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Star and cross dissections


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6 replies to this topic

#1 bonanova

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Posted 08 May 2012 - 07:29 PM

Construct a regular 5-pointed star, and cut it into acute triangles. Or sketch the star and draw lines. The triangles need not be congruent. What is the smallest number of cuts (lines) needed to accomplish this?

A Greek cross is the union of five squares: one each above, below and either side of a central square. Ignoring the lines joining the squares and taking only the outside perimeter, or by constructing the shape, divide a Greek cross into the smallest number of acute triangles. How many?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 Prof. Templeton

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Posted 11 May 2012 - 03:26 PM

Spoiler for Greek Cross

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#3 bonanova

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Posted 12 May 2012 - 04:15 AM

Spoiler for Greek Cross


That's it. Nice explanation.

And the star?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 Prof. Templeton

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Posted 18 May 2012 - 06:38 PM

After making some doodles at lunch-time

star.jpg


Spoiler for I think this is the best way


Edited by Prof. Templeton, 18 May 2012 - 06:38 PM.

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#5 bonanova

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Posted 18 May 2012 - 10:49 PM

Bravo.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 Morningstar

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Posted 18 May 2012 - 11:05 PM

Is that the minimum?
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The cake is a lie.

#7 bonanova

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Posted 21 May 2012 - 08:09 PM

Is that the minimum?


It is, unless you can show a dissection with fewer.

Spoiler for Hint

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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