The fabulous Fibonacci flower formula 

yes!

Instablaster.

Is joy forever

maths made simple

EXTREMELY BEAUTIFUL & ARTISTIC MATHEMATICAL VIDEO. KUDOS TO YOU SIR!

Glad you think so and thank you very much for the compliment :)

+Mathologer yes please keep up all your wonderful work!

one of the best mathematical proof i have ever seen, congratulations

Nobody beats 3Blue1Brown in that area, but this is still fantastic.

@@Mathologer your videos are quite thought 🤔provoking ..finaminal and was part of my inspiration for this theory I've been working for the past few years... and I was wondering if you could check out my video's "best veiw black hole/ partical wave duality" and "talking of [Universal Emulator]" I'm not looking for a math war.. ...I admit I'm atrocious with my notations.... but I'm sure you will under stand everything I was trying to convey and I think I may have found something extra some thing tesla once spoke of and..... you actually just recently uploaded a video about almost exactly the same thing (19th.dd/02.mm/22.yy)..I just dabble with it some times and use the best math I can to describe it.. I find it fun to work large thought equations. 🙂🙂👍

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fat loss srivatsa These are mandalas though.

That's great :)

Me too!!!! Thank you

Great, mission accomplished :)

Same would work for galaxies, right? So now what can we infer about the origin of the universe? God version (which type 'God' not solved): Immaterial** A joins with immaterial B and as a result Material** C exists. Wash rinse repeat. Non-god version: Your video, with math playing the god role. Cuz clearly it's immaterial and clearly is the cause of the material, as its parental marks are everywhere. So: how does immaterial joining immaterial CREATE material? I don't know yet. By indirections, find directions out. *defined as that which is real but neither mass nor energy, so a stasis, set of rules, etc. **defined as that which is real, finite even if iterative, and is somewhere on the energy-mass spectrum.

Brian Outy that is like 20 other videos, not to mention immaterial physics and the existence of indirect effect and maybe even time travel. WHY?

@@brainoutyakabrainout Maybe I am just too stupid to understand what you are saying, but my takeaway from what you said is that it seems like you were presenting a bunch of gibberish or word salad or whatever you want to call it. Maybe it isn't meaningless, but I can't pull anything meaningful from it.

@@alexandertownsend3291 its dunning kruger

Yes, we've had a little party last week :)

Talking about linear algebra, check out 3blue1brown

Glad you like it. You are proving Binet's formula for the nth Fibonacci number using eigenvalues, right ? :)

Mathologer Exactly. I hope to prepare them for the solution of second order differential equations, which they learn a little later in the analysis class. It helps them understand that the term "characteristic polynomial" in both topics is _not_ a misnomer. It really is the same thing. So many more parallels: two basic solutions, two initial conditions determine how the have to be linearly combined.

Some are :) But, to be fair high school teachers simply don't have the two weeks it takes to put something like this together.

We are lucky to be alive now. Just think, a person is able to find so much information just with a few clicks.

You would think they would, after teaching the same course for multiple years.

mathologer are you a teacher in a physical institution, mathologer?

I teach math at Monash University in Australia :)

is the proof in maths? what's the definition of proof here? I have no idea what difference it makes that he proved it if it's just like, true, is he the first person to notice it?

That's great. I usually try to come up with something that you won't find anywhere else :)

How are you 100% certain that they don't do math? They are a living thing, and living things grow. For something to grow, they have to be able to reproduce and communicate. To reproduce is the same as multiplying. If it can multiply then addition is implied. If it can add, it is able to count. If it's able to count it is able to perform calculations and this is math. For something to communicate it must be able to transfer information. In order to transfer information it has to be able to perform calculations. It is my claim that at the least all living things are constantly performing mathematical computations in one way or another. Growing and expanding from DNA instructions, cell reproduction, organ growth, expanding until an age of maturity, reproducing its offspring for the next generation, cycle or iteration. Plants do count! If they couldn't they wouldn't grow! Do you think stars are non living entities or do you think they're living things as well? Within their own environment they are compressing multiple Hydrogen atoms under nuclear fusion and are producing Helium and other heavier elements. They are doing this at an exponential rate governed by at the least quantum mechanics as we currently understand it, and we still don't fully understand it. We are able to count and perform math, yet we are still feeble minded compared to that of the power of the stars. So please tell me again how and why plants can't do math? The Cosmos including our known visible Universe and all that lies beyond I is counting. How and why? Everything is in motion and if something is able to move, it's able to count. And the Cosmos, Universe is moving. It is continuously counting and thus it is a living thing. When I state living, I'm not narrowed to the view that all living things must be "carbon" based. Life here on Earth as we know it within its environment and conditions requires carbon to be considered organic life. Yet we have no understanding of all the possibilities that life can present through the stars. How do we not know that there isn't some arbitrary planet that orbits some arbitrary star has a form of life that is bizarre to us where the conditions there for life as we know it we could not survive its extremely harsh environment for our biological compositions. Take for example, a B or an O blue star that's anywhere from 2-10 times the diameter of our star with 2-100x its mass, with temperatures that are 3-10x that of our star with a higher luminosity, higher radiation, etc. Let's say that this planet is bigger than a super earth but smaller than a gas or ice giant. Let's say it's roughly 15 - 20 times more massive than our earth. It has a slightly higher density and is extremely hot compared to us. The planet in our terms would be baking, even hotter than Mercury or Venus. Let say that its outer layer does have an atmosphere that isn't conventional for us. Let's say that the first 4-5 transitional metals, Scandium, Titanium, Vanadium, Chromium, and Manganese are in a gaseous state, and the next 4-5 transitional metals, Iron, Cobalt, Nickel, Copper, and Zinc are in a liquid state. And something like Germanium which is still in Group 14 with 4 valence electrons acts similar within this star and planets environment as Carbon and Silicon does for us. Let's say it does have a rocky surface where it's lands or mountains are of the heavier rare earth metals that would normally be radioactive to us. The planet's atmosphere is 10x greater than ours, the temperature is 20x hotter than ours, the pressure is 5x greater, the gravity is 7-12x greater, the radiation is 30x greater and the brightness or luminosity due to its bright blue star is 15x brighter than here on earth. There are rivers and oceans of liquid liquid iron similar to but more fluid than our earth's lava. And how do we not know that there aren't growing living things within that environment? That environment can not support Carbon Based Life as Carbon would melt and then boil away it could never take solid except for maybe in diamonds where those diamonds due to the immense temperature and pressure would be metamorphic between a solid and liquid almost as how mercury acts here on Earth... We think we know life, but we barely understand 10% of it. Hell, I'd argue that we are lucky if we only understand 1% it even with all of our marvelous inventions and technology. Take the carnivorous (meat eating) plants here on earth such as the venus fly trap and others. They are designed by their organic chemical makeup to be lethal predators in the form of a trap. They lure their victims in according to the preference of the type of insect or small creature they prefer... Now tell me that's not calculated precision? Life is everywhere! The Universe is alive and it is always counting!

@@skilz8098 so you wrote all of that to be obtuse in response to a 5 year old comment? Only skimmed it, but no, I don’t think plants “do” math, but that natural selection pressured them into a configuration that we can describe mathematically because it was optimal for its survival. Plants are amazing organisms but they don’t have anything comparable to a brain. Why? Because brains are resource expensive and they don’t need them. They can do everything they need just vibing in the sunlight. I’m jealous honestly.

@@jondreauxlaing You're stating that plants don't have a brain. I think our brains are kind of limited to that of all plant life in some ways. Just look at their root systems! You don't think they have the ability to feel pain, or even emotions? Yes they are different than we are and even animals, but they are very much alive! And all living things have a consciousness and are self aware. They may not ponder questions like we do as to how and why 1+1 = 2. Or they may not exactly try to solve a problem such as y = 3x + 2 solve for x when y = 8. No, but the ability to enumerate or count is built within them all the way down to cell structures and DNA. They take in water, nutrients from the ground, CO2 and Sunlight and from that they sprout from seed, grow, mature and reproduce. We can not even fully replicate photosynthesis that plants do within their chlorophyll that turns the energy of sunlight into food. And yet chlorophyll from plants is vital to our bodies. Even non living things can count when they are instructed to. What do you think your computer is doing? What do you think it is made of? It uses insulators, semiconductors and conductors. The semiconductor of modern practical use is Silicon which comes from either pure silica or from sand and sand comes from rocks and salt. We are carbon based and our semiconductor is primarily carbon. Carbon and Silicon are different but also have very similar properties. They both have 4 valence electrons in their outer shells. They can be arranged in many various configurations and patterns, and they can bond with many other elements depending on the state of matter in which they are in. Even non living things can count. What do you think is smarter, an Apple Tree or your computer? I'd put my money on the Apple Tree as your computer can not do anything unless it is instructed to. An apple tree can grow a new branch, blossom, or fruit at will over the course of time and it can reproduce. Do you see computers having offspring on their own? I don't bound my mind to deterministic boundaries or limitations by the "status quo". I don't think inside nor outside of the box. I create and destroy that box at will. There are no limitations within my mindset as I believe that anything and everything is possible! If one can imagine it, even if it doesn't make sense to others, it becomes manifested by the thoughts of it alone!

@@skilz8098 k

@@jondreauxlaing It's just food for thought!

:)

I wonder if visual, elegant proofs would help young students learn the idea of "proof".

videos exhibit* the "are" was accidental.

I use a whole range of applications for making these videos: Adobe Illustrator, Photoshop, Premier and After Effect, Mathematica. Having said that a lot of the animations use Apple's Keynote presentation software and in particular the "Magic Moves" transitions. It's quite remarkable how much you can achieve in this way :)

:)

The numbers of red and green spirals that you start with is not important for all this to work. In this case there are 15 green spirals and 18 red spirals overall. The numbers of that jump out on the path that I follow are really my choices. I could change direction earlier or later as long as I end up with a closed path the proof will go through as I showed. But as you say, it's important to pay attention to such details as you are often lead to interesting facts this way :)

There is a Rubik's cube themed video coming up next. After that I'll do one exclusively on dealing with all sorts of infinite expressions. That one will also cover the 1=2 puzzle. In the meantime maybe browse some of the great answers to the puzzle that were contributed in the comments section of that video :)

Your content is really high quality and I'm looking forward to whatever's coming next. Thanks a lot for all of these!

+Mathologer Rest assured my experience of the video was enhanced :)

:)

Yes, there is a lot more that one can and has been said about all this. Amazing insights wherever you look. I'd be interested in seeing that spiral-based variation of the disappearing piece illusion. Not sure whether you've seen the version where you cut up a square piece of chocolate with sides a Fibonacci number arranging the cuts based on the previous two Fibonacci numbers. E.g. in the version that I sometime use an 8x8=64 is cut up into four pieces that then get rearranged into a 5x13=65 rectangle. All this is based on the fact that f_i f_{i+2}=±f_{i+1} :)

Maybe you are right, I can't find it either. Akio Hizume is the name of the guy who made that puzzle. This is the bottom part of the puzzle (gallery.bridgesmathart.org/sites/default/files/styles/large/public/bridges2014/akio-hizume/cimg2988.jpg?itok=xEYB667j) and he has also made this cool clip (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-PDK8RonFBe4.html).

I think the book 'Foucault's Pendulum' by Umberto Eco would be something for you www.goodreads.com/book/show/17841.Foucault_s_Pendulum The whole book/story is making fun of numerology, esoterics and conspiracy theories of all kinds.

Great :)

And it's only one week old :)

how do you feel about editing?