Forum: Anglais 
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Anglais >> Football réel
Brain Teasers (58)
Courtesy Numpty:
- Can you cut up an equilateral triangle and rearrange its parts to get a square?
I've just seen this.
The simple answer is, of course, yes. In principle you can cut up any triangle and form a square with the parts. The question is where do you make the cut(s)?
I'll have to give it some thought ...
I've given it some thought and maybe have 'half a solution'. :)
I calculated the area of an equilateral triangle of unit length (=1) as √3/4 square units. [The height is √3/2 (Pythagoras), so the area is √3/4.]
The area of the square must be the same, so the length of the 2 sides of the square must be 4√3/2 [4th root].
Half the height of the triangle is √3/4, So the square root of half the height, will give us 4√3/2, which is the length of one side of the square. Once we've got that then we can cut everything to fit.
I then went down a bit of a rabbit warren trying to work out how to construct that, perhaps using a compass. I'm sure it's possible but don't have the urge to spend any more time on it.
How close did I get?
You've got the gist of it, but the devil (or should I say the joy?) lies in the details so maybe you should give it a go.
This is the theorem if you're interested in it, there was an animation of this online but it seems to slip my mind: https://en.wikipedia.org/wiki/Wallace%E2%80%93Bolyai%E2%80%93Gerwien_theorem
Another one:
- Can you cut a square into an odd number of triangles of equal area?
(You can tell me which topic you're interested in as well, I should have something related to it)
I don't really mind which topic. I think it has to be generally suitable so that anyone can have a go at them.
If I get stuck can I ask the kids to do my homework? :D
Lol sure, take all the help you need.
The question about the square is especially enticing.
Do you have your own solution to these puzzles or are they ones you haven't done yourself?
The first one you haven't given a solution exactly where to cut the triangle. The wiki page you posted gives a general diagram but not the precise points where it needs to be cut.
The second one, I give up. Not entirely sure if it's even possible.
Do you want me to post the solutions here?
Yes, I think any questions or puzzles have to be answered at some point by the originator.
But you decide when. I would suggest giving a rough timescale for anyone wanting to have a go before posting the solution.
One thing I would bear in mind with future puzzles is that solutions potentially involving a diagram - or anything else that can't easily be posted in a thread - is going to be more difficult to give clear answers.
It would be nice to see others participate as well
I suspect the thread title is rather off-putting for most people.
Maybe frame it in a different way. 'Brain teasers' 'Logic Puzzles' or something similar.
A bat and a ball together cost 1.10$. The bat costs a dollar more than the ball. How much does the bat and the ball cost?
This is an attempt to gauge participation.
That reminds me of the old aeroplane riddle. A plane crashed on the border of 3 different countries, Germany, France and Switzerland. Where did they bury the survivors?
You don't bury survivors.
