[Search for users]
[Overall Top Noters]
[List of all Conferences]
[Download this site]
| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
1553.0. "Balanced Products" by CADSYS::COOPER (Topher Cooper) Fri Jan 31 1992 13:00
From: [email protected] (Robert D. Silverman)
Newsgroups: sci.math
Subject: Elementary (counter-intuitive) Puzzle
Message-ID: <[email protected]>
Date: 29 Jan 92 18:38:19 GMT
Sender: [email protected] (News Service)
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Here's a cute puzzle I've been toying with. The answer (at least to me)
was surprisingly counter-intutive.
Consider the set of integers. What fraction of them can be written as a*b
(a,b not necessarily prime) where a and b are nearly equal. I define
'nearly equal' to mean that b/2 <= a <= 2b. In other words, a and b
are within a factor of 2 of one another.
In other words, what is the density of integers N = ab such that
b/2 <= a <= 2b.
The answer surprised me in that
(a) It turned out to have positive density
(b) It was rather high.
Maybe I shouldn't have been surprised.
--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1553.1 | fractions are easy... | CIVAGE::LYNN | Lynn Yarbrough @WNP DTN 427-5663 | Fri Jan 31 1992 13:29 | 1 |
| It's not stated, but I think the proposer assumes a and b are also integers.
|