What are its uses in the real world?
In: 79
~~A0 A1 A2 A3 A4 papers, the ratio between the sides is the golden ratio, which allows you to cut A0 in half and get A1, in half again and your get A2 in half again and your get A3 and so on. Because the ratio is constant after you cut it.~~
I was wrong
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
Few, since it has no practical relationship to physics (there is something called the golden chain model). No applications in physics means no applications in engineering.
So it’s kind of just a geometrical/mathematical play thing.
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Few, since it has no practical relationship to physics (there is something called the golden chain model). No applications in physics means no applications in engineering.
So it’s kind of just a geometrical/mathematical play thing.
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Ok so you’re a 5 year old. Would you date a 15 year old? No way! That’s way too old!
Let’s say you are 15, would you date a 25 year old? No way! Too old still!
Now you are 25, would you date a 35 year old? Yeah, maybe, it’s a bit of an age gap but not too unreasonable.
Now you are 35, would you date a 45 year old? Sure. That’s not weird.
The golden ratio is a handy formula that helps people identify a generally acceptable age range for a romantic partner. Take your age, divide it in half, and add 7. That’s the minimum age you could date.
Ok so you’re a 5 year old. Would you date a 15 year old? No way! That’s way too old!
Let’s say you are 15, would you date a 25 year old? No way! Too old still!
Now you are 25, would you date a 35 year old? Yeah, maybe, it’s a bit of an age gap but not too unreasonable.
Now you are 35, would you date a 45 year old? Sure. That’s not weird.
The golden ratio is a handy formula that helps people identify a generally acceptable age range for a romantic partner. Take your age, divide it in half, and add 7. That’s the minimum age you could date.
If you’re a flower, your subsequent petals are of a consistent angle with each other. What angle is that?
Simulate a petal arrangement based on whatever angle of your choice. They’d all look horrible the more rational the angles are.
Nature uses the golden angle, derived from the golden ratio, to ensure maximum petals with minimum overlap.
Nature has decided that it doesn’t get more irrational than the golden ratio.
If you’re a flower, your subsequent petals are of a consistent angle with each other. What angle is that?
Simulate a petal arrangement based on whatever angle of your choice. They’d all look horrible the more rational the angles are.
Nature uses the golden angle, derived from the golden ratio, to ensure maximum petals with minimum overlap.
Nature has decided that it doesn’t get more irrational than the golden ratio.
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