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Problem Idea Equidecomposable Polygons

 2 years ago
source link: https://www.codeabbey.com/index/forum_topic/dbc57ecf458d6a9be10be3a69ec08251
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Problem Idea Equidecomposable Polygons

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Rodion (admin)     2022-03-25 06:07:51
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Vadim, Hi - and thanks for another much curious topic :)

This reminds of classical cutting puzzles like those by Loyd and Dudeney. Though these fellows generally requested minimize number of parts.

I googled a bit to find out explanations (heard of theorem but never knew details).

Honestly, this sounds like a real "coffin" to program :))) Even cutting polygons already requires good deal of coding with memory objects (but this hints about possible intermediate problems).

I probably shall at least try to code this, though perhaps not immediately (much frightened!) - so if you feel in the great mood to provide generator/checker code for such task yourself - just tell :)

Vadim Pelyushenko     2022-03-25 06:23:17
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Honestly, this sounds like a real "coffin" to program

Without having started writing any code for it (but already knowing a solution that would work) it does seem to me like this would be cumbersome in terms of representing the sequence of actions and verifying a solution. Perhaps the solution verification can be simplified if we restrict vertices of polygons (including intermediate polygons) to integer coordinates.

Actually, maybe that would be too easy.

Actually no, that should be perfectly fine. If we use doubles for coordinates, then those are just rational values, and multiplying by an appropriate power of 2 would make them integers. We can use large integer coordinates.

so if you feel in the great mood to provide generator/checker code for such task yourself - just tell

Speaking of this, I actually have another problem which I wanted to suggest adding, which I already have a solution for but wanted to save it until I had generator/checker ready. How should the generator/checker be formed? As in, what format or style should it follow or what languages am I allowed to use?

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