cannot be different if they fit in perfectly and based on the diagram they clearly do. Either his diagram is incorrect or his math is incorrect and you have a true paradox. I know you mathematicians hate paradoxes but they do exist quite frequently. You can rub those two braincells together all day but space cannot be created for where there is no space, it is impossible and that's exactly what a paradox is.
@@tsriftsal9718 open up your standard calculator and prompt it for tan^-1(2 / 5) and tan^-1(3 / 8)
You'll notice that, just like what MaxCruise said above, the angle results are NOT THE SAME.
Therefore, the SLOPES OF THE TWO SMALLER TRIANGLES' HYPOTENUSES ARE NOT THE SAME.
Therefore, the top shape is not a triangle, but a QUADRILATERAL whose topmost two edges have slightly different slopes.
This is not a paradox. The top shape is not a triangle. Please do the math.
I really like how he explained and how he used the example of triangles in a very obvious way so we can see the difference very clearly..
This teacher is one of the best we got!
Yeah, in my opinion the best way to prove something or demonstrate something is to use the extremes. Always makes it more visible.
So what you saw the triangles and instantly knew they weren’t similar?
Love the enthusiasm. Well done, man.
Thanks for explaining that because I was driving myself crazy trying to figure it out and never thought that the angles might be different!
I never loved maths while doing school, but this kind was good enough to keep me focus 5 minutes. Good job man, your lessons aren't boring at all :)
And the last 16 seconds?
@@ghasterblhaster at the last 16 seconds I was inventing something revolutionary to the world
I like that he isn't luke the robots now just saying it's this, this is this, he used the words "i think" and "im pretty sure" using those words actually makes most minds want to finger out if he's correct and draw attention to find out why hes would be , so called *Guessing* on a problem like this.
This is a great explanation. When I was younger, I struggled to understand what the practical point is of learning something like this. When you get in to any profession having to do with tolerances, these optical illusions becomes critical.
Tesla fender gaps for example
A lot of subjects may include stuff that have no practical application, but if you teach the material and have students display critical thinking to come up with correct answers, I think that’s great. I would imagine that helps students realize what subjects they’re strong in and what subjects they’re weak in.
Damn lol.
@@bubblehead4270 I think people also tend to take "real-world application" extremely literally, rather than understanding that some subjects are just to teach rules. The easiest way to explain this would be through a language example.
If your language teacher teaches you "Johnny is a hairdresser and he hates his job"/"Johnny est coiffeur et il déteste son travail"/"Johnny es peluquero y odia su trabajo"/etc., some people may say "I don't know any hairdressers. This is worthless to me". However, the point is not to give you the stock phrase about a person called Johnny being a hairdresser, it's about learning the actual building blocks behind it (What verb is used to describe profession? Do you put an article before the profession? How do you bridge the gap between a statement and an opinion? How do you express opinions of a third-party? How do you translate the possession in "his job"?) so that then when you have to discuss things you WOULD talk about in a regular setting, you know how to put the pieces together.
What are tolerances? And what field are you talking about? Construction/civil engineering?
I have no idea how this ended up in my feed, but this man is an incredible teacher.
I showed this to my math teacher when I was a kid, and he very quickly found out why it happens and explained it. Truly an amazing teacher
you see, THIS is how you actually make math interesting. give the student a problem that is genuinely intriguing that makes them actually WANT to know the answer.
when teaching becomes your job and not your passion its gonna be cheeks, just like any other job
problem is, if you aren't consistently doing this for the entirety of a child's educational life, not to mention if they're neurodivergent
.. they'll inevitably miss fundamentals and no amount of excitement can make up for that.
😂😂🤦🏿♂️
True
No
Fun fact: every single classroom in Australia basically looks like this
This is how i'd imagine most classrooms look like around the world. (Most)
What how did I find 1 of your 2 comments
😭
@@FortFarza nah in my school in the philippines, we may not have a projector but we have an LED screen and a huge and long whiteboard
Yep but in my area of Australia it’s just primary school that looks like this
Ps: I’m a big fan of your channel
Best teacher I’ve seen. Thanks for sharing your talents!😇
I didn't really get to go to school, but I have to say that was very interesting. I wish I had someone so enthusiastic teach me like he has to his students.
That was a perfect explanation. The second he started talking about the angle I knew exactly why there was a missing square
When I was in year 8, we did something similar. We started with an 8x8 square and by cutting it in specific locations, we managed to rearrange it into a 5x13 rectangle.
The secret behind the Disappearing Square is that the triangles' diagonals have slopes that are slightly different but so similar that it's almost impossible to tell with the naked eye. The blue triangle's diagonal has a 40% slope (rise = 2, run = 5), while the red triangle has a 37.5% slope (rise = 3, run = 8). The angle between their diagonals is 180° - (atan(0.4) - atan(0.375)) = 178.755°, which is almost a straight line.
EDIT: Previously I stated that the angle was 179.978°. This is incorrect, as I forgot to convert from radians to degrees when calculating the inverse tangents.
OK, that made it easy for me, thanks.
I'm getting a 1.25 degree difference between the angles. I can't see either difference in the angles.
@@JimCaserta Good catch. Fixed.
i have no idea what this means, but thanks 😀😀
w h a t
This teacher is the true meaning of somebody enjoying and loving what they do!
This is the guy who doesn't pay much attention on his salary. as long as he's enjoying his job and he can eat 3x a day, he's very okay with it
Wish my teacher was that excited during school, a different teacher can make the same lesson completely different
I wish we had more teachers this engaging in school!
I think(only i think) the problem is not the teacher. But the school the things we should learn. In this video we learn about old internet puzzles(maybe not so old). So we excited
Lol me teacher is the same lime this guy
If I have a teacher like this it'll annoy me I think. He's loud. I prefer someone who's chill
U need a brain rather than a teacher
@@user-iv7tx7kn6k ur wrong, if a teacher doesnt engage well with the student they are most likely to not pay attention
Did I just watch a math video until the end and actually learned something????
He's the math teacher we all need, I miss my old 10th grade math teacher, he taught really well and made everyone excited for math
My math teacher got me excited for meth
10th grade math teachers are the best
@@AboveEmAllProduction *a bald chem teacher with cancer
UA-cam algorithms brought me here, I remember doing this problem in school, except my teacher wasn't as energetic and engaging as you are, you're a credit to the profession!
What an explanation! I was completely lost until the very end; I gander that’s a lesson well-taught.
You can tell there’s something wrong when you add up the area of each shape and find that it’s not the same as the area of the total triangle. That means those shapes can’t be arranged in a 5x13 right triangle; they create a different shape.
The large triangle should have area 32.5, but the shapes only add up to 32.
The gradients of the red and blue triangles are not the same
Yep. What appears to be a large triangle is actually a quadrilateral
Yes, the slope of the red triangle is 3/8 (0.375) while the slope of the blue is 2/5 (0.4)
The (apparent) hypotenuse of the upper big "triangle" is concave, while the bottom is convex.
The gap in the bottom one causes a 'bump' to happen. But so small, you have to look much closer to tell.
And in a loosely constructed physical demonstration, like with wooden blocks or something, you could easily fool people to think you have done something "magical", but then why would anyone want to fool someone for any reason? It may seem innocent, but it is deception, lying. Even if it's to teach. It's still lying.
@@peterbelanger4094 I don't think the point of the illusion has ever been to lie. I'm not aware of anyone doing this trick and trying to use it to convince someone that they're a wizard to whom the laws of nature and logic don't apply.
It's always been a brain teaser. The point is to provide some apparent paradox, and stimulate someone to question their assumptions.
@@DaveyKanabus Yeah, a part of the purpose of showing and explaining a conundrum like this to people is to make them realize that for every seemingly impossible scenario that you come accross there is always a logical explanation and you can't just rely on your first impression, nothing is supernatural or magical.
what a fantastic teacher. i didn’t have anyone that taught like this. he is enthusiastic, he seems genuinely interested in the material, and in the students thought processes. instead of saying that they’re right or wrong he kind of asks how they got there and they work through the problem together. i’m moving to australia.
@@goopyguy2699 thanks for the enthusiasm!!
@@goopyguy2699 🧔🏼
@@goopyguy2699 The fact that your name is *ahem* that just makes it worse... but you could be trolling though.
@brotinger_1 tan^-1 isn't 1/tan. 1/tan is cot, whereas tan^-1 is arctan. You're confusing reciprocal and inverse.
@@goopyguy2699 Thank you so much for sharing with us today! ☺️
Even the projector screen magically disappeared right after he ended his genius explanation about the problem. Kudos to you Mr. Woo, you teach the students really well. I'm more interested in paradoxes now. Haven't seen them for long like last one I read about Riemann Hypothesis talking about graphically plotting prime numbers and Fermat's last theorem of an + bn = cn only for n
It's such a shame I have never met a math teacher like you during my school years, so I found mathematics and and geometry very tedious topics to learn.
You, sir, are truly a great teacher and I hope your students know how lucky they are.
I did well in math. Well, that is until I walked into my high school math class: geometry. Prove things? Why? 2+2 = 4. What's there to prove. Nevermind being out of left field. I wasn't even playing the same sport as the class. I failed the first quarter. My parents came home from parent-teacher night to tell me that the teacher said he would have passed me if I had participated. Really? I had no bloody idea as to what was going on. Fortunately I managed to figure things out and pass the class by the end of the year.
@@bikeny It could be a matter of checking your work. Most of the time, "proof" isn't as simple as 2+2=4 and isn't as simple to trace back to the roots.
I hated proof too :)
@@kxt9458 same I just did math memorizing the names of all the geography proofs was painful I've never used it again and promptly forgot it all
so true all the math teachers I've met have seemed to hate there life constantly bored at school or complaining about how terrible the school administration was
well or I've only met two but those psycho ones that brag about how many people failed last year and everyone had to go to after school studying with him (once a week) to pass
Struggle through the high school classes and you might be able to dual-enroll at a community college. It’s more difficult, but you bet your ass those professors are better than a typical high school math teacher.
Apart from doing the maths here (in a very inspiring way), this IS actually a lesson in critical thinking and logic reasoning. Love it!
Absolutely! Looking at a problem, investigating the solution, logically laying it out - true life skills!
I first saw this problem on a subway ad (for tutoring service I think) and enjoyed solving it while going to work; I wish these types of problems were shared more widely.
this is why we do math
@Late Notice exactly :'D people bitch about math so much never realizing there's a reason why its the language of the universe or the queen of science.
To be more precise, you just learned a geometry lesson. The type of math you can literally "see" using geometric shapes instead of boring digits.
Hmmmm…. If you taken out blue and Orange shape from the top and bottom figures, you still have a gap now. So the really issue was the shape placement…… when a two shape having different angle is not the cause of the gap, the angle is the illusion. The gap is cause by the other two shape…… I hope you people understand that……
You’ve made me find math interesting. Truly, an incredible teacher
I was quite the conundrum in college because I learned to love math and was absolutely fascinated by it, but was never smart enough to grasp the abstract stuff (calculus) well. This stuff was always so neat to me.
Teachers like him are a gem.
algorithm: show it to them... now
I was not expecting to see you here.
Now, like any sane person who discovered one of their favorite youtubers in the wild, I shall use this opportunity to ask a question.
How have you been?
Hey sawtooth! Fancy seeing you here! Algorithm is a bless right?