# Writing an integer as the sum of powers of phi

• BSMSMSTMSPHD
In summary, the person is looking for an online applet that generates the exponents of phi for a given integer. They are unable to remember the specific website and are asking for help in finding it. They also mention the possibility of doing it by hand and provide a website with instructions on how to do so. They thank the person for their help.
BSMSMSTMSPHD
A while back, I found an online applet that was located on the front page of the mathematics department website for some American university. The problem is that I can't remember which university it was, and I'm not succeeding in several searches.

Basically, the way it worked was, you type in any integer, and it produces the exponents of phi that sum to your number. For example, if the number was 521, the exponents would be -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 (which is a nice little pattern...)

Anyway - does anyone know what I'm talking about? Do you know the website I'm referring to? It's quite possible that it has been taken down...

Failing this, is there any method you know of doing this by hand?

Thanks!

Thanks! I had disregarded this site since I found it so hard to read. But, upon finding no other sites, I tried again, and it actually makes a lot of sense.

## What does it mean to write an integer as the sum of powers of phi?

Writing an integer as the sum of powers of phi means expressing a number as a combination of powers of the golden ratio, also known as phi (φ).

## What is the golden ratio or phi (φ)?

The golden ratio, also known as phi (φ), is an irrational number approximately equal to 1.618. It is often represented by the Greek letter phi (φ) and has been studied and used in mathematics and art for centuries.

## How do you write an integer as the sum of powers of phi?

To write an integer as the sum of powers of phi, you can use a process called the "Zeckendorf's theorem." This involves finding the largest power of phi that is less than or equal to the given number, subtracting it, and repeating the process until the remaining number is 0.

## What are some examples of writing an integer as the sum of powers of phi?

For example, the number 15 can be written as 13 + 2, which is 1*φ^3 + 1*φ^1. The number 84 can be written as 55 + 21 + 8, which is 1*φ^10 + 1*φ^8 + 1*φ^6. In general, any positive integer can be written as a unique combination of powers of phi.

## What are the applications of writing an integer as the sum of powers of phi?

Writing an integer as the sum of powers of phi has applications in various fields such as number theory, cryptography, and computer science. It can also be used in designing aesthetically pleasing proportions in art and architecture.

• General Math
Replies
2
Views
1K
• General Math
Replies
2
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
2K
• General Math
Replies
7
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
12
Views
1K
• General Math
Replies
7
Views
1K
• General Math
Replies
5
Views
1K
• General Math
Replies
3
Views
2K
• General Math
Replies
4
Views
672
• Engineering and Comp Sci Homework Help
Replies
7
Views
2K