Author |
Topic: one mile straight line with 'not enough' tools (Read 441 times) |
|
gkwal
Newbie
Posts: 25
|
 |
one mile straight line with 'not enough' tools
« on: Jul 16th, 2007, 9:22pm » |
 Quote  Modify
|
Suppose that you must draw a straight line between points a mile apart. Your tools are a geometer's straight-edge and compass of normal size. How do you proceed?
|
|
 IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender: 
Posts: 13730
|
|
Re: one mile straight line with 'not enough' tools
« Reply #1 on: Jul 17th, 2007, 1:55am » |
Quote Modify
|
Can't you just shift the straightedge a bit each time? You can always pack to points on the line, and extend the line through them.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
pex
Uberpuzzler
Gender:
Posts: 880
|
|
Re: one mile straight line with 'not enough' tools
« Reply #2 on: Jul 17th, 2007, 2:21am » |
Quote Modify
|
on Jul 17th, 2007, 1:55am, towr wrote:| Can't you just shift the straightedge a bit each time? You can always pack to points on the line, and extend the line through them. |
|
Presumably the endpoints are given, in which case this doesn't work.
Preliminary thought: | hidden: | | starting from one endpoint, draw a sequence of circles whose midpoints lie on a straight line, such that the first midpoint is the endpoint and each further midpoint lies on both "adjacent" circles. (The straightedge can be used to make sure the midpoints line up.) Doing the same thing starting from the other endpoint, and making sure we are drawing the same number of circles at both ends, at least we can find points P and Q such that |PA| = |QB|. Maybe something like this can be used for a repeated bisection of AB? (Of course, there is a lot of work to be done, but something like this might work.) |
|
|
IP Logged |
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: one mile straight line with 'not enough' tools
« Reply #3 on: Jul 17th, 2007, 6:12am » |
Quote Modify
|
Hmm... for what it is worth, I'd use some thread and red powder. 
|
|
IP Logged |
|
|
|
Eigenray
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 1948
|
|
Re: one mile straight line with 'not enough' tools
« Reply #4 on: Jul 18th, 2007, 1:05pm » |
Quote Modify
|
This reminds me somewhat of careful line construction. But I never was any good with geometry.
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print