Mathologer - 2018-05-11
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) So you all know the golden (ratio) spiral. But did you know that not only the golden ratio but really every number has such a spiral associated with it? And that this spiral provides key insights into the nature of a number. Featuring more proofs by contradiction by infinite descent (my current obsession), infinite continued fractions, etc. Here are some articles that debunk a lot of the golden spiral in nature nonsense: Clement Falbo http://web.sonoma.edu/Math/faculty/falbo/cmj123-134 George Hart http://www.georgehart.com/rp/replicator/replicator.html https://www.youtube.com/channel/UCTl0dASnxto6j2wlVs5Bs2Q Keith Devlin http://devlinsangle.blogspot.com.au/2017/04/fibonacci-and-golden-ratio-madness.html Here is a very good website devoted to everything to do with the golden ratio and Fibonacci http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html Thank you very much to Michael (editing), Marty (nitpicking) and Danil (translating). Enjoy!
9:24 "So we conclude that 3 is irrational."
Whoa, that's quite the jump there.
He meant root 3 but forgot the root part
+Seth Person "whoa that's quite the jump there." No, he just tripped on a root.
yup root 3, but not 3
@RegalT-type r/woooosh
OH MY GOD I CAN'T BELIEVE YOU DIDN'T GET THAT HE JUST FORGOT THE ROOT PART. IT'S ALMOST LIKE YOU ARE STUPID INTENTIONALLY. WHAT IS WRONG WITH YOU.
You can't blame people for loving really thicc golden spirals, that's kink shaming.
No pee jokes!
I don't need you trying to shame my need to label aberrant behavior.
lol
21:35...
Well, it depends if the satellite image is from the northern or southern hemisphere. That island kind of looks like a mirrored Iceland, which would make sense, since that spiral is only cyclonic in the southern hemisphere. The image would have to be flipped for the spiral to by cyclonic in the northern hemisphere. And that is a low pressure system (hence the clouds), so it must be associated with a cyclone, not an anticyclone.
Yep, exactly. That is what the spiral of a southern hemisphere cyclone looks like.
Oh it’s a mirrored image didn’t expect that
But now I think about it, flipped the image is easier than changing the direction of the cyclone
Changing the direction of the golden spiral would be easy.
loved the trump spiral
Nobody makes a better spiral. It's yuge. It's the best spiral ever. That, I can tell you. Make spirals great again!
He's the only thing more irrational than Φ
Φ on him, I say.
I mean, he has a "very, very good brain", so it is only natural that it produces the best spiral ever.
Elliot Grey your comment deserves more likes.
Numberphile rivalry intensifies.
Mathologer ftw
For the final puzzle, the land mass on the top left looks like iceland so this is the north hemisphere, hurricanes in the north hemipshere always go counter clockwise because of the rotation of the earth.
Spot on :)
yep, the image is horizontally flipped
every video you make is a work of art! please upload more ♥
Why are so many people talking about logarithmic spirals all of a sudden?
Mandolinic k.gif
Probably because youtubers can't come up with stuff themselves, so they just repeat whatever others have already posted, trying to generate views from that.
Mandolinic the exact opposite actually.
Nice video!
I love what you do
I think you should do a video about this interesting 4D 2x2x2x2 Rubik's cube in this video: https://youtu.be/kz7Skx5VS_Y
Youtubers tend to get inspired by other Youtubers. This happens with Mathtubers as well. So, you'll see this happen a lot. Especially if a Numberphile video becomes really popular, because Numberphile is aimed more at the general public and the Mathtubers with more advanced audiences want to go into deeper detail.
So, the golden ratio lies between 1 and sqrt(5).
Never thought of (1+root 5 )/2 as an average. Nice :)
Mathologer I wonder if one could define a set of ratios as the whatever mean of 1 and root 5, and whether or not those ratios would have any interesting properties.
Duh!
Mathloger, every time when I see something on Youtube about the Golden Ratio I always wonder why is not shown the relation between the right triangle (with sides 1 and 2 ...while the hypotenuse is √5) and the circle. That puts the sunflower seed spreading/growth into a new light...
math - nothing two b squared of
This is really funny :)
2b^2(m8) - two be squared of m-eight, but that would be a bit too complex, since you have to assume 2b^2 for function
Have I missed it being 'ratio day' today?
Awesome, as always! :)
My guess would be that the fact about the greatest common divisor at 12:03 is due to the Euclidean algorithm (speaking of Greek mathematicians :) ). The construction of the spiral is essentially a visualisation of this algorithm, which is quite an efficient way of computing GCD.
Spot on :)
The x solution is the golden ratio, the thing the numbers have in common is that they are all part of the Fibonacci sequence
Which is also not a coincidence :)
Mathologer well I pretty much guessed it was the golden ratio once I saw the Fibonacci sequence :)
Because the golden ratio comes up in the closed form expression for the n-th Fibonacci number, of course.
Tim Rowe well that much is obvious lol
Probably obvious to anyone who gets this far in a Mathlogger comments section, anyway. Not to everyone. :)
the cyclone is going the wrong way. they spin counter-clockwise in the northern hemisphere, and thats clearly iceland
In order to go clockwise in the northern hemisphere, it would have to be a high-pressure cyclone, but we don't generally get those on Earth.
12:02 Oh wait that's Euclid's Algorithm isn' it? For some reason I feel so happy to realize that lol
Literally a combination of the topics in the 2 most recent Numberphile videos, but with a lot added and done in classic Mathologer style. I'm not complaining at all, just makes me a tad suspicious! ;)
What about non-quadratic irrationals like pi and e? What are the properties of their spirals?
Actually e has a spiral with a nice pattern whereas pi's spiral a bit all over the place. Just have a look at the video I link to at the end which talks about this in terms of continued fractions :)
Wow! This was again a very amazing video by Mathologer. Math is so magic.
um dude idk if trumps hair can be described as nature
Funny story, my dad used to work on his property in Florida, and he swears that before he started running for office he had a lot less hair. So... not much natural about it.
WHEREVER THERE'S NUMBER, THERE'S BEAUTY. LOVE THIS CHANNEL.<3
1:17 had my crackin' up! I love this channel.
Wait, so you're telling me Gyro Zeppeli was lying to me?
Solution of puzzle: Euclid's Algorithm for the gcd puzzle
What? 😲😞😟... Are you really saying it is an urban legend that cats know the Fibonacci sequence as evidence by them seeking out positions of the golden spiral? .... How can this be .... 😒🙁😔😢😢😭,,
"And we can conclude that three is irrational" :P
Great video as always. There was an empty place for silver and other metalic ratios. Hope to see more on that. Also you promised a video on P and NP stuff.
18:32 is now my ringtone//
Would this work for 3 dimensions as well? i.e. for cube roots? My first thought when I saw the infinite spiral was if pi could be drawn like that. Then I remembered it can't because pi is transcendental.
12:07 - I shouted Euclid’s Algorithm before you even asked for it!
I love your videos. I would have loved to have you as my teacher when I was a younger student (which I'm not). I'll suggest my son, who is 17, to watch at your channel. Great job!!!
12:15 that’s just a visual version of the Euclidean algorithm. Very nice link
An elegant presentation of how elegant math(s) can be at times.
Even by the standards of your channel, this was an absolutely exceptional video. It's a masterful example of clear explanations. Awesome.
This really made my day!!! <3
The final square side’s length is due to the Euclidean algorithm which says that ( if a>b):
gcd(a,b)=gcd(a-b,b)
A great video!!
Great explanation on continued fractions! It's interesting how you use geometric modelling instead of the more common algebraic proofs :)
Thank you for making this. It's my favorite video on this channel so far. :)
Hi Mathologer, I love your videos.
What happens when we try making spirals with cubic, quartic root numbers? How does it change from the quadratic case? And then, how does it then change when we move on to quintic roots, as there is no general quintic root formula? Finally, and most importantly, how does the picture change when we used transcendental numbers?
This channel is so good... Your nickname should be Mr. Insight
:)
17:55 The solution is the golden Ratio x1= (1+sqrt(5))/2 x2= (1-sqrt(5))/2
Great video as always ! Really interesting visualization !
Random comment : As showing that any periodic spiral is related to a quadratic formula is simple but the reverse is hard, is it possible to create the cryptographic function from it?
When it clicked that the finite spirals were just visualizations of the Euclidean Algorithm...awesome
Love that shirt!
I like this themed bunch of videos. This should happen more often. You all should talk to each other and do some sort of themed week as a collaboration
1:18 ahahhaha 😂
iI like how you called Euler "one of the USUAL SUSPECTS "
1:17 XDDDDDDDDDDDDDDDDDDDDDDDDDDD
Great video!
One can construct the square spiral of an irrational number, provided their continued fraction is known (and vice versa). But about those irrational numbers which have "kind of continued fraction" like the one in the link below:
https://goo.gl/images/VYSGZN?
1:43 T H I C C
hauslerful - 2018-05-11
Is it a coincidence that Numberphile talked about this as well at the same day? :)
LifeUnder TheMicroscope - 2018-09-28
They are both scum and receive a check to hand nothing but continued ignorance to people.
Nature has similarities and not identicalities. Instead of acknowledge this they play off of this to do more harm in their agenda based educating.
Samuel B. - 2018-11-26
Coincidence is an intersection of probabilities, so yes.
randOmmm - 2019-02-08
Bulk Logan They seem to go on endlessly. Maybe they should start a series on these fractions.. to be continued.
Michael Frith - 2019-11-29
One the golden ratio is in all things. It's changes depending on the magnetic fields, dielectric fields resonance.
well, shit - 2020-01-02
@Marc Telfer Iceland dont have hurricanes though
Oh wait that's pretty far from the country nvm