Four problem suggestions

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laurentypetit     2014-11-11 21:00:19
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Here's 4 ideas which could be funny to deal with :

1) something about the continued fraction

2) use the Monte-Carlo method to approximate a surface (drop randomly -or not - a 2000 points and count the ratio in/all)

3) find the 1st digits of pi with the second-order convergent Gauss-Legendre algorithm (algorithme de Salamen Brent in French)

4) the Conway "look and say" sequence : 0 ; 10 ; 1110 ; 3110 ; 132110

Rodion (admin)     2014-11-13 03:50:59
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Hi!

Thanks for your suggestions, though I'm not sure I can at once understand all of them :)

  1. It looks I should read wiki on Continued Fractions to find some examples :)
  2. What does it mean - to approximate a surface? I thought we can use Monte-Carlo for, say, roughly calculating the area of intersection of two circles or some more complex shapes... Is it what you mean?
  3. Not sure I ever heard of this algorithm (though I found it now in wiki). Problem with calculation Pi is that user can submit first digits from some table :) Though we can try to find some alteration of the task. Probably also method with sequence of polygons approximating the circle could be used. I'll see for it!
  4. At least one thing about which I definitely heard already :) We need to alternate this somehow either to avoid people submitting data from OEIS, or to make it more tricky... Probably using other numeral system can make it more funny. Hope I can create such a problem soon!

Thanks once more, this is a kind of challenge for me and I should try it :)

Moff     2014-11-13 10:15:19
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  1. There are some tasks from PE about continued fractions:

    • (64) Odd period square roots
    • (65) Convergents of e
  2. It seems to be kd-tree?

  3. problem 174. May be some other algorithms?

  4. other numeral system can make it more funny

It would be enteresting :)

Moff     2014-11-13 10:38:51
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At facebook private I have proposed a kind of tasks about L-Systems

Here are collage of images, generated by L-System generator:

LSys

At PE there is task N 220 about Dragon curve

Dragon

Here is my favourite Penrose Tiling, implemented by L-System

Penrose

laurentypetit     2014-11-13 15:42:11
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Splendid fractals ! The L-System seems very funny. When a handfull of tasks about it ?

2) calculating the area of intersection of two circles or some more complex shapes... Is it what you mean?

Yes it is : put the shape in a 100 km² rectangle, drop randomly 2000 points in the rectangle and count them. A ratio of 75% inside the complex shape means that its area is 75 km² (in a former job I had to calculate the area of drainage basin, in order to transform any rain signal into groundwater flow). Here's nice illustration : Monte Carlo integration

But I don't know how to make a problem with that.

3) Though we can try to find some alteration of the task.

It could be something like that : find the necessary number of iteration to find the sequence 416 in pi ? But I hadn't see the #174, otherwise I would not suggest it again.

4) other numeral system can make it more funny

Yes. And the first term can be ramdomly choosen.

Rodion (admin)     2014-11-13 15:54:50
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> But I hadn't see the #174, otherwise I would not suggest it again.

Oh, problem 174 was inspired directly by your post. I wanted to create something about Pi long ago, but have no clear idea until you wrote about it!

> When a handfull of tasks about it ?

Currently I'm trying to solve ProjectEuler#220 myself - Sergey challenged me with this. It looks I should find out how to solve it to create good task... :)

By the way it looks like say-and-see sequence is a special kind of fractal. Probably I'll be able to invent something more interesting with it when I get acquainted with these fractals you are discussing...

UPD I've just solved PE220! :)

Rodion (admin)     2014-11-14 11:37:20
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I've just found the curious puzzle about Look and Say sequence exists at PE: https://projecteuler.net/problem=419

Have anyone solved it already?

laurentypetit     2014-11-15 20:59:51
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Just done PE419, with properties found on the net.

Moff     2014-11-17 13:20:11
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I've solved PE 419 too.

The cosmological theorem is awesome!

Moff     2014-11-17 13:22:11
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> laurentypetit

Please, add me to your PE list.

Here is my FK:

554982_8ffff9c3e81bb397e90ed973ab50f410
nicolas_patrois     2014-11-17 15:19:55
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Mine: 504081_aa922bfd4d937ec4a6cf53e9c2dc610e

laurentypetit     2014-11-17 18:29:26
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> The cosmological theorem is awesome! A very nice physical analogy, indeed !

> Here is my FK Thank's, but I only solved 5 problems (I discovered PE and Code Abbey only last month) Here is mine : 667410_c99078503ee19b91be69e304eac9099b

Please login and solve 5 problems to be able to post at forum