Undergrad How Can You Calculate the First 50 Digits of the Golden Ratio in Hexadecimal?

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SUMMARY

The discussion focuses on calculating the first 50 digits of the golden ratio (φ) in hexadecimal format. Users suggest that existing online converters may not support such precision, and recommend writing custom programs for conversion. Python and Mathematica are mentioned as tools that can be utilized, although their built-in methods may not yield sufficient digits. The golden ratio is defined mathematically as (1 + √5) / 2.

PREREQUISITES
  • Understanding of the golden ratio and its mathematical representation
  • Familiarity with programming in Python and Mathematica
  • Knowledge of number base conversions (decimal to binary to hexadecimal)
  • Experience with writing custom algorithms for numerical computations
NEXT STEPS
  • Research how to implement arbitrary precision arithmetic in Python using libraries like mpmath
  • Explore Mathematica's capabilities for high-precision calculations
  • Learn about algorithms for converting decimal numbers to hexadecimal
  • Investigate existing libraries or tools that can compute the golden ratio to high precision
USEFUL FOR

Mathematicians, software developers, and hobbyists interested in numerical computing and high-precision calculations of mathematical constants.

Malamala
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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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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?
 
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)
 
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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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)
 
You could convert it into binary and then into hex. But you probably have to write your own program.
 
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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