There are 4 bands with the name 'The Square'

1) The fusion instr… Read Full Bio ↴There are 4 bands with the name 'The Square'

1) The fusion instrumental music band from Japan. In 1976, They formed "THE SQUARE" led by Masahiro Ando. In 1978, they made their debut in album "LUCKY SUMMER LADY". They changed the band name to "T-SQUARE" which they used in the case of success in U.S.A. in 1989. In 2003, they celebrated the 25th anniversary of their debut and they regrouped for a limited time.

2) A band from Lincoln, Nebraska. The lead singer was Sean Beste, with James Valentine of Maroon 5 fame as the former guitarist. Their debut and only album was entitled "This Magnificent Nonsense."

3) A Drum & Bass project by Aleksandar Markovic (http://www.myspace.com/thesquarednb).

4) South-East London crew The Square, led by MC and producer Novelist, part of the new wave of grime followed by other London-based artists such as Stormzy. Everyone in the group is aged between 15 and 20 and other notable members would be producer Lolingo and MCs DeeJillz and Elfkid, the whole groups reeks of the old BBK days.

Between
The Square Lyrics

Jump to: Overall Meaning ↴ Line by Line Meaning ↴

Let's go fly a kite
Get me high

Whenever I'm with you
You smoke all my cigarettes
Whenever I'm with you
You drink all my wine
I'd roll another spliff but

I'm fresh outta nicotine
Why don't we just get high

Oh, I'm over the moon
When I'm with you
I'm never blue

Whenever I'm with you
You smoke all my cigarettes
Whenever I'm with you
You drink all my wine
I'd roll another spliff but
I'm fresh outta nicotine
Why don't we just get high

Oh, I'm on cloud nine
And I'm feeling fine
I'm never blue

Eddie Spaghetti

Oh, I'm over the moon
When I'm with you
I'm never blue

Let's go fly a kite
Get me high tonight

Whenever I'm with you
You drink all my cigarettes
Whenever I'm with you
You smoke all my wine
I'd roll us up a joint
But I'm fresh outta uhh
Why don't you just go home

Let's get high

Overall Meaning

The lyrics to The Square's song "Between" revolve around the theme of escapism through the use of drugs and alcohol. The opening line, "Let's go fly a kite, get me high," suggests the desire to experience a temporary euphoria or a state of bliss, much like the feeling one gets when flying a kite. The lines "Whenever I'm with you, you smoke all my cigarettes, Whenever I'm with you, you drink all my wine" depict a person who consumes the singer's resources, further emphasizing the need to escape reality.

The repeated lines "I'd roll another spliff but I'm fresh outta nicotine, Why don't we just get high" convey a sense of dependency on substances to achieve the desired state of ecstasy. The phrase "I'm over the moon, I'm never blue" reveals that being in the presence of the person they're singing about brings immense happiness and a sense of freedom from any negative emotions.

The mention of Eddie Spaghetti can be interpreted in two ways. Eddie Spaghetti could refer to the name of a person the singer feels a strong connection to, or it could be a reference to a comfort food like pasta, suggesting that being with this person acts as a source of comfort and satisfaction.

Overall, the lyrics of "Between" explore the longing for escape, the reliance on substances for temporary happiness, and the transformative effect of being with someone who brings joy and a sense of completeness.

Line by Line Meaning

Let's go fly a kite
Let's engage in something exciting and uplifting

Get me high
Bring me to a state of euphoria

Whenever I'm with you
Whenever we are together

You smoke all my cigarettes
You consume my resources without consideration

You drink all my wine
You take all my pleasures and indulgences

I'd roll another spliff but I'm fresh outta nicotine
I would find another way to feel good, but I lack the necessary means

Why don't we just get high
Why don't we simply seek pleasure and escape from reality

Oh, I'm over the moon
I am incredibly happy and content

When I'm with you
In your presence

I'm never blue
I never feel sad or down

Oh, I'm on cloud nine
I am in a state of utmost joy and bliss

And I'm feeling fine
I am experiencing a positive and contented mood

Eddie Spaghetti
An additional lyrical expression without clear meaning

Let's go fly a kite
Let's engage in something exciting and uplifting

Get me high tonight
Bring me to a state of euphoria this evening

You drink all my cigarettes
You consume my resources without consideration

You smoke all my wine
You take all my pleasures and indulgences

I'd roll us up a joint but I'm fresh outta uhh
I would find another way to feel good together, but I lack the necessary means

Why don't you just go home
Why don't you leave and stop consuming what is mine

Let's get high
Let's seek pleasure and escape reality

Lyrics © O/B/O DistroKid
Written by: Zachary Suarez

Lyrics Licensed & Provided by LyricFind

To comment on or correct specific content, highlight it

TRACKS

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01ハワイへ行きたい4:38

02The Rest Of A Romance4:45

03脚線美の誘惑4:27

04Hearts6:02

05Love's Still Burnin'4:44

06Change Your Mind4:12

07Between1:20

PT1M20S

The Square

08Full Circle4:31

09MEMORIES OF ALICE4:45

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Most interesting comments from YouTube:

@gcecchelli

4y↑1

Hi, I think there is an alternative way, which I found more elegant, although it involves solving a complex trigonometric equation. I you consider the arc formed by the horizontal diameter (or you can call it the "base") and the segment between the center of the left circle to the upper right corner of the square, and call it "2 alfa", then alfa is the angle between the base and the segment starting from the leftmost intersection of the base with the left circle. In this way you can form a triangle inscribed inside the left circle, and this triangle is a right triangle. Using this result, you can come up with formulas that describe the vertical and horizontal sides of the square, ending up with a 2 by 2 equation system with "x" as half of square side, and "alfa":
1) 2x = 1 - 2x tan(alfa)
2) x = sin (2 alfa)

After some substitutions you end up with:
sin (alfa) = 1 / (4(sin (alfa) + cos (alfa)))

Resolving for alfa you find multiple solutions but you have some constraints: alfa is surely less than 30 degrees. And x is more than 0.25 but less than 0.5.

You find the approximate solution (I did it numerically) of alfa = approx 0.212, which gives x = approx 0.41, which gives an Area = approx 0.677

@harrysvensson2610

Just focus on the left circle
The shape of that circle is y = sqrt(1-x*x)
put our center at (0.5,0)
y = sqrt(1-(x+0.5)^2)
since we're looking for a square, look at where a line with angle 45 degrees crosses the curve, x = sqrt(1-(x+0.5)^2)

Add a simple low pass filter by adding x to the number you're trying to find and divide by 2.
x = (x+sqrt(1-(x+0.5)^2))/2

Same thing but more mathematical is like this:
Start with x = sqrt(1-(x+0.5)^2))
add x to both sides
2x = x+sqrt(1-(x+0.5)^2))
divide by 2
x = (x+sqrt(1-(x+0.5)^2)))/2
Same thing as the low pass filter, the reason for why we use it is to make the sporadic numbers that pop up behave smoothly so we converge to the result slowly instead of jumping away to infinity.

Start our guess of x at 0

The value of x for each iteration is...
0
0.433012
0.396428
0.419808
0.406087
0.414588
... do this 10 more times
0.411459

That's the number that makes x = sqrt(1-(x+0.5)^2) true. Since we positioned ourselves at (0.5,0), the value of x is half of a side length, so when we square x we only get a quarter of the square. To get the area of the whole square we have to square x and multiply by 4, like this: 4*x^2 = 0.677196

@shadrana1

Label the upright rugby ball shape ABCDEF in a clockwise direction starting at the top.
Blue square is FBCE,G is midway between F and E.
Let side of blue square =2y.
Using the intersecting chords theorem,
y^2={(1-2y)/2}{2-(1-2y)/2}
This breaks down to;
2y^2+y-3/4=0
y= (-1+sqrt7)/4
Area of blue square= (2y)^2=4y^2= 4*(sqrt(7)-1)^2/16
=(sqrt(7)-1)^2/4=(8-2sqrt(7))/4
=0.6771243445. square units.
Basically,the same method as used by Presh.

@afarhan21

My first reaction was to figure this out using Coordinate Geometry.
Take the origin on the left circle's center
The equation of the right circle with center (1,0) and radius 1 is (x-1)^2+y^2=1
i.e. equation of circle is y^2 = 2x-x^2
Now to find x so that y is half the length of square's side
Let's say side of square is '2P'
we have, y=P and x=(0.5-P)
Substituting in equation of circle we get: P^2 = 2*(0.5-P) - (0.5-P)^2

P^2 = 1 - 2P - 0.25 + P - P^2
we have 2P^2 + P - 0.75 = 0
P = ( sqrt(7) - 1 ) / 4

Area of square = (2P)^2 = 0.67712434446770470474919212318037...

All comments from YouTube:

@rupasarkar8276

4y↑8

This channel often remind me of my school days. In school we often used to solve difficult problems. It truly gives nostalgia. You are doing a good job.

@martint1775

4y↑75

I remember just calling it the ABC-formula. Good times good times

@KelfranGt

4y↑7

We used to call the quadratic formula as the abc-formula lmao

@GoldfishCorner

4y↑10

I saw several debates about the maths history. For those nonChinese speakers, I like to clarify that “GouGu” or “勾股” is actually not someone’ name in Chinese. It is simply means long side and short sides of a Right Triangle. No matter what you prefer to call it, history is there.

@sadsongs7731

I'd rather not push CCP propaganda, just out of principle.

@Eru-

4y↑15

I'm glad kids nowdays dont need to pay Kumo_ to learn this. Youtuber teaches everything we need👍

@MatheMagiX

4y↑36

The triples were known in Egypt, Babylonian, Mesopotamia. In India they only knew them as a solution to the a^2+b^2=c^2, but no connection to circles/triangles, no general proof. The text Manjul Bhargava mentions (Zhou Bi Suan Jing) gives a geometrical proof to a 3-4-5 triangle, by showing how a square of side 3 fits into a square side 5. Despite unknown date of the "proof" (could be anytime between 1046–256 B.C., whereas Pythagoras lived 500 B.C.), it's not a general proof. For all we know, Pythagoras used geometric methods, most likely with similar triangles and proportions, to prove the theorem's general case. The first axiomatic proof dates to Euclid 300 B.C., which may be earlier than Zhou Bi Suan Jing. Even though Euclid does not mention Pythagoreas, Plutarch, Cicero, Athenaeus, and Apollodorus do and credit him with a "famous proposition". Socrates also gives hints about knowing the general proof. All in all, the first axiomatic, general proof of the theorem, as for now, is due to the Greeks, and they (along with some Latin writers) credit Pythagoreas. "Pythagorean Theorem" is clearly the right name so far, so I respectfully disagree with prof. Bhargava and you.

@niklas3265

4y↑2

I agree

@killallbots1012

4y↑2

No. It should be called "Law of Right Triangles" or "Right Triangle Theorem"

@dhruva8538

And Pythagoras learnt it from Brahmins in India so Bauddhyan prameya (theorem) is correct name

@sweetygupta972

4y↑3

I am in love with your channel. Math is one of my favorite subject but I've been losing my connection with it lately. Watching your videos might be helping me reconnect again. I'm really thankful to you.

@Ramakrishna-fm5ig

So is in my case🙂

@taewankim8419

4y↑39

Technically, Plimton 322 (1800 BC) is older than 周髀算经 (1000BC), so I would call.. Plimton 322 theorem?

@perseusgeorgiadis7821

This does not prove or establish the Pythagorean theorem. It’s simply a set of numbers that satisfy it. Pythagoras was the FIRST known mathematician to establish it. That’s why it’s called the Pythagorean theorem. Believe it or not, when I was little, I had also developed my own set of triples that satisfied the Pythagorean theorem to calculate the distances my friends had to cover to catch me when we played tag. Should we just call it the Georgiadisean theorem instead? Don’t think so

@pantsik2

4y↑130

Changing theorems names results in bigger confusion.

@leif1075

Did anyone reallynsolve the way he did in the video?

@yurenchu

@Leif, I did it in exactly the same way.

@JamesWylde

4y↑7

I wish Presh would stop that crap, he is a smart guy and does a great job of making complex math approachable, but this Guongu crap just makes him come across as arrogant.

@strippledzester5435

He explained it and if u cannot discern that anyway u shouldn’t be watching these videos bruh

@Rohit-oj5dv

@Kane Exley U r right. He explained the origin of Gougu theorem. Ppl can Google as well before condemning him. Presh hs justifiably defended all his words. Just see, how clearly he presents each video n explains everything with crystal clarity. The graphic representations in his videos r so accurate n precise. I salute Presh.

@erikshure360

4y↑48

I appreciate the sentiment of mentioning other names for the pythagorean theorem, but honestly throwing more names -- that mean the same thing -- into the mix of mathematical jargon just makes things unnecessarily complex.

@bag.a.6465

the whole changing names for historical justice is kinda bad for convenience. eventually some isolated regions will use the old name and newer regions more connected to the outside world will use the newer names, with divisions already existing. I mean, sure those guys discovered first, but if the guys who called it Pytaghorean theorem managed to spread that name far and wide, why not use it?

@Robi2009

4y↑120

Oh yeah, inventing new names for theorems that has been around for over 2000 years... Great idea

@Tfin

4y↑8

Indians, Egyptians, and Chinese didn't bring this formula to me, or even to Pythagoras.

@dudeoffbeat1370

Bro Greek compiled Thier work
They have not invented as such even proof

@dhruva8538

4y↑7

Yes Pythagoras learnt it from India Brahmins in India taught him that

@monikagupta7094

@Tfin google it, you will see that gougu proved it.

@Tfin

4y↑4

@Monika Gupta Google the word "irrelevant."

6 More Replies...

@michellauzon4640

4y↑225

Why your never use circle equations? Put the origin at the middle of the intersection. The equations of the circles ares (x ± 0.5) ** 2 + y ** 2 = 1, and the four extremities of the square are (±a , ±a)
(a , a) belongs to the left circle, so (a + 0.5) ** 2 + a ** 2 = 1. The rest is the same.

Very often, circle equations simplify the solutions, like for your three chords problem.

@moneti5091

4y↑5

Maybe he just doesn't want an analytic solution.

@rbdgr8370

4y↑1

so according to you '2a' is the length of square side. Right??

@Dgsrgv

4y↑5

what a beast u are

@michellauzon4640

4y↑6

@iggaboi1729 You are probably right, but he often offered two or more solutions and rarely analytics ones, even when they are simpler.

@michellauzon4640

@RB DGR8 Yes, that's right.

37 More Replies...

@huwpickrell1209

4y↑1

Nice but simple problem. I used Cartesian approach. Equation if circle is (x+1/2)^2 + y^2 = 1 intersection with corner of Square lies on line x = y. So we have (y+1/2)^2 + y^2 = 1
Solve to get y=(-1+√7))4
Double then square this to get area of 2-√7/2. Simples

@nibedanmukherjee3060

4y↑14

Thanks Presh! for sharing the problem.

@ikarus1955

https://drive.google.com/file/d/1Z8JgbG9CXcXEKJUxcyLTORtNLfkT8OZ-/view?usp=drivesdk

@randomdude9135

What are you studying? IIT?

@nibedanmukherjee3060

@Random Dude BS & MS From Stanford. Scientific Researcher at NASA

@randomdude9135

@Nibedan Mukherjee wow bro. But serving in ISRO would have been great for India. India needs talented people like you

@nibedanmukherjee3060

@Random Dude Thanks for your approbation buddy! One of my patent is at ISRO , PDS(Planetary Data Systems).

3 More Replies...

@simonjohnson1505

4y↑1

I love this channel. I get about half the questions right. Thank you.

@palashpratimdeka230

4y↑13

Thank God, I solved the question after trying for 40 minutes☹️

@gabrielpetre3569

4y↑251

Presh 2030: since we found a lost tribe that did math before us and called addition munchin, from now on in the videos 1+1 is to be refered as one munch one

@hattorikanzo2793

4y↑10

Triggered White

@Coolkid245

4y↑10

Lol its a joke

@adityaghosh3234

4y↑1

Lmao

@cinemarat1834

4y↑31

@Hattori Kanzo irrelevant if one is triggered or not, the fool is still the one insisting on changing names for ideas as if it's relevant to the idea itself. Don't have anything to do with skin color my guy.

@lisakeitel3957

So, if someone says an invention is his, and popularize the invention, we shouldn't care about patents, or copyright, because yeah. "But it happen a millenia ago". So we should keep teaching a lie?

5 More Replies...

@mtmath1123

4y↑39

Easy but simple and beautiful.

@fighoss1

right 🙏🙏

@jakubfrei3757

yep

@MikeDunn

4y↑4

Doesn't make sense to say "easy but simple".

@shreyan1362

@MikeDunn lol

@TheDBest1994

4y↑295

I will still call that Pythagoras instead of Gougu theorem, I really like Pythagoras more. Sorry.

@sumukhhegde6677

4y↑12

That's why i don't like Christian and Muslim.. because you people always consider Hindus Buddhists Sikhs and atheist as low class people 😡😡

@MrBedBringer

4y↑80

@Sumukh Hegde are you alright mate

@pvhufpvhuf3751

4y↑60

@Sumukh Hegde Dude, Pythagoras was neither Christian or Muslim and predates both centuries. It seems to me you're suffering from an inferiority complex.

@bingchilling4717

4y↑9

@proteusx i am from europe too. That makes me a racist?

@leonardlangner9949

4y↑13

proteusx your a racist for saying that.

25 More Replies...

@georgechen8028

Got the answer correct. The key to the question is knowing the distance from the side of square to the center of another circle equals (1-a)/2, then you have a right triangle, and finally find the side of square a = (√7-1）/2. I once thought the line between vertex of the square and center of circle divide the angle evenly, but that's totally groundless.

@anjanmukherjee7997

4y↑16

Amazed to see a problem suggested by an Indian Bengali.

@anjanmukherjee7997

4y↑1

I agree. That's true.

@nibedanmukherjee3060

4y↑2

@Adam Romanov Admire your statement mate, thanks for your approbation .

@aaronleperspicace1704

@Nibedan Mukherjee are you the person he mentioned in the video???

@nibedanmukherjee3060

4y↑2

@gore buster yes!

@nibedanmukherjee3060

@Adam Romanov yes true, but it's rather obvious by fagnano symmetry (*Fagnano transformations). Buddy! solving geometry problems is my obsession. Still I try to grab some time from my oderly sample space for solving this wing of mathematics. (* I'm a scientific researcher by profession)

2 More Replies...

@presidentworld5360

The only thing that matters about mathematical rules and theorems is their application... The way we identified them should be universal and unique... I once loved and thought that mathematics is pure beauty where the publisher is not required in the equation to satisfy this beauty...

@gcecchelli

4y↑1

@JWentu

4y↑66

I think I will call it "PythaGougurean Theorem" in order to please everyone

@dhruva8538

4y↑2

Naah Bauddhyan was the original person to find this rule

You can't please all don't try

@supercool1312

4y↑1

Dhruv A nah actually god invented maths, thus it should be called the god theorem, and therefore every theorem is now called the god theorem

@preetisrivastava5341

@ya yeet ignorant

@anandk9220

2y↑1

Solved it the same way using Pythagoras theorem in square. Initially assumed one length wrong but as I watched the video midway, I realized and corrected the mistake and eventually got the correct answer.

@srijansharma8522

4y↑1

This channel must grow

@robert33232

4y↑1

Finally solved it!!!

It was easy to find the solve plan but I was getting elementary mistakes, so they pushed my solution progress back 😃

@avisharma5394

What I Love About these Questions is Not their Difficulty But Their Elegance!

@rishiagarwal4643

4y↑2

India has given the world basics to advanced mathematics

@vasiliosmouzas2792

4y↑63

The worldwide accepted proof about the correlations between the parameters of right triangles derived from Pythagoras. Before his work there are references about those correlations but not any proof in the form of classic geometry & mathematics.

@monikagupta7094

4y↑1

There is proof partial from india but fully proved by chinese in written, google it

@vasiliosmouzas2792

@Monika Gupta it's seems you're right. I'll accept it while I'm continuing the research about that subject.

@monikagupta7094

@Vasilios Mouzas even i dont know much about it, its just that my teacher at school called it with same name and he told us that it was not Pythagoras who proved it and i googled it to confirm he was right.

@georgechouchlias9400

Do you want to sse any one of you the original mathematics here in Greece;?a book from pythagoras συμπλήρωμα άλγεβρας 3ης λυκείου ίσως το πιο καλό βιβλίο για μαθηματικούς 5 τόμοι

@georgechouchlias9400

Αυτά είναι στα σύνολα κ υποσύνολα 1 γυμνασίου στην Ελλάδα έχουμε 6 χρόνια σπουδές μαθήματικα φυσική χημεία βιολογία γυμναστική κτλ από τότε που βάλανε την ρομποτική ως τρίτο εισαγωγικό εκπαιδευτικό πήγαν όλα 100 χρόνια πίσω

4 More Replies...

@justin6630

4y↑1

If I’ve learned anything from this channel it’s that everything always comes down to a quadratic equation.

@luisguillermo6216

4y↑2

I did it in a different way. I instead extended the top side of the square until it intersected the left circle and then connected this intersection with the bottom right corner of the square. Due to thales theorem, the latter will be simply the diameter of value 2, I named X as the whole side of the square, and finally the other side of the triangle will be X+1. (I visualized that when we draw the radius being perpendicular to the right circle and move it either up or down, it will not need to change lengths to touch both circles).

Finally, we get
x^2 + (x+1)^2 = 2^2
Which in fact is equivalent to solving the equation in the video.

@alohamark3025

You have my vote for the Gougu theorem. Let us give credit where credit is due. The vote should be restricted to those with a PhD in mathematics, or math publications to their credit. We do not need politicians voting for anything related to mathematics history.

@AyushSingh-vz8sc

4y↑15

Thumbnail was cool though

@Scorpionwacom

I decided to watch Presh’s videos several times until I’ll finally understand the solution.

@NetAndyCz

4y↑92

Might be better to drop the name, a lot of civilisations figured these things out at similar times, some maybe repeatedly and so much stuff is lost to history that the name might change with every new historical discovery. We know that Greeks copied a lot of math stuff from Egyptians (and Egyptians themselves might have copied from other cultures) that it is tricky to know who was really the first. If we keep changing the names it will become unintelligible what is actually meant by that.

@4chiron

4y↑7

Nonsense. The Greeks provided proof and this proof was subjected to peer review. The Egyptians and the rest did not.

@vasileiospapazoglou2362

4y↑1

We didn't copy anything if you want to know we have pyramids that are 2000 years older than the first Egyptians.of course Egyptians were well respected and when we lost our knowledge due to a catastrophe they gave us back some f it.

@dudeoffbeat1370

4y↑1

Bro indians were first to give the proof (although practical proof) and later theoritical proof after them it was Chinese and epytians then Greek compiled Thier work and presented it as a new style

@monikagupta7094

@4chiron chinese and indians did, google it

@Pteromandias

4y↑3

And it doesn't matter who came first. It's not like they created it. A mathematical truth exists independently of discovery. Before it was written, it was true. If no one ever discovered it, it would still be true. Just because one person discovered it at one time, and another discovered it at another time, it doesn't mean that one's discovery was any less than the other. Especially if the two discoverers didn't even know of each other.

2 More Replies...

@ib9rt

4y↑4

Let sin(2t) = 3/4. Then the length of a side is 2 * sin(t) and the required area is 4 * sin^2(t).

@nupellot

A hard-looking problem turns out to be extremely easy to solve after watching a video on this channel. Again

@bpark10001

You can do the same thing (with algebra and Cartesian system) by setting origin at center of left circle. Circle equation is x^2 + y^2 = 1. Equation of line from center of square along diagonal is y = x - 1/2. Substitute this into circle equation and solve. You get X = [1 +/- sqrt(7)]/4 But this diagonal crosses X-axis at X = 1/2. Subtract 1/2 from X, double, and square to get same answer. Origin can also be set between the 2 circle center's.

@Ignoto_

Easier than I thought. :0 amazing

@vishnukumarsharma3441

Your questions are very helpful for me

@jesusortizmerodio3193

4y↑40

I think calling with different names theorems and laws that the scientific community and everybody else use is not a very wise example of "minding your own decisions"

@roygalaasen

Totally this!!!

@monikagupta7094

But we should atleast give the person who really found and proved this some credit.

@roygalaasen

4y↑2

Monika Gupta and they are doing that. Just no need to change an established name. It will just cause confusion. Almost every single science video I am watching the editor has been careful to mention the history behind and who invented/really invented certain items/formulas/algorithms/etc.

@monikagupta7094

@roygalaasen but whats problem with that, no one is forcing you to call it by this name, if you want to call it as pytho theorum, you are free to. He just wants to tell is real history behind it, which is nothing wrong i beleive, then why this discussion on who invented it. We are not the ones who decide that. It helps you solve maths problems thats it.

@roygalaasen

4y↑2

Monika Gupta it is a free world. You can choose to make plans for a house and pick measures made in units made out of body parts as well. But you are not sure your house will be exactly the way you expect it to be if you decide to talk a different language than everybody else either.

@CaravaggioRoma

Well, I use trigonometry for the general inscribed rectangle. The area is 2sinx(2cosx-1) where x is the angle. The condition for the square becomes sinx=2 cosx - 1; thus x becomes arcos4/5.
By substitution in the first equation you get area =18/25

@eshaan570

Lets go this is the first problem from this channel that i got right without help

@deanshulze931

I solved it using sin and cos. I drew the same lines and labeled the angle a. The vertical side of the square is 2 sin a. The horizontal side is 2 cos a -1. Solve 2 sin a = 2 cos a - 1 for a.
Plug in a in the length of side equations.

@exhalerwolf1272

4y↑2

Right angled triangle: exists
Gougu: hold my green tea

@WarmWeatherGuy

I got rid of the circle on the right. I centered my coordinates on the left circle. I drew a line from (0.5, 0), the center of the square, with a slope of 1 up and to the right until I hit the circle. That line has the equation of y = x - 0.5 and the circle has the equation of y = sqrt(1 - x^2). Then I solved for the x position of the intersection of that line and the circle. From there the math looked a lot like what you see in this video.

@eliashowe8418

Dang. I ended up with the equality 2sinx = 2cosx -1, which I don't remember or perhaps never knew how to solve. I verified it using your answer. I like your way better.

@weather2456

you just gougu the theorem, good job

@pedroloures3310

I took the same steps as you, however it was very difficult for me to spot this right triangle. It took me a long time

@alberca90

Who cares what to call it, instead of saying "based on the <name> theorem, we know that a squared plus b squared equals c squared" just say "since we know a squared plus b squared equals c squared etc etc"

@stevenkhan5199

When I see a light bulb on a seeling with no lamp shade it makes two circles like show on here, like the eye of a needle with the shadow on the seeling so I was wondering is it light that is the answer?
As in the speed of light?

It's also on maps or some with the eastern world and western world meeting in the eye of the needle or whare great Britain and GMT runs laterally through from north to south.

I have not received much education in my life through school due to moving around a lot but I have always wondered and seeked as much knowledge as I can through whatever means I come across , latest being the internet and YouTube.

So is phy / pie or the speed of light the answer or riddle to the needle between the two circles?

@dhruva8538

Appreciate the hard work

Ignore the vast majority of the hate on historical accuracy
We need the actual names hurray for sridharacharya Bauddhyan & brahmagupta

@jackjumbo2321

4y↑31

Im from Hong Kong, and I’ve never heard of anyone named Shanggao or anything called the Gougu theorem in my 14 years of education. I couldn’t find the Chinese names of them, and we just call it Pythagorus theorem（畢氏定理）btw could someone plz tell me what does Shanggao and Gougu translate to? Many thanks! I would like to know

@derekbaugh6360

Jack Jumbo https://wuu.wikipedia.org/wiki/勾股定理

@derekbaugh6360

Shang Gao 是數學家的名字

@jackjumbo2321

Derek Baugh 可是勾股是甚麼意思呢？還有數學家是叫高尚？🤔😂

@timguo6858

@Jack Jumbo 是商高。勾opposite，股adjacent。无知不值得骄傲，不懂可以自己去查。

@vishalmishra3046

Apply coordinate geometry to any vertex of the square (say top-left (-x,x) vertex) and find distance to the center (.5, 0) of the right circle. which must be equal to radius (1). So (-x - .5)^2 + (x)^2 = 1 or (4x+1)^2 = 7 and Area of square = (2x)^2

@michaelmulla6178

4y↑1

You made it way harder than it is, i solved it within half a minute, since the circles hit each other at each others middle point, the blue box has to have a length of 1,then we can imagine a square shape around the circles, this shape has a length of 3 and width of 2, and since the blue box is 1/3 of the width its 2/3 since its width is 2, so 2/3 • 1 is 2/3

@Malincanada

But you saw that 2/3 wasn’t the actual answer?
You can’t say ‘I have an easier way’, if that way doesn’t actual find the answer.

@michaelmulla6178

@Malincanada i thought it is 0.677 which equals 2/3?

@malcolmmcleod8994

@Michael Mülla 2/3 = 0.6666666666666666666......
The actual answer was shown at about 3:10 as (4 - sq(7))/2 which is an irrational number, but which the video shows as being approximately 0.677 if you put it in a calculator.

@qwertyuiop-ip8rc

4y↑1

I sat this exam and was one mark away from qualifying for gold and the senior kangaroo. This paper was a fair bit harder than the previous years.

@kimsmoke17

It’s quicker to solve by writing the equation of one of the circles using the coordinate system that has the origin (x,y)=0,0 at the center of the square: (x+0.5)^2 + y^2 = 1. Then solve for the (>0) case where x=y. That is solve the quadratic equation (x+0.5)^2 + x^2 = 1, or simplified, 2x^2 + x - 0.75 = 0 then 4x is the area of the square.

@MarCamus

After watching this video, I came up with my solution using intersecting chords theorem. Took me like 15 minutes to solve this my way cause I didn't write the equation properly...

@theosalt1

The real clever part is when you deduce that the altitude of the right angled triangle is x + 0.5. [I did not see that coming]. The rest follows and just uses Pythagorus's Theorem [or whoever you attribute it to] to solve for and then calculate the value for (2)^2 for the area of the square.

@jagesharya2243

4y↑1

I love very much this chanel.

@hgdolder

My first approach left me at cos(a) - sin(a) = 0.5, (from a I could get x = cos(a)). Then I started over and I came up with the same solution shown here.

@12mkamran

Was a great chance to use the new easier method of finding roots of quadratic equation

@killallbots1012

4y↑140

Theres a debate about whether calling it "Pythagorean Theorem" or "Gougu Theorem". Why not just call it "Right Triangle Theorem" then? It would then be easier for the students.

@sujatasharma8560

4y↑2

I also use to prefer that way.....

@marcushendriksen8415

4y↑30

I agree that we should just call it the right triangle theorem, but you're wrong about there being a debate on the topic, it's literally just Presh that has a problem with it

@georgesamuelson4003

4y↑1

Might aswell go with Talwalker Theorem

@arvindupadhyay6877

4y↑3

For laymen the debate is redundant but for those who research on the topic it is quite necessary to know the origin and originator. Also the inventor must be remembered and appreciated for their excellent work.

@georgesamuelson4003

4y↑6

But there wasn't one specific inventor for this Theorem. There were multiple all with different discoveries. So why name it after one, disregarding all the other?

18 More Replies...

@BGiordanio

4y↑1

We also can solve the problem with Al-Kashi formula in a triangle (1;0,5 ;y; 135°) where « y » is the semi-diagonale of the square and 135° the angle between the sides (1;0,5) 😎

@viniciusfernandes2303

Thanks for the video!!

@stromboli183

So this question is about the straight (horizontally oriented) square inscribed in the intersection of the two circles.

Alternative questions: what is the largest possible square, and largest possible rectangle in any orientation (i.e. it may be rotated) that fits within the two circles’ intersection?

@jaishankartiwari4526

You are right about naming it gougu theorem
But please focus on mathematics only
History doesn't matter in front of mathematics
Keep your videos interesting and keep up the good work

@dhruva8538

Naming is important
Bauddhyan prameya for original person to make the rule

@JustAnthon

4y↑1

@Dhruv A If naming is important, we shouldn't start changing names of ancient rules and laws. In modern times, it's not about giving credit to people who have died in millenia past, but to establish common ground to communicate on.
So it should stay Pythagoras' Theorem, solely on the basis that we need a name for it, and that's the one we've used for ages. Changing it would really start confusing people, especially students, and lead to basically nothing.

For many, Pythagoras is just the name people associate with right triangles. It's not even that they're giving credit to him or cherishing his work, but just a name and nothing more.

@alg2301

Me encantó. Buenisimo!!!

@harrysvensson2610

@AR-vp3qh

4y↑4

Can you help me what is the advantage of square root of 2 that no square root of any number has

@marcushendriksen8415

4y↑3

I'm not sure what you mean by "advantage", but I like the square root of 2 for the fact that it is the hypotenuse of a right triangle with unit legs

@AR-vp3qh

4y↑1

@Marcus Hendriksen oh thanks. I thought that also this is a question from my teacher. I'm from Iraq

@nirihannemann5494

4y↑3

I have got a question.
Where is the mistake?
e^(i×pi)=-1
Which follows e^(2i×pi)=1
On both side ^i
e^(-2pi)=1

@ivanhuertas5307

is the diagonal of the square igual to the radio of the circle?..what is its value?

@sreenathc

So many people commenting on renaming theorems to reflect original discoverers....if something is wrong we try and correct it shouldn’t we? It must start somewhere...why not here? If a fields medal winner says that the origin of the right triangle relations is Gougu then it must be correct...Love your videos Presh. Can you also do some of those harder Proof Without Words problems and explain...keeps my aging brain agile!

@amegatron07

Lol, I solved this task independantly, and though my answer is correct, my solution is quite harder, cause I involved trigonometry. The starting point was identical: center of the square, and a radius from one of the circles to one of the corners of the square. But then I followed the way of determining the "radius" of the square (line from the center of the square to it's corner), which involved some trigonomentry (we have a triangle with 2 known sides and one angle, which we got from (360-90)/2, where 90 is the angle between two "radiuses"). When I found that "radius" (r), S = (2r)^2/2 - diamond square.

@timchocolate7220

4y↑2

勾股定理, it doesn't really matter about the name, just remember the formula

@OzzMazz

4y↑1

I came up with the following two equations:
1) 2(x+y) = 1
2) x^2 + (2x+y)^2 = 1

y is the gap between the square and the centre of the circles.

@OzzMazz

About what?@Aditya Gupta

@ananyagangwar8896

4y↑1

Can you please explain why the line joining the centres will bisect the side of square.... BTW great question!

@mehrdadassar2542

That is actually JOUJU theorem because JOUJU published it 2 hours before GOUGU paper appeared!!!

@shadrana1

@maaifoediedelarey4335

Good point ! I had forgotten that theorem, to be honest !

@_sanket__gupta

Yeass!!!!I solved this problem just from the thumbnail

@MathematicalScienceYT

29w

Semicircle radius 3 . Circle with radius 2 touches the centre of semicircle . Find the area of the square inside the overlapping circles .

@ankitdas6748

4y↑4

How did you got (4-√7)/2 after simplifying?

@jeconiahjoelmichaelsiregar7917

4y↑2

((√7 - 1)/2)^2
= (7 - 2√7 + 1)/4
= (8 - 2√7)/4
= (4 - √7)/2

@maaifoediedelarey4335

@R3Volt. Thank you.

@gmchess7367

I have solved this in 10std it's too easy question but very nice problem 👍👍

@iandavidson471

Would it be possible to draw the square in the first place without knowing what size sides it would need? 🤔

@eagleeagle7360

After several days I was able to solve it xD Fun Problem.

@udayadityabhattacharyya7496

4y↑5

The Pythagorus' theorem was actually in the Yajurveda. Shulwa sutras of Yajurveda written by Boudhayan contains the theorem. There are two shlokas, one for the diagonal of a rectangle and the second is for the diagonal of a square. So the theorem is of Boudhayan and I teach my students such.
Again, what you called Brahmagupta's formula is known as Sreedharacharya's formula in India.

@ottokard1243

4y↑1

THESE NAMES ARE TOO LONG

@cryptonym1214

Udayaditya Bhattacharyya No matter what, it is 勾股定理 because Chinese prove it first.

@HRicKbelo

how can you prove that the line who conect the two centers is parallel to the side of the square?

@DanBurgaud

THAT was so simple!

@yoloswag6242

4y↑3

LOL this is the most alternative history version of math class i've ever seen

@afarhan21

@mcbotface

Sir, could you prove that the line segnent joining the centres of the circles bisects the side of the square ?

@abhishekhurkadli4183

Can the solution be 0.5 if we rotate square 45* even its area remains same and now the diagonal length is 1so the side will be 1/√2 the area will be 1/√2×1/√2=1/2=0.5

@social6332

you are so smart!

@hanantabacaro7532

Why does the connecting line between the two centers biceps the side of the square?

@amyrahmadanti2971

What's the name of the music at the beginning of the video?

@dikshitaagnihotri

Sir great of you to use the name of our ancient mathematician Brahmagupta... Your questions are awesome.. keep helping us to want to master maths

@chengkakful

Is there anythi g on the area of a star with all lines equal?

@Tiqerboy

My solution was similar to yours except I used Al-Kashi's law of cosines, so there!

@mohammadelsayed5715

Great video

@homopolemicus3449

4y↑12

Nice problem. However the historical Polemic of naming a theorem on who discovered it first isn’t quite right. The question is who gave the theorem prominence and who made its use prolific. The world we live in today was created with knowledge gained from the greeks. The chinese and Egyptians may have also found this but that route was truncated and became obsolete.

@maaifoediedelarey4335

Whoever applied it first for a significantly useful purpose, should be the name carrier.

@dhruva8538

Original inventor Indian Bauddhyan give credit to original painstaking research not the one who copied it and broadcasted it as his own

@homopolemicus3449

Maaifoedie De La Rey, The point is that the transmission came from the greeks to the modern era and its use, refinement and propagation occurred in the west. Other may have come up with it simultaneously but they can’t take credit for it’s almost universal usage now.

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