Exploring the Golden Ratio in Hexadecimal: How to Calculate the First 50 Digits

In summary, the conversation is about someone looking for a program or place to obtain or compute the first 50 digits in the hexadecimal representation of the golden ratio, ##(1+\sqrt{5})/2##. They have found the golden ratio up to 1,000 digits in decimal, but are unable to convert it into hexadecimal using built-in methods in Python and Mathematica. They are asking for suggestions or help in converting this ratio into hexadecimal for a personal project.
  • #1
Malamala
299
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I am not sure if this is the right section for this, but i didn't find it anywhere and I really need it. Can someone point me towards a place/tell me a program where I can get/compute the first (at least) 50 digits in the hexadecimal representation of the golden ratio? Thank you!
 
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  • #2
Ration or ratio? You typed it twice (once in the title and once in your post), so it seems like it's not a typo. But what is the Golden Ration? Can you post a link?
 
  • #3
berkeman said:
Ration or ratio? You typed it twice (once in the title and once in your post), so it seems like it's not a typo. But what is the Golden Ration? Can you post a link?
Oh sorry I meant ratio: ##(1+\sqrt{5})/2##. (It actually appears ratio in the title for me)
 
  • #4
Malamala said:
I am not sure if this is the right section for this, but i didn't find it anywhere and I really need it. Can someone point me towards a place/tell me a program where I can get/compute the first (at least) 50 digits in the hexadecimal representation of the golden ration? Thank you!
I have found the golden ratio up to 1,000 digits, however, decimal. I guess you will have to write your own program to convert it. I don't think converters on the internet allow so many digits.

Btw., why do you want to know this?

Edit: In order to forget the link again, here are the decimal digits:
6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144381497587012203408058879544547492461856953648644492410443207713449470495658467885098743394422125448770664780915884607499887124007652170575179788341662562494075890697040002812104276217711177780531531714101170466659914669798731761356006708748071013179523689427521948435305678300228785699782977834784587822891109762500302696156170025046433824377648610283831268330372429267526311653392473167111211588186385133162038400522216579128667529465490681131715993432359734949850904094762132229810172610705961164562990981629055520852479035240602017279974717534277759277862561943208275051312181562855122248093947123414517022373580577278616008688382952304592647878017889921990270776903895321968198615143780314997411069260886742962267575605231727775203536139362
 
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  • #5
fresh_42 said:
I have found the golden ratio up to 1,000 digits, however, decimal. I guess you will have to write your own program to convert it. I don't think converters on the internet allow so many digits.

Btw., why do you want to know this?
It's just for a personal project. I tried with Python and Mathematica, but they don't give me enough digits (the built in methods, i mean)
 
  • #6
You could convert it into binary and then into hex. But you probably have to write your own program.
 
  • #7
Malamala said:
(It actually appears ratio in the title for me)
Yes, it looks like one of the other very helpful Mentors has fixed the typo in your title now 😉
 
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What is the golden ratio in hexadecimal?

The golden ratio in hexadecimal is a mathematical constant, approximately equal to 1.618033988749895, that is often found in nature and has been used in various fields such as art, architecture, and design.

How is the golden ratio represented in hexadecimal?

In hexadecimal, the golden ratio is represented as 1.9E3779B97F4A7C15F39CC0605CEDC834.

How is the golden ratio used in design and art?

The golden ratio is believed to create aesthetically pleasing proportions and is often used as a design and composition tool in art and design. It is used to create balance, harmony, and symmetry in various visual elements such as paintings, photographs, and logos.

What is the connection between the golden ratio and the Fibonacci sequence?

The golden ratio is closely related to the Fibonacci sequence, where each number is the sum of the two preceding numbers. As the numbers in the sequence get larger, the ratio between them approaches the golden ratio. This relationship is seen in the spirals found in nature, such as sunflowers and seashells.

Are there any practical applications of the golden ratio in hexadecimal?

The golden ratio in hexadecimal has been used in various fields such as cryptography, coding, and data compression. It is also used in computer graphics to create realistic and visually appealing images. However, its practical applications are still being explored and researched.

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