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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# Star and cross dissections

Started by bonanova, May 08 2012 07:29 PM

6 replies to this topic

### #1

Posted 08 May 2012 - 07:29 PM

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

- Bertrand Russell

### #2

Posted 11 May 2012 - 03:26 PM

Spoiler for Greek Cross

### #3

Posted 12 May 2012 - 04:15 AM

Spoiler for Greek Cross

That's it. Nice explanation.

And the star?

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

- Bertrand Russell

### #5

Posted 18 May 2012 - 10:49 PM

Bravo.

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

- Bertrand Russell

### #6

Posted 18 May 2012 - 11:05 PM

Is that the minimum?

The cake is a lie.

### #7

Posted 21 May 2012 - 08:09 PM

Is that the minimum?

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

Spoiler for Hint

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

- Bertrand Russell

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