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        riddles >> medium >> 1/5 th of a square
        
(Message started by: JohanC on Nov 26^th, 2005, 4:37pm)

Title: 1/5 th of a square
Post by JohanC on Nov 26^th, 2005, 4:37pm

Given a square, construct a new square which occupies 1/5th of the area of the original square.
The only allowed operations are:
- connecting points with straight lines,
- form a new point being the intersection of two lines, and
- add a point in the middle between two existing points

Title: Re: 1/5 th of a square
Post by Eigenray on Nov 26^th, 2005, 5:37pm

Okay.

Title: Re: 1/5 th of a square
Post by JohanC on Nov 27^th, 2005, 2:12am

Nice solution, Eigenray.
And to the point.
I had a more symmetric looking solution in mind.
Maybe let somebody else figure out that one?

Title: Re: 1/5 th of a square
Post by JocK on Nov 27^th, 2005, 3:15am

Any Greeks on this forum?

Title: Re: 1/5 th of a square
Post by Barukh on Nov 27^th, 2005, 5:06am

on 11/27/05 at 02:12:53, JohanC wrote:

I had a more symmetric looking solution in mind.
Maybe let somebody else figure out that one?

Title: Re: 1/5 th of a square
Post by JohanC on Nov 27^th, 2005, 7:14am

Yes, Barukh, that's it!

Title: Re: 1/5 th of a square
Post by JohanC on Nov 27^th, 2005, 8:14am

By the way, Barukh, which software did you use to create this nice image?
Or did you write it directly into PostScript?

Title: Re: 1/5 th of a square
Post by Barukh on Nov 27^th, 2005, 10:26am

on 11/27/05 at 08:14:58, JohanC wrote:

By the way, Barukh, which software did you use to create this nice image?
Or did you write it directly into PostScript?

I use an old demo version of Geometer's SketchPad software.

Creating directly a PS file is too hard for me... ;D