Four problem suggestions
Back to General discussions forum
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
Hi!
Thanks for your suggestions, though I'm not sure I can at once understand all of them :)
- It looks I should read wiki on Continued Fractions to find some examples :)
- 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?
- Not sure I ever heard of this algorithm (though I found it now in wiki). Problem with calculation
Piis 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! - 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 :)
There are some tasks from PE about continued fractions:
- (64) Odd period square roots
- (65) Convergents of e
It seems to be kd-tree?
problem 174. May be some other algorithms?
other numeral system can make it more funny
It would be enteresting :)
At facebook private I have proposed a kind of tasks about L-Systems
Here are collage of images, generated by L-System generator:
At PE there is task N 220 about Dragon curve
Here is my favourite Penrose Tiling, implemented by L-System
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.
> 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! :)
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
Please, add me to your PE list.
Here is my FK:
554982_8ffff9c3e81bb397e90ed973ab50f410
> 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