I'm also into Origami, though haven't been practising much lately. More examples here:
https://www.flickr.com/photos/stven/albums/72157632084579552/with/8506729268/
Hi James,
The Torus displayed was made by first gluing together 10 Trapezoidal shaped lengths of different coloured hardwoods, each about half an inch thick, into approximately 15 lengths.
These I left for several days to ensure the glue was fully set.
I then turned assembled lengths to approximately 2 inch diameter.
The next job was to cut these 2 inch diameter lengths into wedge shaped segments.... the "wedge" angle being set to 12 degrees (360 /30 segments)
The segments, being hollow, greatly assisted in the assembly of these pieces.
I then finished the assembled torus just by sandpapering, buffing and polishing.... quite an easy and satisfying job
The math of this torus was very easy... just 360 / number of segments.
I am really fishing for somebody who could help me sort out the math for a torus knot.
I have been thinking about this problem, on and off, for several years.
Joseph
Hi Stven,
Great... will reply, in detail, later,,,, have to shoot off now
Joseph
I am really fishing for somebody who could help me sort out the math for a torus knot.
Join a mathematics forum and ask around. I'm sure you'll get a lot of suggestions there.
DroneBot Workshop Robotics Engineer
James
Hi James,
An excellent suggestion... I do not want anything too mind boggling and, I feel, I need to frame my question to a Math forum very carefully.
Food for thought.... thanks
Joseph
Hi Stven,
The Origami shapes look very attractive.
I know very little about Origami other than it is associated with Japanese culture... but I do like its form, colour and the obvious dexterity required to arrive at its quite delightful form.
I will look at various websites displaying this craft for inspiration.
Joseph
Nicely done. Love it when a design becomes a thing.
An excellent website (and YouTube channel) with easy-to-follow video tutorials is happyfolding.com. I completely got started there.
The only problem with this video "algorithm" is it's bogus! With 43 quintillion possible sequences there is no way to devise a 25 step rule to solve the cube. About the only way this can be demonstrated is by going thru the algorithm backwards from a solved cube and then following it forward which of course will bring it back to it's solved state. This algorithm idea has been floating on the internet for some time and while this one is pretty well done in hiding how he "scrambled" the cube it is folly. That's why he says that sometimes, (quotes some random statistics) it will require going back to the top and starting over. He is giggling at the fact that many people will try this over and over wondering what they did wrong. It's a great gag, but seriously?
The only problem with this video "algorithm" is it's bogus! With 43 quintillion possible sequences there is no way to devise a 25 step rule to solve the cube
Why not? Just because there are 43 quintillon ways to go wrong doesn't mean that there can't be 25 correct steps to solve it.
Think of it this way, say you have a 5-digit combination lock on a briefcase. If you had to guess at the code you would need to try 99999 different numbers. So there's 99998 ways to go wrong. But you can still open the briefcase in only 5 moves if you know the correct combination.
So the number of ways you can go wrong has nothing at all to do with how many steps it takes to solve something.
Having said the above, you may indeed be correct. I've never touched a Rubik's Cube in my life. I have no clue whether the solution in the video works or not. It could be a bogus video. In fact, I was just wondering what would happen if you started the algorithm with a solved cube? When you're done would it have gone from solved back to solved? That doesn't seem right. So I have my own suspicions that something might not be quite right there.
In fact, I was half tempted to run out and buy a Rubik's Cube just to see what happens when you start the algorithm with the cube in a solved state.
There must be people out there who have access to a Rubik's Cube. Why not put it through this algorithm and see what happens? I don't have one here to play with. So I don't know. Maybe you're right and the video is just a joke.
DroneBot Workshop Robotics Engineer
James
Since you brought this up I did some searches. Based on what I have found the Rubik's Cube can actually be solved from any of its 43,252,003,274,489,856,000 states in exactly 20 moves.
The guy in the video offered an algorithm that uses 25 moves. It could have still be a crank video. But apparently solving the Rubik's cube in even as few as 20 moves is possible.
Unless these web pages I've finding are also crank websites?
As I say, I don't have a Rubik's Cube here to even try these algorithms on. So I have no direct experience with any of this.
DroneBot Workshop Robotics Engineer
James
Hi James,
Thanks for all your much valued information.
I have decided to go for the direct method … just crank in the algorithm and figure how to stop this algorithm when the cube is solved... first method will most likely be a little pushed button pressed at the correct time.
Let me tell you exactly where I am up to... the base model is finished. The four servos are mounted, wired up and these work in pairs.
I have 4 Nema 17 Stepper motors... the brackets and fittings are ready for mounting.... these are not wired up.
My knowledge of Arduino programming is a bit basic.... I reckon I could write a sketch for the Servos and the Steppers individually but combining them together I am not sure about.
As I see it at the moment one pair of servos will open allowing the Stepper mounted on the opposite servo to turn the layer of the cube... the servos will close and the next servos will open.... and so on
Have to dash.... somebody just rang and I need to go
Joseph
20 moves is the quickest solve for any scramble, but it usually requires a computer to figure out the correct moves since every starting position will have a different solve. The 25 move algorithm is also valid. Any scramble will find its solution somewhere along that algorithm, but sometimes you will need to go through the algorithm more than once.
it’s amazing to me that some math genius was able to prove there is a god number and that number is 20.
i can certainly run the 25 move algorithm on a solved cube and let you know what happens but dealing with the grandkids just now.
i can certainly run the 25 move algorithm on a solved cube and let you know what happens but dealing with the grandkids just now.
@squeaky @Stven, the algorithm in that video I posted is a joke. It says so right on the video! I didn't even read the information under the video. It says right on it:
WARNING! This video's a joke! The algorithm is 100% made up and it wont solve your cube. Sorry. But fear not! If you have a Rubik's Cube thats scrambled and you genuinely want to solve it then use the REAL tutorials I used here: (he then posts links to other videos).
So you'll need to look into other methods that actually do work. I know there are legitimate algorithms for solving the cube, but you might need to be able to sense the configuration of the faces first in order to use them.
DroneBot Workshop Robotics Engineer
James
Hi James,
It did seem a bit too attractive …. I had wondered why people, in several videos that I have watched, had gone to the expense of buying these little cameras when it appeared that they were not really needed. I am doing some initial trials with a colour recognition sensor and I am looking at the twisted torus project.
All good fun!
This week I will also be busy domestically... on Friday we are going on holiday down to the Sussex Coast. Hope the weather will be O.K.
I am quite happy pottering about in my workshop …. but, to keep the peace, one has to somewhat conform.
Great chatting with you... If I manage to knock something together on the twisted torus project before Friday I will send you some photographs.
Joseph