8 equilateral triangles with 6 lines
zev...@zscdz.zhpz.com
Perusing rec.puzzles archive, I found a puzzle that asks how to make
4 equilateral triangles using 6 toothpicks. The answer can be found
in the archive.
Surprisingly, this puzzle was not in the archive:
How do you make 8 equilateral triangles using 6 toothpicks?
The answer is pretty obvious. Maybe that's why it isn't in the archive.
zev...@zscdz.zhpz.com (Anti-spam address. Remove all "z"s before replying.)
Jacob Lipman
Make a pyromid, or however you spell it.
Yakof
Jean Lemire
Jacob's pyramid is called a tetraedron.
It has four triangular sides (each one being an equilateral triangle).
So with six toothpicks you end up with four triangles not eight.
So the puzzle is not solved yet since we need eight triangles. I supposed
that the toothpicks cannot be broken. Am I right Evan?
Jean Lemire.
gHoTi
SPOILER:
Build a tetrahedron (pyramid) on a mirror.
--
---
ghoti AT earthlink DOT net
oooO
( ) Oooo
\ ( ( )
\_) ) /
(_/
Noam Elkies
In article <6616kb$a63$1...@walton.videotron.net>,
Usually spelled "tetrahedron", but what the heck.
>It has four triangular sides (each one being an equilateral triangle).
>
>So with six toothpicks you end up with four triangles not eight.
For 6->8, you don't even need to leave the plane...
...though you do need some smaller triangles. Arrange the
six toothpicks to make a Star of David, which will contain
two full-size triangles and six of 1/3 size, for a total
of 2+6=8, Q.E.F.
--Noam D. Elkies (elk...@math.harvard:edu)
Dept. of Mathematics, Harvard University
Jacob Lipman
Jean Lemire wrote:
>
> Jacob's pyramid is called a tetraedron.
>
>
> So with six toothpicks you end up with four triangles not eight.
>
> that the toothpicks cannot be broken. Am I right Evan?
>
> Jean Lemire.
woops, thought he said 4, and please, call me yakof.
yakof
zev...@zscdz.zhpz.com
Jean Lemire (j.le...@tecsult.com) wrote:
: So the puzzle is not solved yet since we need eight triangles. I supposed
: that the toothpicks cannot be broken. Am I right Evan?
: Jean Lemire.
There isn't any trick to this puzzle. No broken toothpicks, and
it isn't done with mirrors. Draw 6 straight lines on a piece of paper
(or use 6 toothpicks) to make 8 equilateral triangles. This puzzle
isn't that hard, especially during this time of year.
Evan
zev...@zscdz.zhpz.com (Anti-spam address. Remove all "z"s before replying)
Wayne Hacker
Jean Lemire wrote:
>
> Jacob's pyramid is called a tetraedron.
>
> It has four triangular sides (each one being an equilateral triangle).
>
> So with six toothpicks you end up with four triangles not eight.
>
> that the toothpicks cannot be broken. Am I right Evan?
>
> Jean Lemire.
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I would have thought that David would be the star of this solution.
Wayne
Jacob Lipman
> I would have thought that David would be the star of this solution.
>
> Wayne
Actually, its not called David's star. That is an incorrect translation
of "david's shield". In fact that isn't really what he had on his
shield. He had the first letter of his name crossed upside-up and
upside-down on his shield. The greeks, substituted a delta for the
hebrew letter, thus it looks like an upside-up and upside-down delta
(triangle) interlocked.
Yakof
Risto Lankinen
Hi!
Noam Elkies <elk...@ramanujan.harvard.edu> wrote in article
<661fu1$ho0$1...@news.fas.harvard.edu>...
>
> For 6->8, you don't even need to leave the plane...
>
> ...though you do need some smaller triangles. Arrange the
> six toothpicks to make a Star of David, which will contain
> two full-size triangles and six of 1/3 size, for a total
> of 2+6=8, Q.E.F.
This is but one of infinitely many solutions. The others
can be obtained by offsetting the centers of the full-size
triangles by any amount, as long as they intersect in six
distinct points.
In most solutions, the sizes of the six smaller resultant
triangles are different, though.
terv: Risto L.
liquidg...@gmail.com
> In article <6616kb$a63$1...@walton.videotron.net>,
>
> >
> >So with six toothpicks you end up with four triangles not eight.
>
>
> ...though you do need some smaller triangles. Arrange the
> six toothpicks to make a Star of David, which will contain
> two full-size triangles and six of 1/3 size, for a total
> of 2+6=8, Q.E.F.
>
> Dept. of Mathematics, Harvard University