Author |
Topic: Fractions (Read 840 times) |
|
Benny
Uberpuzzler
Gender: 
Posts: 1024
|
A unit fraction is a rational number with numerator 1. Is it true that every positive rational number can be written as the sum of distinct positive unit fractions? If so, how do you do it; if not, why not?
|
|
 IP Logged |
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
|
|
|
Eigenray
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 1948
|
 |
Re: Fractions
« Reply #1 on: Feb 18th, 2008, 11:27am » |
 Quote  Modify
|
The greedy algorithm does work. Try to find a pattern.
|
|
IP Logged |
|
|
|
Benny
Uberpuzzler
Gender:
Posts: 1024
|
|
Re: Fractions
« Reply #2 on: Feb 18th, 2008, 12:43pm » |
Quote Modify
|
I searched and found a link that helps
http://kevingong.com/Math/EgyptianFractions.pdf
|
|
IP Logged |
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
|
|
|
cool_joh
Guest
|
This may help.
|
|
IP Logged |
|
|
|
Eigenray
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 1948
|
|
Re: Fractions
« Reply #4 on: Feb 18th, 2008, 7:50pm » |
Quote Modify
|
When applying the greedy algorithm to x, the first n terms are Hn = 1+1/2+1/3+...+1/n, the largest harmonic number < x. After this, we always take the largest unit fraction less than the remainder. Once we reach this point, what happens to the numerator of the remainder?
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print
Remove