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Best Answer Yoruichi-san, 02 July 2013 - 07:23 AM

Spoiler for Okay, the *doh* solution...
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9 replies to this topic

#1 witzar

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Posted 29 June 2013 - 03:17 PM

Each point of the plane is painted either red, green or blue.

Prove, that there exists segment of length 1 with both ends of the same color.


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#2 TimeSpaceLightForce

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Posted 01 July 2013 - 04:53 PM

Spoiler for

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#3 witzar

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Posted 01 July 2013 - 05:42 PM

Spoiler for

Spoiler for


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#4 TimeSpaceLightForce

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Posted 01 July 2013 - 07:58 PM

Spoiler for points w/ paints


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#5 witzar

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Posted 02 July 2013 - 02:09 AM

Spoiler for points w/ paints

This is not true.
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#6 Yoruichi-san

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Posted 02 July 2013 - 02:48 AM

Spoiler for Proof by contradiction

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

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#7 Yoruichi-san

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Posted 02 July 2013 - 07:23 AM   Best Answer

Spoiler for Okay, the *doh* solution...

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#8 TimeSpaceLightForce

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Posted 03 July 2013 - 08:36 AM

 

Spoiler for points w/ paints

This is not true.

 

Spoiler for


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#9 witzar

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Posted 03 July 2013 - 01:28 PM

 

 

Spoiler for points w/ paints

This is not true.

 

Spoiler for

Pick a random real number from interval [0,100]. What is the probability that picked number is not 7? Clearly 100%. Does it follow, that picking 7 is impossible or that number 7 does not exists? Clearly not.

Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too).

You have an "impossible" blue-green circle.

In fact you can take just one arc (1/6 of circle) and paint it any way you want. Then for each point P of the arc take a regular hexagon H inscribed in the unit circle such that P is a vertex of H, and paint the other 5 vertices of H alternately (regarding color of P). Again you have an impossible blue-green circle.


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#10 TimeSpaceLightForce

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Posted 03 July 2013 - 05:06 PM

 

 

 

Spoiler for points w/ paints

This is not true.

 

Spoiler for

Pick a random real number from interval [0,100]. What is the probability that picked number is not 7? Clearly 100%. Does it follow, that picking 7 is impossible or that number 7 does not exists? Clearly not.

Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too).

You have an "impossible" blue-green circle.

In fact you can take just one arc (1/6 of circle) and paint it any way you want. Then for each point P of the arc take a regular hexagon H inscribed in the unit circle such that P is a vertex of H, and paint the other 5 vertices of H alternately (regarding color of P). Again you have an impossible blue-green circle.

 

"Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too)."

Then "all red centered circles" are painted that way. Making  0 deg-green, 60 deg-blue. But the points are alternated so 30 deg is green (even).

Therefore all ends of 60 deg arcs is two colored while all ends of 30 deg arcs is one colored.

If two red centered circles , where one has twice the radius of the other intersects at P2 and P1 ...

                                                                       P2


                                            
                                         r1  60deg                                                                   30 deg      r2                                                    



                                                                       P1

are P1 and P2  same colored or not ? or 1 is colored cyan?


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