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Re: Euclid

Posted by Steve Smith on Mar 06, 2015; 4:33pm
URL: http://friam.383.s1.nabble.com/Euclid-tp7586103p7586109.html

Shawn -

Good to hear from you stranger!  

I'm pretty confident in my solution, I'm not sure why the program doesn't acknowledge it.  Do you (or anyone) see any problem with it?

The method was
  1. construct an arbitrary line segment OP through B spanning the circle
  2. construct a parallel line segment MQ to OP through A 
  3. construct rays OM and PQ to find homothetic center R
  4. construct circles of radius RA and RB centered on R
  5. find intersections of each circle at S and T and  U and T
  6. construct rays through RUT and RVS to match the criteria

steps 4 and 5 could delete one of the two substeps as redundant.

not sure how GeoGebra actually determines a match with their own "solution".

Hi Robert, Steve,

One way to arrive at a solution is to make a third circle with radius r2 - r1 (https://en.wikipedia.org/wiki/Tangent_lines_to_circles, under external tangents).  This reduces the problem to finding a tangent to a point outside of the new circle (https://en.wikipedia.org/wiki/Thales%27_theorem, bottom figure for instance). Since the tangent is invariant to this type of transformation, you can scale your solution to the original circles.  Interesting game; thanks for posting.


Shawn


On Sun, Mar 1, 2015 at 11:43 PM, Steve Smith <[hidden email]> wrote:
I am also stuck at 23, but I'm not sure it is from lack of success...
RVS and RUT "should" match the criteria (using your homothetic centers "R" hint).



<img moz-do-not-send="true" alt="" src="imap://sasmyth@mail.swcp.com:993/fetch%3EUID%3E.INBOX%3E91839?header=quotebody/;section=1.2?part=1.1.2&amp;filename=Screen%20Shot%202015-03-01%20at%209.38.50%20PM.png" width="684" height="498">

I had at least one other approach which *also* failed to "pass".  I'm a little unclear on how the "snap to grid" and/or "snap to intersection" works, which *might* be bolloxing things up?

I'm wondering if *anyone* else took your bait?   I ripped through these "pretty fast" stumbling on 16 I think for a little extra time.
I have to confess I got stuck at Level 23 because, I'm claiming, I wasn't familiar with the geometry of homothetic centers.  Is there a complexity site that does the same sort of thing?  It looks like a great way to extend one's education on an otherwise relatively difficult subject.

Robert C

On 2/27/15 2:54 PM, Robert J. Cordingley wrote:
A new but possibly entertaining productivity sink? http://euclidthegame.com

Robert C

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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com


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Meets Fridays 9a-11:30 at cafe at St. John's College
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