A classic Japanese circle problem.
Рет қаралды 1,140,339
3 жыл бұрынWe present the solution to classic Japanese Temple Geometry problem involving three mutually tangent circles.
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@anonymous10567 3 жыл бұрын
The relationship between the circles is that they are the Pacman family, with Mom and Dad sheltering their child.
@aeliasstatic4376 3 жыл бұрын
🥺🥺
@edwardhudson815 2 жыл бұрын
ex dee bro
@hartmut-a9dt Жыл бұрын
Pacman family is the intuition of this complex calculus! Sweet!
@polymathecian 3 жыл бұрын
Prof: What is the relationship between these circles? Me: Papa Circle, Mama Circle, and Baby Circle.
@user-hf4pi5do9h 3 жыл бұрын
haha lmao
@hiankun 3 жыл бұрын
Baby Circle, Baby Circle, Where are You~~ ♬
@osdoiscarascanal0011 3 жыл бұрын
@@hiankun Here I am, here I am, How do u do~~ ♬
@MarcosGarciaKneeBeforeZod 3 жыл бұрын
Maybe there are two dad circles! (One just smaller) or two mom circles! How dare you... 🤣
@daddyleon 3 жыл бұрын
and they're called: Xircle, Cyrle, and Zircle.
@victorp.1219 3 жыл бұрын
when he paused in the middle of the lecture cause he messed up, i thought he was mad at people for talking or sum so i got scared lmao
@hellypalli 3 жыл бұрын
I thought he was just about to go postal
@ronniechilds2002 3 жыл бұрын
He forgot to edit it out.
@vdinh143 3 жыл бұрын
Happens to me everyday. There are some words that describe what I have in mind but I sometimes can't quite find them in the moment, or the expression comes out more complicated and unnecessary than I had anticipated.
@TSKseattle 3 жыл бұрын
I think this is the raw recording, and it would be edited for his online lecture
@momo13022000 3 жыл бұрын
I was reading this when he did that and what happened next was just like in school ... i was looking away for 10 seconds and when i got back to his video the fucking blackboard was filled with so much new stuff 😂
@Vettehed 3 жыл бұрын
"And that's a good place to stop" Yeah, I'm just going to have to take your word for it
@Timespider 3 жыл бұрын
Yep, I feel completely stupid
@KerryKworth 3 жыл бұрын
No it's not. It's a terrible place to stop. He should rationalize the radicals and add the resultant fractions. He may be decent in basic computational mathematics, but he is not very good at the fundamentals of what answers should look like.
@hybmnzz2658 3 жыл бұрын
@@KerryKworth cringe. Rationalizing denominators is an old practice that was helpful before the age of calculators. It had to do with long division. Schools that still teach to rationalize denominators just teach it because "why not". I'd rather be decent in basic computational math then worry about the aesthetic of my answer (which is funny because the way he wrote it is appealing and memorable).
@FrostDirt 3 жыл бұрын
@@hybmnzz2658 a good deal of solving limits with roots are done with rationalising right?
@PubicGore 3 жыл бұрын
@@KerryKworth Wow, you clearly haven't watched this channel much. This guy has a PhD in math. His field of study concerns vertex algebras, maybe you've read a PDF he's worked on: "Permutation orbifolds of rank three fermionic vertex superalgebras." But I'm guessing you haven't, because anyone who actually knew anything about Michael Penn would know he is very good at math. Also, he's assuming the audience is smart enough to do that on your own. Instead, he's faced with someone like you.
@themightyparthos 3 жыл бұрын
What is the relationship between the circles? They all touch each other, but never cross the line.
@Thankz4sharing 3 жыл бұрын
Nothing improper here so long as no minor arcs are present.
@ValeriePallaoro 3 жыл бұрын
thanks .. cause I was wondering what he was talking about and why
@khymaaren 3 жыл бұрын
Great. Just like my uncles and I, when I was little.
@DiscoFang 3 жыл бұрын
They are a Friend Zone venn diagram.
@johncoops6897 3 жыл бұрын
@@DiscoFang - LOL, well said!
@catkeys6911 3 жыл бұрын
2:56 A little voice in his head tells him "Stop- they're all just laughing at you!" Actually, i think after he stumbled over his words, he figured "Well, I'll just edit that part out."- but then he forgot to.
@MrRyanroberson1 3 жыл бұрын
does it quite often too- i wonder how many more are edited out?
@Tokarealwayalright 3 жыл бұрын
@John to be honest, I think he is really good
@---cr8nw 3 жыл бұрын
I'm glad he left it in. It makes it more real.
@johnstanley3939 3 жыл бұрын
I thought they were kind of humorous
@constracted7331 3 жыл бұрын
No little voice in his head told him that.
@moseskim3942 3 жыл бұрын
Man, this was so satisfying to watch. The guy just explained things so clearly and I was mesmerized by his presentation. Great chalkboard skills too.
@masishida7522 3 жыл бұрын
As a Japanese, I may have encountered this problem as a student around somewhere in Junior high or high school, but couldn't make it. I really enjoyed the step by step way you solved the question. It was very understandable, thank you. I also felt a bit near to you, because I also get nervous and tangled up when explaining. That is human being, and that is what differs from a perfect computer readouts. It's what makes things alive. Yet, maybe making some jokes or two, would make it more entertainable. Anyway, I loved the content and the times for writing gave me time to understand, so I prefer you write, better than powerpoint. Thank you. And have a great day !
@user-dd2fn2wi7t 3 жыл бұрын
I'm Japanese and I'm always entertained by your videos! During the Edo period, there was a custom in Japan to dedicate a math problem to a shrine as a thank to the gods when they were able to solve a difficult math problem.This problem is one of them, and it is included in the textbooks of junior high schools in Japan.These problems are called "Sanngaku(算額)" and many other difficult problems, including plane geometry, are still around today.
@gld1076 3 жыл бұрын
galileo:"who masters math masters the univers".
@shareika 3 жыл бұрын
Agreed, thanks for sharing. It's incredible that this would be included in textbooks at a Junior High level. Sounds like a very high standard of mathematical education. And the way it even seems to be embedded in cultural tradition is admirable.
@johnjordan3552 3 жыл бұрын
Sonn Goku!
@ingekaasen8517 3 жыл бұрын
You seem to be a very wise man. Can you please tell me if this "PROBLEM" (or the solution thereof) has any practical meaning or application whatsoever? The whole thing looks like a joke about the distances between several different cities. You can always put those in some relation to each other but it does not mean anything AT ALL.
@shareika 3 жыл бұрын
@@ingekaasen8517 This mathematical relationship holds true for circles of all sizes. So it cannot be applied to some joke about the distances of cities...which frankly I do not know. But it stands to reason. The practical applications are as various as they come. As are the applications of such relationships as that of a circle's circumference to its diameter...also known as Pi. Also, even though this might be lost on some, this solution is just plain beautiful and satisfying.
@danielnewby2255 3 жыл бұрын
I love that you left the blunders in this time.
@boxlag2071 3 жыл бұрын
Yes he definitely did it on purpose, not just to save time.
@Junjokar 3 жыл бұрын
I gave the video a like just because of the courage in leaving those in for the world to see.
@boxlag2071 3 жыл бұрын
@@Junjokar Thank you Roni, very cool!
@nonstopgames7591 3 жыл бұрын
I love that its currently 11:53 pm and I still understood all of that
@robertrocheville7769 3 жыл бұрын
That was on purpose?
@regal_7877 3 жыл бұрын
Man I miss the days when teachers in school used to write on blackboards with chalk instead of whiteboards. Also, coloured chalk. What a throwback.
@somerandomguy6268 3 жыл бұрын
Its an OG trait 😎👍
@element5377 3 жыл бұрын
they only had white chalk at my american school 1964-1977
@element5377 3 жыл бұрын
widespread use of colored chalk only came long after colored television.. except maybe in india
@daniel9525 3 жыл бұрын
we do it like that in our school
@Jogade 3 жыл бұрын
Not OG but my mom whose a teacher talk about how dirty whiteboards can get but say its easier to clean blackboards
@iCanadai 3 жыл бұрын
Why did this just randomly pop into my recommended, why did I watch it until the end, and why do I feel like I understand what happened even though I could never repeat the process to get to the final equation, let alone explain it to someone else
@NiViX92 3 жыл бұрын
I would also like to have an answer these questions, I was watching Age of Empires videos...
@logan-rt2se 3 жыл бұрын
KZfaq just wants you to be good at math, you know because you are a fine educated one
@danbee6407 3 жыл бұрын
@@NiViX92 I was watching 'Half Off by Cyanide & Happiness' and now I'm just half lost :P
@Krustee78 3 жыл бұрын
and that's a good place to stop
@robert-andreiionita2827 3 жыл бұрын
Also why did I have the exact same thought process you just described, when I watched the video myself?
@armeli 3 жыл бұрын
I haven't done maths of this level in over 10 years and you made perfect sense to me. You are truly and awesome teacher!
@gamerdad5509 3 жыл бұрын
Over 20 years for me, still made sense
@henrylinter6627 3 жыл бұрын
Over 100 years for me, and it still made sense
@kuznetsov5172 2 жыл бұрын
@@henrylinter6627 over a millennia for me
@MensGymnasticsAnalysis 2 жыл бұрын
Okay that was amazing and I'm also here after a long time not studying maths :)) I just couldn't get the multiplication by √xyz of the entire equation. Is that a property? I don't remember unfortunately
@artsmith1347 3 жыл бұрын
Well done! Clearly explained, well organized -- and the visuals: good penmanship, dark lines, round circles, helpful use of colors. Thank you for posting this.
@galinpaskalev6262 3 жыл бұрын
I appreciate the fact that you go through the length of doing re-takes of things just so that it makes the flow of explanation clearer. Many thanks.
@bugoobiga 3 жыл бұрын
you could have edited a few things out, but you keepin' it real-mad props to you sir.
@TwilightBrawl59 3 жыл бұрын
9:46 “We know that a + b equals a + b”
@IsomerSoma 3 жыл бұрын
but ... can you proof it?
@sword7163 3 жыл бұрын
speak for yourself
@ushasingh6204 3 жыл бұрын
@@IsomerSoma it's an axiom
@IsomerSoma 3 жыл бұрын
@@ushasingh6204 oh really
@jadegrace1312 3 жыл бұрын
@@IsomerSoma Yeah, the reflexive axiom. It's a property of equality.
@goodplacetostop2973 3 жыл бұрын
10:59 Back-to-back brain resets at 2:54 and 3:02
@goodplacetostart9099 3 жыл бұрын
Good place to start 0:00
@danielrc9016 3 жыл бұрын
Thank you for your service sir!
@V-for-Vendetta01 3 жыл бұрын
I'm dying lmao
@050138 3 жыл бұрын
The distance between the points on both circles touching the line tangentiallyyyy....
@digitalconsciousness 3 жыл бұрын
This is pretty much how it goes when trying to explain something on video. I tried once and the amount of mess ups was staggering. I had no idea.
@sean4stats 3 жыл бұрын
I respect you for not being "perfectionist" by editing and cutting the video when you trying to name the tangent to y-circle and z-circle as 'a'. The fact you stuck there 3 times and still continue to finish the whole video in one shot is commendable.
@adeadgirl13 3 жыл бұрын
Either that, or he just forgot to edit it out. If he didn't care, he would have just continued the sentence from the stumbled word instead of trying to start the sentence from the beginning. So wanting to be a perfectionist but too lazy to pull it off.
@sean4stats 3 жыл бұрын
@@adeadgirl13 nah... I'm gonna give him the benefit of the doubt for the work in this video... Sometimes it happen to some of us when we are trying to convey a sentence but got stuck and we tried to repeat it and it happen again. Continue from a stumble sentence would've caused misunderstanding. But yea, I get what you're trying to say.
@adeadgirl13 3 жыл бұрын
@@sean4stats Fair enough.
@user-zs4zs4yt7h 2 жыл бұрын
Great Video ! Math is the most beautiful of all subjects - I am from Japan! We had gotten a research assignment from our school on this problem! Helped me a lot thanks!
@javizaragoza1463 3 жыл бұрын
No one will ever know why this comment has so many likes
@AvalonWizard 3 жыл бұрын
I think he forgot to edit that part out.
@annereilley4892 3 жыл бұрын
I thought he was about to have a stroke.
@B3Band 3 жыл бұрын
@@AvalonWizard youdontsay.jpg
@goofygoober6211 3 жыл бұрын
lol I laughed so hard when he turned around and looked like he was about to lose his mind
@nashvillain171 3 жыл бұрын
😂😂😂
@gregwarner3753 3 жыл бұрын
I have not thought like that in decades. Thank you.
@davidgillies620 3 жыл бұрын
This is a surprisingly deep result. If we build a _Farey sequence_ F(n) for some n (F(n) is all the reduced fractions, i.e. rational numbers, between 0 and 1 whose denominator is at most n) and associate a circle with each element p/q of the series such that the circle has centre (p/q, 1/2q^2) and radius 1/2q^2 then the circles will be 4-wise tangent to each other and the x-axis (which we can think of as a circle with infinite radius). These are called _Ford circles._ As n increases without limit, the associated Farey sequence recapitulates the _Stern-Brocot tree,_ which is an infinite binary tree that contains all the rational numbers, in order (!). Remarkably, the total areas of the circles can be shown to have a link to the Riemann zeta function.
@getaclassmath 2 жыл бұрын
So intreresting, thanks!
@paulsancheski8618 3 жыл бұрын
Man, that's beautiful. Knowing two yields the third. Glad I bumped into your video, because this solution really helps with something I've been working on... Thank you!
@mendelovitch 3 жыл бұрын
Sangaku or San Gaku (算額; lit. translation: calculation tablet) are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes. - Wikipedia
@MichaelPennMath 3 жыл бұрын
I just ordered a book with a ton of these problems.
@giotto4321 3 жыл бұрын
I was going to ask why it's called a Japanese circle problem, thanks for explaining.
@caesar_cipher 3 жыл бұрын
Michael - please do some combinatorics problems. Since many interesting combinatorics problems can be solved by counting in different ways, it makes for interesting problem solving strategies
@MrStekcoptoh 3 жыл бұрын
This was explained really well and easy to follow. I was trying to figure out what this relationship tells us in English and found one way to look at it. Given two circles that are tangent to the same line, and knowing what the radius of the two circles are, you can derive the radius of the largest circle that will fit between the two circles that is also tangent to the same line. There probably are other ways to apply this but this was the first that came to mind.
@the_main_chow 3 жыл бұрын
Adding this to the "videos I didn't ask for but didn't know I needed" playlist.
@jeffetdesmaths 3 жыл бұрын
Awesome! Finally, it's like a resistance equivalent to two resistors in parallel, but with square roots (the Pythagoras touch!).
@tomatrix7525 3 жыл бұрын
Just found this channel by youtube recommendations (was watching alot of other guys before) and this channel is great!
@AeroCraftAviation 3 жыл бұрын
Same here! Just found it. Amazing videos.
@B3Band 3 жыл бұрын
Wow! I watch a lot of others guys too! That's crazy!
@wojtekgliwa6956 3 жыл бұрын
Explained simply and logically. Great.
@danwhit7828 3 жыл бұрын
I loved this explanation and presentation! Well done!
@quantumgaming9180 3 жыл бұрын
Orange: *exists* Michael: "Peach color"
@manucitomx 3 жыл бұрын
Quantum Gaming which is great!
@pbj4184 3 жыл бұрын
It _is_ more peach than orange, to be honest
@GeneralPotatoSalad 3 жыл бұрын
Yellowred.
@050138 3 жыл бұрын
@@GeneralPotatoSalad Redyellow
@seanm7445 3 жыл бұрын
It’s just a light brown, really.
@Bloodray19 3 жыл бұрын
Never understood this at school, will never understand it in my whole life. But you are presenting it so chill and interesting, that I watched the whole video
@chandu7898 3 жыл бұрын
I hope still u didn't understand.. Lol
@dorogadoroga1217 3 жыл бұрын
I like your videos a lot. Explanation is clear, and you are enterntaining to watch. Thank you very much!
@buttcaner 3 жыл бұрын
So this appeared in my feed, I have no idea why but I am always impressed by people who love and understand stuff. After I watched it all the way through I still had no idea what he was doing but credit where credits due I stayed amazed at his handling of the problem. But in the end I was left wondering why do we need to know the solution to the classic Japanese Temple Geometry problem involving three mutually tangent circles. And how am I going to use it in the bar tomorrow? But hell I didn't even know there was a problem.
@VibingMath 3 жыл бұрын
Love it Professor! If there are infinite circles inscribed between the circles and tangent, we can derive ζ(4) for the total area of circles using this relation
@blackpenredpen 3 жыл бұрын
Oh wow! That's very cool!
@VibingMath 3 жыл бұрын
@@blackpenredpen Thank you bprp!
@utsav8981 3 жыл бұрын
Love from India❤❤❤ A beautiful application of this question came in the IIT-JEE Examination, thanks for the approach
@l1mbo69 3 жыл бұрын
Which question? I don't remember doing such a problem
@meenuluthra4397 3 жыл бұрын
Yes I also remember Common tangent question
@genericusername1243 3 жыл бұрын
how did y'all do ..as results are out
@l1mbo69 3 жыл бұрын
@@genericusername1243 only in XI lol
@ThatITGuy-jj4cp 3 жыл бұрын
It came in CAT '19 as well
@NikonCrayzee 3 жыл бұрын
Very elegantly presented.
@Zhurak 3 жыл бұрын
I have no idea why I watched this or what I would ever need to know this for, but I enjoyed it. I miss my math college days. I always loved algebra and geometry, just never found a real use for it post school.
@potaxe8048 3 жыл бұрын
La Geometría es tan nítida, tan elegante, tan refinada, tan bella... es un suspiro del espíritu humano. Gracias Michael por presentarnos y guiarnos tan amablemente por este bello problema.
@empe360 3 жыл бұрын
4:35 that's a bracket I can relate to
@WienerTash 3 жыл бұрын
You draw straight lines so well hahaha very cool video!
@LimeEngine 3 жыл бұрын
really cool presentation, enjoyed it a lot! I like that you didn't cut it so much. it makes it much more humane and authentic :)
@4GENS 3 жыл бұрын
2:54 Lmao love how he didn't edit that out
@jq747 3 жыл бұрын
Props for using an old school chalkboard =D Unlike whiteboard markers, dirty filthy things, chalk never runs dry (although it does snap occasionally), AND makes a nice ASMR sound ;)
@casalsincero9721 3 жыл бұрын
Loved the explanation, very interesting!
@Dmacxxx77 3 жыл бұрын
This is super cool. Thanks for sharing this video!
@jkanasu 3 жыл бұрын
7:10 Connecting center of green circle with center of peach circle. We say the length of the line (hypotenuse) is y + x. This can be true only if the straight line passes through the point where the circles touch each other i.e. tangent point. The line may/could pass through two different points on each of the circle. How can we be sure that the line passes through that contact point?
@paulcooper2897 3 жыл бұрын
Because the contact point is radial tangent between the two circles.
@AG-po7bl 3 жыл бұрын
To prove they touch each other he should’ve drawn a tangent line between x an y circles. Then he should’ve shown that they both meet the tangent line at a 90 deg angle. Since the angles from both sides are same, it is the straight line with length of x+y.
@TelleoStar 3 жыл бұрын
A straight line is by definition the shortest possible distance between two points on that line. Drawing a line between the centers of the two tangental circles requires that the line travel at minimum the radius of Circle X and the radius of Circle Y - that IS the shortest possible distance. Therefore, for the line to have a value greater than Y+X, it would have to be larger than the smallest possible distance. In other words, if the line did not pass through the tangent point, it would not be a line - it would be an angle.
@rpc717 3 жыл бұрын
No, if two circles are tangential, the centers and tangent point are colinear. Stack the circles vertically and it becomes intuitive.
@nicstroud 3 жыл бұрын
A problem I never knew needed an answer, yet I'm oddly fascinated. What intrigues me more though is, what makes this _classic_ _circle_ _problem_ *Japanese?*
@terutakeabe4327 3 жыл бұрын
This is the simplest version of the type of problems that the Japanese were obsessed with during the 17-19 centuries. You can see some examples here ryugen3.sakura.ne.jp/kadai11/kadai359.htm
@jedi774 3 жыл бұрын
I’m amazed. Despite never actually taking geometry, I was able to follow everything about 98%. Couldn’t have done it my self. And still couldn’t... but every step of the way, I was able to follow and understand the why behind. I have no idea what a practical application would be... but it sure is a fun puzzle.
@rongarza9488 3 жыл бұрын
I used something similar when creating a double helix -- two same radius, bare wires -- separated by two smaller radius, enameled wires, all wrapped around a wooden dowel . Then any current carrying material could close the loop. The smaller wires were just a bit bigger though, in order to separate the larger wires.
@skyborne6393 3 жыл бұрын
Circle: what is the relationship between x, y, z? Triangle: what is your point? Circle:
@mahdimuhib 3 жыл бұрын
I don't know why I'm watching this. Glad I did tho.
@turpialito 3 жыл бұрын
Pretty useful if you want to learn to think algorithmically. This is the kind of logic and reasoning necessary for coding. Keep feeding your mind. Cheers, mate.
@3mon3y94 3 жыл бұрын
I don't know why I'm watching this. Glad I did tho.
@turpialito 3 жыл бұрын
@@3mon3y94 Sadly, though, the algorithm isn't recommending similar stuff, despite clicking like and watching till the end.
@ethanjensen7967 3 жыл бұрын
Love this channel!
@scowell 3 жыл бұрын
Now I'm prepared to blitz this out on an interview question... cool! Holds for any three circles tangent to a line and each other.
@maxamedaxmedn6380 3 жыл бұрын
2:57 easy sir "The distance frome here to here is enough"
@dancoulson6579 3 жыл бұрын
Q: "What is the relationship between X, Y, and Z?" A: They are all a radius.
@joybee7258 3 жыл бұрын
They are all consecutive letters in Alphabets.lol
@Odb718 3 жыл бұрын
I do like the complete lack of value of this video. Wasn't sure if anyone else noticed. Can anyone post a time stamp of X =, or Y =, or Z=??
@santyclause8034 3 жыл бұрын
Correction - they're all just radii. The plural of radius is radii (not radiuses, just saying).
@wangzisworks 3 жыл бұрын
@@Odb718 you can find that by yourself by modifying the end equation.
@wangzisworks 3 жыл бұрын
E.g 1/z = 1/x + 1/y is the end relationship. If you want to solve for z just multiply everything by z^2 Z = z^2/x + z^2/y Or isolate y and solve for y. 1/y = 1/z - 1/x // multiply by y^2 Y = y^2/z - y^2/x And continued with x. You don’t need to find the numerical answer to solve for the relationship, because all you need are two values of the radii to solve for the third, a good follow up would be “if x = 3 and y= 5, what does z equal” and you just plug them in and solve.
@YiannisSfakianakis1 3 жыл бұрын
I think your explanation was good enough. You really did, it the way everyone who knows a few of geometry, can easily understand. Congratulations!!!
@KirbyTheKirb 3 жыл бұрын
Really nice, I didn´t intuitively know how to approach this question and learned a lot. Good job.
@palomino73 3 жыл бұрын
Who in his right mind could ever have a problem with such fine, colorful circles, sitting peacefully next to each other? Only square-heads, I suppose.
@wty1313 3 жыл бұрын
Math teacher: "What is the relationship between X, Y, and Z?" Me: "They're the last 3 letters of the alphabet!"
@akbarudinmajid 3 жыл бұрын
😂😂😂 good answer
@dproduzioni 3 жыл бұрын
Oh boy, this was wonderful!
@chrisberardi2304 3 жыл бұрын
Very nice! I enjoyed that explanation.
@hulexable 3 жыл бұрын
Me: y>x>z Harvard: You want a scollarship?
@cityvisual 3 жыл бұрын
LOL You crack me up.
@Thankz4sharing 3 жыл бұрын
Nah. Maybe a Harrverd scholarship, though.
@shadowjfd 3 жыл бұрын
It's been 16 years since I took a geometry class, and I hate math... Yet, I watched the whole video like a kid in class
@thunderborn3231 3 жыл бұрын
right? also i was surprised that i remembered alot of the process, but he definitely skipped steps, as in, if this was an example of explaining it to someone who is learning he did them a disservice by skipping the logic behind why he added 2xy etc to each side of the equation, but i think he was in a hurry to get done because he was nervous.
@bengoacher4455 3 жыл бұрын
and watching it I am glad I dont have to do geometry ever again, at least not in a hypothetical sense where I'm graded on my results
@drmudasirz 3 жыл бұрын
Relatable 👍
@whiteoaknectar 3 жыл бұрын
@@drmudasirz It's been 16 years since this guys been laid. I"m a total math geek, but come on dude.
@eramires 3 жыл бұрын
@@bengoacher4455 I still do, as a game developer. :( suuuuuuccs.
@parachute3725 3 жыл бұрын
Great video! The color chalk is very helpful
@harryjohnson2 3 жыл бұрын
This guy is a very good instructor. It was not this easy to follow when my teacher was going over this.
@BeornDeMirkwood 3 жыл бұрын
Given two of these circles, is there a straightedge and compass construction of the third circle ?
@iwanmommaerts5960 3 жыл бұрын
@BeornDeMirkwood well with this formula, if you have the radii of two circles you can calculate the radius of the third one, by adding the one you know (x) and the one you need to find (y) you can draw a circle with radius = x+y with the centre being the centre of x and do the same with Z (so z+y with as centre point z) and where the two circles intersect is the centre of circle y Hope this helps
@BeornDeMirkwood 3 жыл бұрын
@@iwanmommaerts5960 Thanks for the idea. But I was wondering if it was possible to construct the third circle without calculations, using only a straightedge and a compas.
@XplosivDS 3 жыл бұрын
@@BeornDeMirkwood I mean you could, but it may not be exact
@MegaWinner16 3 жыл бұрын
I'm pretty sure yes. WLOG, let length of first circle be 1, and the other length of the circle is x. Then using the video's answer we have 1/root(z) = 1 + 1/root(x), Which give root(z) = root(x)/(root(x) +1) = (x-root(x))/x-1 (rationalize the denominator). z = (x^2 -2root(x)x+x)/(x-1)^2. The above expression can be constructed given x and 1. See en.wikipedia.org/wiki/Straightedge_and_compass_construction#Constructible_points_and_lengths. Hence, it should be able to be constructed. Of course, doing it this way is tedious and there might be a more elegant method, but theoretically it is possible. NOTE: We can use WLOG at the beginning because length without a unit reference is entirely arbitrary, so we can merely use one of the circle's length as unit reference.
@GuyMichaely 3 жыл бұрын
2:50 did you mean to leave the outtakes in?
@financicalliteracyIND 3 жыл бұрын
Nice concepts, I just loved it❤️
@dylandowdy3687 3 жыл бұрын
that was really cool, thank you for sharing!
@BeansEnjoyer911 3 жыл бұрын
I feel like he intended to do some Video editing but then was like “eh I’m sure it’s fine”
@okej7749 3 жыл бұрын
I've had a D in maths my entire life. I gotta say that 6 years since my graduation have passed, and I'm still holding on to that D level pretty strong.
@hachikiina 3 жыл бұрын
D as in diligent? :^)
@x1plus1x 3 жыл бұрын
i love this kind of stuff. I wish I had gone further in school, because I think these types of problems are fun to solve.
@laithmajeed9252 3 жыл бұрын
Thank you for the explanation
@Mr152008 3 жыл бұрын
When you reach 9:46 *Kronk meme* "Oh yeah. It's all coming together."
@andresquiroz2008 3 жыл бұрын
i was lost after he said "A classic Japanese circle problem."
@Jogade 3 жыл бұрын
I thought it was about to go horny, got worried
@goranvujo 3 жыл бұрын
Good explanation, all steps presented, congrats.
@VijayaGopala 3 жыл бұрын
Man, you have an excellent blackboard and chalks. Infinitely superior to the screechy slippery non-stick types we had in our Soviet school.
@shashankkumar6625 3 жыл бұрын
How did you assume that the centre of two circle and their point of intersection are collinear? (As you have written y+z or x+z)
@rpc717 3 жыл бұрын
It just is. It's an assumption for two tangent circles. Rotate the figure so it looks like a snowman. It becomes obvious that a line, now vertical, runs through the centers of the circles and their tangent point, regardless of the sizes of the circles. Or, you can start with a line segment, pick three points, and make the outer two points the centers of circles and the inner point the tangent point, then draw your circles to make your snowman. Now lay the snowman down for a nap on line ab and you have the basis for this problem.
@edga69 3 жыл бұрын
Because the circles are tangent to each other, and the radii connecting the centres of the circles are both (and always) perpendicular to the tangent, therefore colinear.
@jamesbelshan8839 3 жыл бұрын
One way to know it is true is to think of what it would mean if they were not. Keeping in mind that the shortest distance between two points is the line, and each circle consists of all the points that are 'y' or 'z' from its center, then if the distance between the centers was more than y+z, the circles would not be touching, so the distance would be y+z+(gap). If the distance between the centers was less than y+z, say y+z-(overlap), the circles would be touching in two places. Those points would each be distances y and z from the circle centers, total length y+z, but not collinear. Pull the circles apart until (overlap)=0, and you end up with tangent circles, centers at distance y+z apart.
@vince7777 3 жыл бұрын
"and that's a good place to stop" yes, yes its is.....
@johnjordan3552 3 жыл бұрын
Yes. We should know when to pull back so in the end climax will be even more emphasized, when we solve the problem
@dubbydub9245 3 жыл бұрын
When you were searching for a term for the two points creating the triangle base "a", I was repeating "Intersecting Points." The two points where the circles intersect the line.
@JLvatron 3 жыл бұрын
Brilliant! Thank you for this video.
@robbags2118 3 жыл бұрын
I just learned something new, I should be fun in parties. XD
@ianwalker6546 3 жыл бұрын
Lovely clear explanation, no bells and whistles, just the maths
@shriekingbushpigshrieking 3 жыл бұрын
Really well done!
@sridharyavvari8682 3 жыл бұрын
This is a problem given in JEE MAINS-2019 Entrance test (India)
@jbtechcon7434 3 жыл бұрын
Each time you pack a circle into the gap between two circles and the floor, you create two new such gaps. Derive a formula for the SET of all the radii of the 2^n circles in the nth layer beneath the circles in this diagram, in terms of n, x, & y. Your answer must not be recursive.
@O2OW 3 жыл бұрын
Nice one. You make it look easy!
@OlivierGeorg 3 жыл бұрын
I started trying it. Like him I identified 3 triangles, so I had 3 equations but 5 unknowns (x, y, z, a and b), and I kept looking for another equation. But things magically arrange to give the solution!
@dodgeplow 3 жыл бұрын
i haven't studied geometry in 35 years. Why am I watching this at 2 am?
@giso79 3 жыл бұрын
it's 1:30am for me but same question. Why do i watched that? ... anyway gn8
@jonknocks111 3 жыл бұрын
You're drunk?
@michaeljakeusman 3 жыл бұрын
i bet you didnt get to use that geometry knowledge in 35 years XD
@trendingNOW1824 3 жыл бұрын
The relationship MUST be, they all live in the same house as they are definitely not social distancing.
@jtflypegasus 3 жыл бұрын
That is simply beautiful!!
@nathanbrown492 2 жыл бұрын
I tried forming 4 triangles (1 non-Right angled triangle connecting the centres, and the 3 Right angled triangles to calculate the angles on the non-Right angled triangle). It works; you can get a system of equations, but you're left with asin & acos everywhere.
@giantpune 3 жыл бұрын
Why is youtube recommending this to me? Its 11pm, I'm in my 30s and have been out of school and college for 2 decades. Interesting video, but really, youtube.
@Stretch7586 3 жыл бұрын
Yea, same lol
@Zhurak 3 жыл бұрын
100%! Right there with ya! still enjoyed it.
@niko3485 3 жыл бұрын
yep. I'm from Spain. I don't even speak english. I do watch building stuff videos
@MJTeh1 3 жыл бұрын
holy shit that came waaaay to close to my current situation lol
@manishchoudhary6404 3 жыл бұрын
how do you draw these circles so well? do you use an instrument?
@YouRich92 3 жыл бұрын
The secret is just to practice.
@pondconker1 3 жыл бұрын
yes, chalk
@simonl7784 3 жыл бұрын
Thanks Michael
@chandragupta34 3 жыл бұрын
Great video !
@macfrankist 3 жыл бұрын
That was fun. Not so challenging like other stuff.
@jorgealexandre4616 3 жыл бұрын
Indead
@giotto4321 3 жыл бұрын
@Corat Oh, I know this one, it's half of the square root of 1/(You can't spell 'you're').
@arya6085 3 жыл бұрын
@Corat you've never had sex before