Sequences 5: Golden Rectangles

[spenc193]

The golden ratio is used everywhere in the media and elsewhere. Alot of old furniture used to use this ratio in its design. It appears more perfect to the human eye...wonder why that is ;).

Probably because its at the heart of creation.

[waltbeale]

This is the ONLY interesting thing about math that I have ever seen...

[latinflip325]

so i have to do an essay on this... how the fuck do i explain this without drawing it D:

[Naptitude]

Why the fuck am I watching this. D: I'm horrible at math

[bananatheory]

Anyone notice Twitter's most recent layout design? Yep. It's golden.

[TMOMFXD]

i just like how happy he looks when he does maths

[Freddie181]

now if i could apply it to life :)

[IslamChika]

You have no idea how excited this made me! Math is so awesome! Man, I missed it.

Great set of videos you've got here.

[GogatsuKyu]

What was the curve's circumfrence in the beginning?

[arenics]

thank you master.

[TwoDigitz]

Hey thanx Lowie i see it now, it was the fact that the drop down looked too free hand obviously the guy can free hand squares better than circles but im not making excuses for my foggy attention span because its staring me in the face. I wonder is it possible to work out how you would create a golden triangle using this same method ?

[kquah]

clearest explaination on the internet!

[TwoDigitz]

Very interesting stuff but i dont understand why the "Drop Down" line is so arbitrary ?

[lowie1771]

@TwoDigitz it is a circle using the radius; the segment from the midpoint of the square to the corner is root 5 in a 2by2 square.

[superninjaspy]

@TwoDigitz | I understand what he's doing but I have no idea why he didn't just use a compass or a string or something to show that it was a circle.

[pbhlcm]

This man deserves a medal.

[TheSilligirl]

How the hell can this video get a disslike?

[vhingsky]

thanks sir! its been a great help for creating my floor plan....

[Jgewelz]

yah..

so how do we use it to ttake over the world?

[VoteforJimJepson]

There's nothing gold about it.

[velociraptorTheone]

WWWwwwwoooooooooooooooooWWWWWW­WWWWWWWW, i get it, i get it

[rajasta22]

it's a bit slow.

but it's nice anyway. doing mathematics is like attending a mass a 1000 years ago: you feel connected to (and part of) everything

[hyperhumana]

dziadek!

jesteś jebnięty!

ale kocham Cię!

pijany filozof z Polski.

[DJPirrone]

What a great guy

[goatnuts8288]

This made me shit my pants.

[airbrusherz]

this video is well done. I have seen many videos of people hacking through instructions on how to make the golden rectangle. Its refreshing to see someone do it right.

[cutiesing3]

thankyou thankyou thankyou thankyou thankyou!!!!!!!!!!!!!!!!!

[kurleyfries93]

Okay it's a ratio. What's the point?

[kurleyfries93]

@asolutionforyou And what the heck is your point? I said ratio bro

[Yezpahr]

OK, so you convinced man-kind of the Golden Ratio.

Now get that smirk off your face!!

Good movie.

[andymillerisdabest]

The bit that I don't get is at 0:30 when he draws the arc down. There doesn't appear to be any control over it, it was just a freehand arc - surely it could have landed an inch or so to the left or right?

Please don't flame me, but if anyone can help me out, it'd be appreciated.

[mikevanderheiden]

@andymillerisdabest Im not sure why he left this out on the video but: If you have a compass place the point on the middle of the bottom of the square ( where its divided) lengthen the compass so it aligns to the top of the corner of the square( where he begins to draw) and swing the arc down. He should hand draw it since its not accurate. hope this is helpful

[melinatrix]

Thanks for your explainations, very clear. Did you see Nature by numbers video? I have a question about the hexagons if you don't mind I will ask. thanks

[MsNazi777]

You are awesome

[superuser6]

This feels a bit random.

[Hijabi101]

THANKS SOOOOOO MUCH HELPED SOOOO MUCH

[Hijabi101]

omg thanks so muchhhhh this helped sooooooooooooooo much :)

[tttybhgf]

Ever heard of the platinum ratio? It kicks ass

[LAURATHEALIEN]

thank you mr.God

[mikedjmix]

i am lost...

[IrnBruFiend]

Awesome, thanks this helped!

[frostyfredson]

Drop it down? You need to explain that this is done with a compass and has to be precise in order to represent the golden ratio. This is a critical step that you are leaving out. This will leave students confused and misinformed.

[MarioMario666]

@frostyfredson Thank you. "Drop it down" is not mathmatics

[lolzorsPwnage]

Hey i cant here the fucking video because of the coolness of this old man breaking it down

[Jbeliski]

Oh O get it, why didn't the guy just say it. I mean he's taking the time to make this and he's leaving out obvious stuff. And why does he say drop it down. What kind of mathematical term is this? Geeze

[Jbeliski]

How did you measure the ARC degree drop!!!!!!!!!!!

[WoWKoest]

90 deg. arc is easy to approximate.

[jetsonjoe]

You neglect one very important step to the understanding of this process...the divided square base...the diagonal you create....this end point on the base is anchored...fixed...to assist to create the arc...the other point of the angle line ...is the end of the line...which forms the arc...in case anyone was wondering how the heck he got this arc and from what...Important step to the understanding and construction..

[MujagaWudakhi]

GREAT VIDEO... really helped me with my college task!!! muwu Croatia!!!

[antihero1980]

you are supposed to use a compass when you drop it down.

you would put one side of the compass to the mid point on one of the sides and the other side of the compass to the corner of the square.

follow the diagonal line.

[HaoProductions3]

i dont understand the part where he drops the rounded part from the top right vertex of the square. Arent you supposed to measure it? Is it supposed to the circle from the midpoint of the base of the square?

[pockmarkedbuttocks]

poopyshart! just kidding. I was hoping to here about the chambered nautilus....

[fulltimepassgiri]

Thanks for the awesome and clean explanation.

[nillawafer96]

at 1:22 how did he get the hypotenuse to be the square root of 5?

plz answer i need to know!

[ajckiller]

(1² = 1) + (2² = 4) = square root of 5

[TuPP3]

You are stating false equation there

1+4=5 ≠ √5

Correctly: (X is the yet unknown hypotenuse)

1² + 2² = X²

X²=5 | √

X=√5

[novatodeguitarra]

please tell me how do you type the square root the non equal and the square symbols thanks

[TuPP3]

I just copied and pasted them from special characters list (type in google "special characters")

Or you can press ALT down and then type sequence in numpad, like ALT+253=²

Find out those sequences on web.

[HolliValsMusic]

If you'd have been my mathematics teacher I might actually have done something else than just drawing in math classes. I never got what they said, but it all makes sense here.

[mikelmok]

this was so much easier than my architecture teacher.. maybe it was also because i was so tired.

[PunkyBurger]

"...so important they put it on a postage stamp."

[farzero]

Are there any other ratios that create the same perpetual cycle?

[rolfch1p]

Your explanations are very clear and easy to understand.

[vengops]

Gr8 one xD

[ukimia]

thank you soooooooo much

[stameyjd]

yes, yes, yes, BUT HOW DO WE USE IT TO TAKE OVER THE WORLD?

[plurBey0ndL0gicplur]

LOL

[sacred8510]

its easy... just memorize each of the numbers in the golden ratio...

[fulltimepassgiri]

lol awesome comment!!!

[victorolsen1]

@stameyjd hahaha xD !

[mikedjmix]

@stameyjd LMFAO!

[rivers221]

Thank you, you've been a great help

[chrislongden4]

Since this video is titled "Sequences" I was expecting you to explicity link the Golden Ratio to Fibonacci Series. Either way, great video.

[bo0o90]

you are AWESOME

[LordGodofIsrael]

thanks very much for your video, i needed to do this for my interior architecture course and just couldn't understand it when it was written on paper. i guess i'm more of a visual learner :P thanks again.

[FlickDad]

Well paced and informative. I bought a book that talked about this spiral and tried to do it but the book didnt actually tell me how to figure out the dimensions.

Excellent. Thank you.

[Nanumir]

you are awesome, I've been into math for 3+ years now and never saw it this way!

-Mathmithy

[dracentsparkle]

It's called genetic engineering-warping energy into frequencies into vibration. Thanks for the kind sharing*

[25380421859]

nice eyebrows xD

[SherrieLeaLaird]

someone gave you a thumbs down and we gave you a thumbs up and it cancelled itself out and there you have it. More math!!! lol.

But true enough he is Awesome!!!!!!!!!!!!

Illuminati/Freemasons have built and try to destroy a world based on math...

[MathTV]

Interesting Sherrie, I just gave my talk on Islam, Mathematics, and Culture to the Masonic Lodge where I live. I've never been in their building before. It was very enjoyable and they were a very accommodating group. I like your youtube channel.

[25380421859]

thx for that xD

[superpeter238]

wow. this REALLY helped. thanks a lot!

[hedwig63]

the clip is flashing..is there something wrong with the player?

thanks for posting... he is very good.

[katarina68]

Thanks this helped me with my HW a lot!

[stargirlsusan]

good teache better than my teacher

[sz42781]

whats the square rout of this channel

[thesymphoniclife]

u r a very smart individual, thanks for all the help, I have a better chance on the GRE now.

[Blobadelics]

math is boring

[cake89]

lol

[BryceHathaway]

I've always been interested to know whether there is a purely geometric proof that the construction used produces self-similar rectangles. Using algebraic numbers is really quite easy, and I feel offers less insight into what may be a rather deep geometric insight. If I ever find it, I'll post a video.

[80amnesia]

this man is number 1

[rogermoore27]

the best part was when the equation went off the screen. I'm kidding. What I want to know is how do you know how the arc should be drawn?

[skibee50]

he needs to be consistant where he makes his new smaller rectangle so the curve is accurate. But good explaination anyway. Q. How did pathagarus come up with the 3,4,5 therom

[muntasir20]

great vid explianed alot to me when my teachers tryed to explain it i didnt get 1 word thks alot!

[jianchen0628]

Thank yOu for conveying the knowledge!

Simply great! When I need to find this knowledge, U have already explained it in a very comprehensible way. TERIMA KASIH!

[tonyrueb]

also the inverse of the golden ratio 1/1.618 is the one less then the golden ratio 1.618 - 1

so if you do 1/x = x-1 you also get it

[Kizluk]

You can find the golden ration easily by finding the positive solution of the quadratic equation x^2-x-1 = 0.

Use the quadratic formula and you get (1+-sqrt(5))/2

[chopperhead2011]

That's interesting, where did you learn this?

[joshrocks4178]

"so important they put it on a post it stamp"

[andhisband]

He says, "postage stamp." Twice. Did you mis-hear or were you trying to be funny?

[glbert6]

he knows how to find it, but does he know what it means?

[chopperhead2011]

Geometry pwns all

[Mafakae]

hahaha LOL!

[YoungJatt91]

@brco2003 - what he did was he took root20 and split it into root5 and root 4, root4 can be expressed as a whole number as it is not irrational. So root4 become 2 and 2*root5 is equal to root20 (2 * root5 = root20).

[brco2003]

1:40 - why is length root5 (and same for root20 in the next one)???

[Mafakae]

Listen closely to this...

1+0=(1), 1+1=(2), 1+2=(3), 2+3=(5), 3+5=(8), 5+8=(13), 8+13=(21), 13+21=(34), 21+34=(55) etc etc etc

(answer + previous answer = new answer)

Now put all those bracket numbers together:

1, 2, 3, 5, 8, 13, 21, 34, 55 etc etc

all those numbers in order is the ratio: 1.618 (the Golden Mean). Thats the simplist way of finding it out and how it was derived in 'number' concept.

peace and respect!

[Ren520]

can u elaborate more on this?? i dont understand what u mean by the ratio turns out to be 1.618....

[Mafakae]

well if u get one of the answers (which i typed in brackets) and then divided it by the previous answer (in brackets) u get 1.618. eg: 55 divided by 34 = 1.618 or even: 34 divided by 21 = 1.618. That is, 1.618 is called the golden ratio/mean. it is seen in nature pretty much everywhere! the guy in this video is just showing how to work it out and look at it 'visually'

[lipslacedwitpoison]

He just means the ratio of l/w which turns out to be 1 + root 5 over 2: then he just divided to get the decimal.

[decatetron]

This is the Fibonacci sequence. Take any term and divide it by the previous one to get an approximation to the actual value of the Golden Ratio (1+sqrt.5)/2. The larger the number in the sequence you do this with, the close it will approximate the G.R. but it will never be equal!!!

The Fibonacci sequence is not the generating principle behind the Golden Ratio. Its the other way around.

[dantheman163]

sqrt[(-29+sqrt(29^2+4))/(2)+29­+29]-6

[abbesieyes]

test

[ticktockfool]

How would I find the Golden section of a line that was say... 1050 mm long?

[QuadmanSwe]

1050*.618

[daneeehhhh]

great explanation =)

I would have added some information about Fibonacci and what this spirals represent.

Thanks for your time spent in making this great videos !

[khaled9999buet]

I saw this ratio in fibonacci number. kth fibonacci number = nearest integer to (1/sqrt(5))*((1+sqrt(5))/2)^k. - source "intro to linear algebra - Gilbert strang"

[DaanRiver]

good video!

but why is this ratio so special?!

[lofy63]

because the ratio of 1:1.618 is very appealing to the eye, which is found in design, and is also found in nature. you can even find the ratio on the human body: your wrist to the second knuckle on your finger to the the finger tip shares that ratio, as well as your finger tip to your wrist to your elbow shares that ratio. it's basically found everywhere. a very interesting number theory!

[BabyAppleCakes]

I understand everything until you assume that the bottom is 1 + sqrt 5.

Where'd that come from?

[482ksd]

He did not assume that. 1+sqrt(5) is actually the radius of the circle to which that curve belongs. It is actually done by keeping a compass needle on the midpoint of that side and drawing a curve. I think my explanation is not clear enough so please watch the video again.

[devinsbrother]

im a 6th grader in a 8th grade level math class and i have an A,because im a nerd.but this math is crazy hard i dont know wat hes talking about lol

[caspa7]

Then u are definitely NOT a nerd.

[capitalone1]

Well done-this is short,simple and to the point-thankyou

[SnakeCIA1]

yes it appears this is more useful than mapple

[rodrigogalindez]

excellent video!!! thanks :)

[Bonkios]

Muy buen MAESTRO de matematicas. Good job!!!

[Doodsrsly]

Awesome, just awesome!