Well, when I saw the "Done with maths contest" for first time I thought about doing crazy math calculus or something with sequences like te Fibonacci one (Very original one, nobody I'm sure nobody had that idea...), but being a bit obsessed with chess like I am, and chess is very related to maths and has a lot behind it. I had to used it in some way.
First of all I hope everyone reading this knows what chess is, and knows at least how to move the pieces.
If you don't, I'm happy to tell you that you will learn something knew, at least to move the pieces that it's what I'll use to design my figure.
If you do know how to play chess, I'm glad you do, i hope you love it and have fun playing it, but you probably want to skip that part.I will be using the "8 queens puzzle", you may have heard about it, if you don't I'm explaining it later.
So briefly explained, I'm using chess positions to make a decorative figure you could use for whatever you want, a key chain, to display it on your desk or to cheat in the "8 queens puzzle" without anyone noticing it.
Well as I have done all the hard work you just need a 3D printer if you want to get the figure.
But if you are curious about what I've been using during the design process here it is:
-Pen and paper for the thinking and first prototyping of the idea. (When facing a contest like this one, you'll probably want to do some brainstorming as I did)
-3D Design software, just use the one you know, keep it simple, I mostly used characteristics contained in all editors. I learned fusion 360 and that's the one I used.
-3D printer, for obvious reasons, i guess that if you have great skills and time you could use other hand-made methods, not my case though.
-Basic chess knowledge, you probably know, but i'll provide you the basics if you don't.
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Step 1: Let's Learn the Basics About Chess (Skip If You Know How to Move Pieces)
Chess it's a board game, a sport or art, depending on who you ask, very complex and with a lot of history behind, for the purpose of this project it's only necessary very basic knowledge, so if after reading this you play and discovered there is more, don't blame it on me :)
Well chess it's played on a 8 x 8 rectangular board, with alternating white and black squares, always place a white one the bottom right corner and you'll be fine.
There are 6 different pieces: Pawns, king, queen ,knight, rook and bishop.(look at the photos for a visual description of the movements of each piece)
Pawns, just move 1 square in front on them.
King, 8 squares around him.
Rook, lines and columns, as many squares as he wants.
Bishop, Through diagonals, but maintains always the same color squares. If it starts on a black square, it will only move though the black diagonals, same for white.
Queen, it's a combination of the rook and the bishop, it can move through lines, columns and diagonals.(THIS ONE IS THE ONE WE ARE GOING TO USE )
Knight, It move 2 squares straight and one to the side.(Hardest one to learn, you may want to see the image)
Finally you need to know that pieces can capture other pieces that are in a square that they are capable of moving to.( Pawn it's an exception, captures to the 2 first diagonal square in front of him )
Congratulations, you know how to move the pieces,I would like to encourage you to give chess a go and try to learn more about it, you won't regret.
If you want to know more, I'm providing you with 2 links, an instructable that explains the chess basics and Lichess web page, it's and open-source, non-profit web page were you can play chess and also has some nice tutorials for you tu learn.
Step 2: 8 Queen Puzzle
Now everyone reading this should know how the queen moves (If not, read step 1 again).
The 8 puzzle it's a chess problem that consists of place 8 queens in the 8 x 8,( or extending the puzzle to a n number of queen in an n x n board, we will be using 8 x 8) in a way that queens can't capture each other, so there are no queens sharing line, column or diagonal, that's it, simple.
Before continuing i would like to encourage you to give it a shoot and see if you are able to archive it, you can do it in a chess board or just draw the 8 x 8 grid on a paper.
If you have been able to do it, congrats, for some people it's and impossible task to solve.
If you didn't, don't worry, I have friends that tried it for months, later they discovered they could just search it on the Internet and finally got it.
Well there are a total of 92 different solutions to this puzzle, but only 12 of them are different positions, the other 80 are obtained by rotating the board.
So the plan it's to wok with this 12 positions and make a figure of this positions.
Step 3: Working With the Solutions
Look at all the inserted images, the first 12 of them are the 12 different solutions, and the next 12 you can see the have been edited.
The last 12 images have been square color coded, with one criteria, que further the square it's from a queen, the lighter it's, I'm creating a map that later will be used to give different depth to each of the squares, meaning that the squares containing a queen will be deeper and the ones that don't have a queen near will act like a mountain.
Step 4: Creating a Volume From the Positions
Now we have the faces of our volume prepare for the final 3d figure. As we have 12 different faces, we can't do an easy and well known cube, as you may have guess we will be using a dodecahedron, as it has the 12 faces we need.
Yes, we have a slightly problem the faces of the dodecahedron are pentagons, our chess boards are squares, so we need a way to transform then.
I tried different methods and chose one I found the coolest, consists of the following:
- We divide a pentagon in half, from the top vertex to the half point of the side under it.
- We pick the dividing line from the previous step and divide it in 8, we also take the bottom right side and divide it in 8. Finally we connect the 8 division from both sides.
-We pick the upper right side and we divide it in 4, we do the same with the base and as in the previous step we connect them.
-Finally we mirror what we have done with the right side in the left.
Maybe it's not the best geometry explanation, but seeing the image I'm sure you'll understand it.
So after this we are left with a let's call it " 8 x 8 pentagon " and now we only need to apply the depth to the faces and build up the volume
Step 5: Generating the Depth in the Faces
Now it's time to combine the depth map and the " 8 x 8 pentagons" so I took the pictures with the depth map and for each of them I assigned different heights, adding 0,2 units ( as it was later scaled for 3D printing measures are different but proportions the same) for higher (further from queens) level. look the photos for some examples.
And finally I arranged the faces forming a dodecahedron.(For those wandering the angle is around 116.6º)
Step 6: Final Step: 3D Printing.
Finally we only need to take export the stl file to the slicer and after it send it to the printer. Remove the supports and we are done.
It was printed in a ender 3, maybe not the best settings, as I'am still a starter of this amazing world, but it looks good.
I scaled it to be 4cm tall, and from the 2h 8 min, it actually only took 1h 58 min, which is nice.
I have attached the stl of the object(not the direct gcode as I keep running in internal server error when uploading it), feel free to edit it.
I really hope you like my project, I'am looking forward to seeing if any of you tries to do maybe a 10 x 10 one, modify it in coolers ways or whatever your brains are capable of creating.
Thank you for reading and congratulations for being able to read until the end, I am sure not everyone will. Votes and comments are appreciated, ask if anything is not clear.
Participated in the
Made with Math Contest