Golden Ratio Visual Computation

This is a short, animated visual proof of showing how to compute the value of the golden ratio (which is the positive number satisfying x=1+1/x) without using the quadratic formula explicitly. Instead, we use a Tatami diagram and compute the areas of the included rectangles and squares to find the total area of the outer square in two ways.. #manim #math #mathvideo #goldenratio #goldensection #mathshorts #geometry #animation #theorem #pww #proofwithoutwords #visualproof #proof #area #algebra #pww​​ ​ #proof​ #areas #mathematics​​ #mtbos

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[mathflipped]

Interesting way to solve an equation geometrically. Great job!

[Tezhut]

I had never seen this method before. Very good stuff.

[Leonar]

Gorgeous! My compliments for this really nice animation (and, of course, to the author of the original paper) :D

[kleincio]

Congrats for your channel, you're a hero, thank you for ur content.

[Tiggster-qrmw]

Alternatively, you could have solved the equation like
x = 1 + 1/x
x = x/x + 1/x
x = (x+1)/x
x^2 = x+1
x^2 - x - 1 = 0
Then, by the quadratic formula,
x = [-(-1) +or- (1^2 - 4 (1)(-1))^0.5]/2(1) = (1+5^0.5)/2 or (1-5^0.5)/2, and we reject the latter, due to the problem stating that x must be positive.

[phiarchitect]

And now we know why 5 is at the heart of the golden ratio.

[gg-neqw]

pizza mozzarella pizza mozzarella rella rella rella rella

[Mutual_Information]

lol this channel has the greatest music for math in the game

[thomasolson]

I like to try to turn these types of things which are x^2-x-1 into a*x^2+b*x+c. Don't know if I can on this. Will try it later.

[danhadaway]

Great video - love this channel!

But there’s one thing this math amateur is still not understanding.

I can see how you get from your givens (x>0, x=1+1/x) to the number, Phi. But why did you choose your givens? How is “x” Phi?

[benjaminlum]

Ohh so that's where the square root of 5 comes from!

[chrisalex]

Math is unintuitive to most people because it describes the process of reality, not the existence itself. What I mean is that everything in math is taken from its context and turned into numbers and variables, which can only provide an extremely exact and thorough, yet overly technical, expression of the universe. That is fascinating in its own right, but I feel like people who are really good at math, lack the sensibility to see the universe as it actually is. In other words, the universe as seen through math is always described. The universe as seen by human beings is experienced. Math describes the experience to perfection, even the physics of gravity. Because of this, math allows for the manipulation and accurate interaction with our universe in ways that generate real results for everyone. The problem is not in what math is, but in what it is not. Math lacks the totality of what something is precisely because its nature is to break things down from their whole in order to describe how that whole is composed in the first place. Therefore, the only kind of math professor who could ever truly teach math to everyone is one that is also sensitive to reality with a total absence of math. Only that kind of person could teach math to anyone. This video is not an example of that because it is all description. There's no actual explanation of the process itself. Listing the steps is not an explanation, but only an instruction. In short, math today lacks explanations. The only thing that links reality to math is the reasoning behind it. Most mathematicians are only concerned with solving problems (in other words learning math by doing math), not by actually understanding the reasoning behind it in a non mathematical way. In fact, they usually try to turn problems into mathematical concepts as soon as they encounter them. This creates a total disconnect between the world in which people actually live, and the incredibly complex mathematical ways that exist to understand it through description.

Imagine the golden pyramid, not its dimensions, not its perfect proportions, but just the pyramid itself. What does it make you feel? Can feeling ever be linked to math? Not really. By its very nature, reality and math can only be linked by the person doing the math. The problem lies in that usually that person tends to also see the universe as a mathematical description. Einstein might have been someone who understood both, which is why he linked math to reality through imagination. He worked backwards, not seeking to describe reality but experiencing reality in his mind and then finding the mathematical descriptions as to why reality is what it is. Most mathematicians don't work like that. They tend to think of ways of defining the workings of reality rather than experience them first and then let that experience (through imagination) find its correct place in a mathematical description. I wrote this long comment because this video made me truly realize today why most people are not good a math. Most people who are good at math, have always been good at it. The real interesting event would be to see a person that is bad a math become a genius at it. Goodnight

[aazam]

It have 2 solution
x = (1 ± √5)/2
❤

[grahamgrover]

I need help. I'm confused by the x = 1 + 1/x VS x = 1 - 1/x

[NohFR-]

Hontoni... Hontoni, nante toi mawari michi...