Honestly, it’s massively blown out of proportion. It is a mathematical relationship which describes the ratio between a regular Pentagon’s side length and diagonal length. It crops up a lot in geometry.

There’s a lot of woo and nonsense about it being related to the shapes and structures of different things – in most cases its bad pattern fitting or just plain nonsense. There are some examples of it cropping up in nature, but no more than other relationships

The vast majority I’ve witnessed has been memes which overlay the Fibonacci spiral over mundane pictures, then claim that whatever clearly mundane thing was framed is perfection manifest.

And, honestly, it’s a good use for it. A lot of the claimed legitimate uses in, say, framing a picture can just as easily be explained by other mathematical relationships or just by appealing to shared intuition. The spiral, and the sequence which underlies it is of very limited practical application, so it’s fitting that most of its uses in the last decade have been internetfolk using it to poke fun at its misapplications.

Trying my best to explain it to a 5 year old here.

Imagine a circle. I tell you to place a point as you travel half way through the circle(1/2 of the circle) , then you can only draw 2 points on the circle before going back to your first point.

If you travel 1/100 th of the circle, you can draw only 100 points on the circle before reaching your first point.

If you want to keep putting points without overlapping the earlier points, normal numbers won’t work, you have to use irrational numbers. The numbers that cannot be represented as a fraction.

There are a few irrational numbers with pi being a famous one. The golden ratio is the most irrational number. Which means it’s the hardest to be represented by a fractions.

You can think of it as the ugliest number without the least symmetry, but that is how tha magic happens.

If you point a point on the circle every 1/goldenratio = 0.6180… You could fit the most number of points on the circle before they overlap each other, because as you keep going arround, you will never reach your first point.

Have you ever seen a flower with lots of petals arranged in a pattern that looks really nice? Or a shell that’s all curly and has a shape that’s pleasing to look at? That’s because the golden ratio was used to make those things look so pretty! Nature wants to arrange the petals so they don’t overlap over each other or grow leaves on a tree to they take the most sunlight, golden ratio is used. Same for drawing and designs.

Honestly, it’s massively blown out of proportion. It is a mathematical relationship which describes the ratio between a regular Pentagon’s side length and diagonal length. It crops up a lot in geometry.

There’s a lot of woo and nonsense about it being related to the shapes and structures of different things – in most cases its bad pattern fitting or just plain nonsense. There are some examples of it cropping up in nature, but no more than other relationships

The vast majority I’ve witnessed has been memes which overlay the Fibonacci spiral over mundane pictures, then claim that whatever clearly mundane thing was framed is perfection manifest.

And, honestly, it’s a good use for it. A lot of the claimed legitimate uses in, say, framing a picture can just as easily be explained by other mathematical relationships or just by appealing to shared intuition. The spiral, and the sequence which underlies it is of very limited practical application, so it’s fitting that most of its uses in the last decade have been internetfolk using it to poke fun at its misapplications.

Trying my best to explain it to a 5 year old here.

Imagine a circle. I tell you to place a point as you travel half way through the circle(1/2 of the circle) , then you can only draw 2 points on the circle before going back to your first point.

If you travel 1/100 th of the circle, you can draw only 100 points on the circle before reaching your first point.

If you want to keep putting points without overlapping the earlier points, normal numbers won’t work, you have to use irrational numbers. The numbers that cannot be represented as a fraction.

There are a few irrational numbers with pi being a famous one. The golden ratio is the most irrational number. Which means it’s the hardest to be represented by a fractions.

You can think of it as the ugliest number without the least symmetry, but that is how tha magic happens.

If you point a point on the circle every 1/goldenratio = 0.6180… You could fit the most number of points on the circle before they overlap each other, because as you keep going arround, you will never reach your first point.

Have you ever seen a flower with lots of petals arranged in a pattern that looks really nice? Or a shell that’s all curly and has a shape that’s pleasing to look at? That’s because the golden ratio was used to make those things look so pretty! Nature wants to arrange the petals so they don’t overlap over each other or grow leaves on a tree to they take the most sunlight, golden ratio is used. Same for drawing and designs.

Short Answer: the golden ratio is the “most” irrational irrational number

Many numbers in math are irrational, meaning there’s no way to represent them as a ratio of 2 integers. However, often times you can approximate them, such as approximating pi as 22/7. It turns out there’s a way to generate these approximations that gets better and better the more iterations you do. These iterations are called continued fractions and each iteration gets more accurate by some amount, some gain a lot of accuracy, some gain the (mathematical) bare minimum.

So the question people had is, “if we find a number that during this process, gains the bare minimum of accuracy per iteration always, it can be considered the “most” irrational number.” And that number is the golden ratio.

Regarding real world uses, it shows up in biology when a plant choses where to grow branches/seeds to try to make sure they never line up. It also shows up in financial modeling and many other non ELI5 things as well.

Video: https://www.youtube.com/watch?v=sj8Sg8qnjOg

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