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pj


Total Posts: 3353
Joined: Jun 2004
 
Posted: 2016-05-01 20:32
Me and my kid stumbled on the following homework problem.
The following phish should be cut with two straight lines
into three parts and reassembled into the square.
The fish can be used to pave the plane (we verified that),
and thus easily cut into four parts to be reassembled into a
square. But three?

Any ideas?

I saw a dead fish on the pavement and thought 'what did you expect? There's no water 'round here stupid, shoulda stayed where it was wet.'

Nonius
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Nonius Unbound
Total Posts: 12705
Joined: Mar 2004
 
Posted: 2016-05-02 11:00
numbering the semi-acute angles clockwise starting with the mouth, a1,a2,a3,a4,a5,a6,a7,a8. what are your assumptions about these values? presumably a1,a2 and a8 are right angles. what about a3 and a7? or a5?

Chiral is Tyler Durden

NeroTulip


Total Posts: 997
Joined: May 2004
 
Posted: 2016-05-02 11:45
They do MELT in skool these days?

Inflatable trader

pj


Total Posts: 3353
Joined: Jun 2004
 
Posted: 2016-05-02 11:57
@Nonius
since the fishes tile, you may assume they are all right angles.
Although I wouldn't bet that any of them is a right, even the
lines are not so straight.

@NeroTulip
U tell me.
The teacher is a bit mad, but he teaches the real math.
I like his style, and we were able to do other problems,
which also required some thinking.

I saw a dead fish on the pavement and thought 'what did you expect? There's no water 'round here stupid, shoulda stayed where it was wet.'

Nonius
Founding Member
Nonius Unbound
Total Posts: 12705
Joined: Mar 2004
 
Posted: 2016-05-02 13:19
hmmm too bad in Euclidean geometry we can't assume they are all right angles......unless the fins are infinitely thin. maybe I'm MELTING?

Chiral is Tyler Durden

goldorak


Total Posts: 1000
Joined: Nov 2004
 
Posted: 2016-05-02 16:32
"Horizontal line from front head to fin's inner curve, diagonal from head bottom to top fin corner, and diagonal from head top to bottom fin corner" was your four parts solution?

If you are not living on the edge you are taking up too much space.

pj


Total Posts: 3353
Joined: Jun 2004
 
Posted: 2016-05-02 16:39
Solution

And I was already going to prove that "ça n'existe pas."

I saw a dead fish on the pavement and thought 'what did you expect? There's no water 'round here stupid, shoulda stayed where it was wet.'

Nonius
Founding Member
Nonius Unbound
Total Posts: 12705
Joined: Mar 2004
 
Posted: 2016-05-02 17:19
ah, ok. the original diagram didn't lend itself to such symmetry, but I gotcha.

Chiral is Tyler Durden

goldorak


Total Posts: 1000
Joined: Nov 2004
 
Posted: 2016-05-02 17:32
Well, you ALWAYS can find a solution to that kind of problem... you just need imagination...


If you are not living on the edge you are taking up too much space.

pj


Total Posts: 3353
Joined: Jun 2004
 
Posted: 2016-05-02 18:05
"s'il n'y a pas de solution c'est qu'il n'y a pas de problème"
Shadoks TM
"If there is no solution, that means there is no problem to solve"

I saw a dead fish on the pavement and thought 'what did you expect? There's no water 'round here stupid, shoulda stayed where it was wet.'

Nonius
Founding Member
Nonius Unbound
Total Posts: 12705
Joined: Mar 2004
 
Posted: 2016-05-02 19:49
I like Moscow Puzzles for kids. Maybe too many match stick problems though.

Chiral is Tyler Durden
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