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So, is there no other way than Geogebra?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

Without making the tree myself I never would have figured out any way at all. That is the purpose of that type of software. You see, when you are actually building or experimenting with the process it helps you to gain insight into how to solve it.

I am not yet done with this problem and now have an experimental answer of greater than 26.5 and less than 29. This is not yet tight enough but I will try to refine the answer until we have the 10 digits required.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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But, would you explain it from the first principle? I mean, how does the software calculate it even?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Agnishom;

Remember this is a programming problem and a tough one at that. There may be a math solution to it but first we will get the answer and then we will later try to work back to the math.

How does the software calculate it? It doesn't, I used geogebra to build the tree and then I measured the box. The bound is crude but it is a start. While using G to construct it, I noticed a trick that may make this easy. I am still working on the program.

Please keep in mind this is one of the toughest problems over there. Only 305 people have solved it worldwide. You have picked a toughie.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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bobbym wrote:

How does the software calculate it? It doesn't

If it doesn't then how does it calculate the box?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

You take and draw a rectangle that encloses the tree. This is what the question asks for. Geogebra knows how to compute the lengths of the sides of any polygon you draw.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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So, please start explaining

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Agnishom;

I just completed the first program that might just work. I was using the idea of the slope but it failed. I am trying to use a little bit of vectors, yecchhh!

Nothing to explain yet, I do not know if this will work.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Unfortunately, I have to leave for school. I have my formative assesments going on

Catch you later

*Last edited by Agnishom (2013-02-04 17:09:24)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

Okay, have a good day.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Agnishom;

Became the 307th person to solve the problem!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Congratulations, bobbym.

Now please cast some light into the problem

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Agnishom;

First of all, it requires a lot of tinkering because I was hampered by not knowing geogebra's full range of uses. I had to use mathematica for the programming instead.

Anyway, take a look at benice's picture in post one. The one on the left if rotated 180 degrees counter clockwise is what the tree looks like. Had I been able to do that using geogebra I would have solved the problem in 10 minutes instead of 4 days.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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So, you used Mathematica?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Yes, I did it by hand with geogebra for about 12 - 13 iterations. Normally that would have taken 8192 squares to draw. But there is trick that reduces the problem down quite a bit.

When I spotted that pattern, I used mathematica to do the 110 iterations using the trick. This would have required drawing 1298074214633706907132624082305024 squares by brute force! But instead it only took 880.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Trick? Is it a mathematical trick or a programming one?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

No just commonsense. It occurred to me that you only had to keep one branch of the tree going up, down, right and left. This saved much work.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Is it really that tough even if you have things like Geogebra and Mathematica?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Agnishom;

I thought it was. You have to predict how high and far to the left, right and down the tree grows.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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And would it be completely impossible if there was no mathematica or Geozebra?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

No, people used C++, Java, Basic, Ruby, Mathematica, Python, Pari etc. Many of the solutions were a lot shorter than mine some were cleverer. No one used geogebra except me. That makes me very happy.

Here is a picture of the bounding rectangle they are talking about.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Hi;

That looks brilliant from a distance

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Not the way I do it!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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I did not get you

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Sorry, just that the word brilliant and me do not go together. Sort of like putting a bed in an elevator, doesn't belong.

*Last edited by bobbym (2013-02-11 01:49:43)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**