5th International Conference on Origami in Science, Mathematics and Education

Now I know what the full name of "5OSME" is.

As readers of this blog will know, i'm part of an informal group of Origami folders in Singapore, called (surprise surprise) Origami Singapore. Next July, the group is going to organize 5OSME, which is something something "Origami for Science, Mathematics and Education". It's going to be an awesome event with seminars where people present papers on the relation between origami and science and stuff like that, a free public exhibition and origami classes! For the program of the last convention, 4OSME, click here.

What I'll be anticipating as well is the screening of Between The Folds, an origami documentary! It's about origami and science and art, and from the trailer below you can already see that the documentary is gonna be good stuff.



I'll post about definite details for 5OSME when I can, so please support the event next July! ^_^



Origami as Pure as Snow
Shonen

Revival

Long time no see! I just realised that my blog died on September 11 2008.

The purpose of this post is to highlight what's gone on after my blog died, and the thing that kept me busy throughout the holidays...

First, my exams ended, and there were post-exam activities. One afternoon after such an activity, a math teacher suggested to me to do a math project on origami. I was quite ready at that time because I knew a lot of results I had (my "building block method") and could extend for the project. I started on it in mid-November, and burnt my holidays away working on a report in almost all of my free time, but it was all worth it. I finished a 49-page and over 11,000-word report for my project "Folding Prismatoids Using a Form of 3-D Origami". What my project did was to investigate how to use geometrical constructs (e.g. perpendicular lines, midpoints) to draw lines on paper, i.e. draw a crease pattern with black mountain folds and red valley folds etc. such that when the crease pattern is folded it becomes a 3-D Prismatoid sticking out of the paper. It all started with the cuboid Building Blocks, which I extended to Convex Prisms (check out the Prismatoid link!), Concave Prisms, Convex Frusta, Concave Frusta, Convex Pyramids, Wedges and Convex Cupolas. Because my methods needed a special form of net of the final solid as a basis, my report also included a way for users to generate those nets of a random shape even if they don't know how it looks like in real life.

My project was submitted to the Singapore Mathematics Project Festival 2009 (SMPF), and it proudly won the Gold medal (2nd Place) and the Creativity and Originality Prize! Check the results here (Senior Section). I might also be publishing a shorter version of my report in the Mathematical Medley, a biannual publication of the Singapore Mathematical Society.

The next things that happened were that the same math teacher again gave me two opportunities: setting up a booth during my school's annual Speech Day, and conducting a June workshop for gifted primary school students, both of which I accepted eagerly.

First up was Speech Day. I rallied together my Origami models (half of which you can find in this blog and the rest created during my SMPF project), wiped off the dust and boxed them up for transport to school. I also created a summarised version of my SMPF finals presentation slides for use at the booth. On Speech Day itself, the principal mentioned my project as one of the achievements our students have made so far. The guest of honour, Lim Chuan Poh, chairman of A*STAR, then came to visit all the booths that were set up in the school concourse. He was quite impressed with my project, and he also requested to take back one of my models with him. He knew how to pick, he took my Concave Prism, one of the hardest to make!! ^_^

After Speech Day, the same math teacher again suggested that I could set up the same booth for the school's Open House. I accepted happily again, and set up my booth (with the same models from Speech Day) again today at school. Lots of parents came and asked me about my project, and I explained to each one of them the gist of the project. What I said to each of them was something like this:

(opens up one of the models) "See the lines on the paper? The main purpose of this project was to investigate how to draw the correct lines on any piece of paper so after folding it becomes a 3-D solid sticking out of the paper." (Folds the model again) "I created many methods to do so and produced many different shapes as well." (Points to other models in my project)
(Points to other "Building Block" models) "These are special cases of my methods because Their folds align with a square grid. This is an easier case, so I can manipulate it more easily to get more complicated products."
(Parent Q & A)

I manned the booth for about 5 hours!!! So tiring hahaha

That's it! The next event coming up is the June workshop, hope it will be a success! ^_^

Green Origami

In Math (Trigo) class, my teacher was giving out these mint chocolates to the class, and after I finished eating mine I realized that I had quite a nice bit of foil-backed paper right in front of me. I just had to hide the plastic edges and I had a nice long rectangular piece of folding material. After fiddling a bit with it, pleating it and making random reverse folds, I thought that maybe I could make an arm with fingers out of it. It's a rather basic skill, used rather commonly in boxpleating to form hands with recognisable fingers. I'm not gonna go too deeply into it, but I think you should be able to reverse-engineer it from the pictures anyway.



And the underside...



Should be quite clear now ^_^

Then, I saw the wrapper left on the table by my neighbour and I was still bored, so I took it and folded another hand so I now have a matching set (With the thumbs in the right place, of course). Then I got hold of another few wrappers and started folding legs.



A view of the foot from its owner's perspective (i.e. looking downwards):


By the way, I've finished off all the dark-coloured paper I have, so I had to use my Year One Orientation T-shirt to provide the black background. I did that witht he last post too. (:

I quickly made a matching set of legs again, and I started having fun placing the "emo frog parts" into interesting arrangements.



The part providing the "body" and "head" is actually a sample of the original sweet. Mint Chocloates yum ^_^

Someone remarked that when viewed at an angle, it kinda looks like someone in a traffic accident.



Ouch.

In case you're wondering, the book I used was a copy of Hikaru No Go manga.

That was fun, random doodles in class are always the best ^_^

These techniques are always useful, so it's good to rememeber them.

Ta-ta!



Origami as Pure as Snow
Shonen

Origami Cards

Sorry sorry sorry sorry for killing this blog for two months, I've been really busy and tired all this time... forgive me forgive me T_T

I hope not many people stopped visiting this blog because of the lack of activity...

I shall do a post stuffed with pictures to make up for it ^_^

First up is a random doodle that I did during Biology class because I was too bored.



I made it out of an envelope I found in class:



You might be able to see how I folded it now =D

Next up is a folded version of the 202 class logo created by tiong suan.





Please don't kill me if it looks crappy, because 1) I was bored and tired at that time 2) This was a prototype that I did with printing paper 3) 30% of my mind was on the Beijing Olympics Opening

The following are the most important; remember the building blocks? Well, instead of using a boring square grid, why not use an equilateral triangle grid instead? I came up with a hexagonal and triangular building block...







and this is what they look like from the flipside...





Warning: the previous picture might prove to be misleading if you use it to try and figure out the folding method.

The above models can function like building blocks; their dimensions can be varied to a certain extent.

Surprisingly, I also managed to fold a little tetrahedron sticking out of the paper.





The flipside...



Mysteriously, this picture always turned out rotated 90 degrees anti-clockwise when I tried to upload it on blogger. The problem was solved when I rotated the picture file myself one whole round then trying again.

Its negative version...



... and its flipside.



Finally, here's a cool model that I did during the Origami Singapore meetup today



Cool, eh?

Hmmm I might post CPs some other day... *yawn*

seeya~




Origami as Pure as Snow
Shonen

Cross Grave - Variations

Hi everyone!

Following my Cross Grave post, Cupcake, another folder, did a variation on the cross model that turned out very well. ^_^ He kindly allowed me to show you guys his model, which changes the dimensions of the original cross (7 x 5) to a smaller one (4 x 3). The model become smaller and easier to fold, but most importantly, it shows how a versatile folder can change a design if he plans it well enough.

Click here to see cupcake's model in his flickr account (I had the picture but somehow it doesn't show up)

Very nicely done! Judging from the picture, I thought he used a 15 x 15 grid for this model (but he told me that it was really 16 x 16 ^_^) ; a very interesting feature of this type of "pop-out" origami is that any square grid can be used. Theoretically, the paper can be extended without bound on all four sides, but the model, jutting out from the centre and thus not needing the edges and corners, will remain intact. This is what gives "pop-out" origami an unlimited (at least, in my opinion) potential for the combination of models.

Now for a little exercise: how many squares does this cross take up from the paper? Try it out if you're interested!

As to how Cupcake managed to make his cross, it probably went something like this: please refer to the pictures in my last post, and scroll down to the second picture from the top. In that step, instead of forming two 2 x 1 x 1 building blocks each two squares away from the central square, he folded two 1 x 1 x 1 building blocks each one square away from the central square.
He then proceeded on with the rest of the steps until his cross reached a certain height. Folders may want to try this model out, and more adventurous ones (with very thin paper available) may want to extend the method to make a cross with dimensions 10 x 7! (figure out how I arrived at those two magical figures yourself ^_^)

I hope this post has managed to convince you guys that it is possible to create variations of models with enough planning! Then again, if any of you guys have folded any of my models, please let me know, and I may feature it on this blog!

Thank you very much Cupcake for folding my models! ^_^



Origami as Pure as Snow
Shonen

Cross Grave

My second post in a month!! Cheers guys! Thanks for your support! =D
D.Gray-man rocks more than Bleach now ^_^


I mentioned in the last post that knowing how to superimpose or combine sub-models to form new designs is very important. The model that will be shown in this post is formed by a combination of building blocks of various dimensions and placed strategically around the model to give the planned end result.

Behold, the Cross!



Dang, somehow I just can't get the lighting right ^_^

Next, I'll be showing pictorial instructions to making this model, but you have to be familiar with how to make building blocks of varying dimensions. Here's a little tip to help you control the height of a building block: create a buidling block of height 1, then treat the paper as though it were flat and form an identical building block at exactly the same spot using the same creases. Keep repeating this step and eventually the building block will reach the desired height.

The italicized sentence is extremely important in the combination of sub-models; experienced folders in this form of "pop-out" origami can skip it, but the technique described in the sentence can help beginners to combine sub-models efficiently.

Start with a 32 x 32 grid. Choose a central square which will eventually become the square on the highest point on the cross (refer to the previous photo). As there is no central square (the grid size is even), choose one that is as central as it can be. Next, form 2 identical 2 x 1 x 1 building blocks such that they are on opposite sides of the central square and there are two squares between the central square and each of the building blocks (as to how the dimensions of the building block are to be interpreted, refer to my last post). The result so far:



Next, treat the paper as if it were flat and construct a 1 x 1 x 1 building block whose topmost surface is the central square. As we are treating the paper as if it were flat, do not be disturbed by any places which are thicker when folding.

At this stage, it should look something like this:



Treating the paper as if it were flat, form another 1 x 1 x 1 building block at the exact same spot.



You'd be wondering what these three prongs are for, but you'll see in the next step!

Do that step yet again, i.e. treating the paper as if it were flat, form another 1 x 1 x 1 building block at the exact same spot.



See now? ^_^

The disadvantage of treating the paper as if it were flat is that the paper is not flat, and the layers build up and prove to be a nuisance sometimes, as in this case, where the paper is so thick that I cannot press the layers down flat into the required shape for fear of damaging the structure.

The remaining steps are just performing the previous step again...



... and again and again until the cross reaches a height of your choice. I felt that a height of 7 was the best in this case, but the height can be varied to your wishes.



This is what the paper looked like once I finished folding. My friends from Origami Singapore had recommended "Elephanthide Paper" to me, but true to its name, it refused to submit to creases easily... In this model, the paper near the "joints" puffed up like a spring because of extra thickness there, and the extra paper at the base also piled up because of all the layers of paper accumulated there. Only one way to sort things out... wet-folding!

I restrained the puffed-up parts with rubber bands (I just had to run out of them at that critical moment) and put the cross under the tap for a few seconds, shook off the extra water and laid it on the floor to dry with heavy books (thank goodness for the World Book series) pinning down all those layers at the edges. I left the entire set-up overnight, and removed the rubber bands in the morning to get the final result.

A picture of my valiant efforts to subdue the thickness of paper:



Now for an explanation for the title of this post; Firstly, my parents thought of a tombstone the moment they saw this model (which was a little disappointing T_T), and "Cross Grave" appears in D.Gray-man!

As mark of my new anime affiliation, I will end off this post in a new way...



Origami as Pure as Snow
Shonen

(My eternal thanks to the creator of this excellent picture! ^_^)

有口福

My sincere apologies for the over-one-month gap between posts. Because of my exams, I haven't been able to fold much... Well, its the June Holidays, so I might be able to post a lot more often than usual from now on! Thank you so much for supporting this blog, even though my posts have been rather scarce! *bows* ^_^

Now, to business! Remember my last post which taught you how to fold a "Negative Building Block"? (suggestions for its name are very welcome... heheh) Well, these little sub-models are rather useless unless you can incorporate them into a new design. If you refer back to the model in "Pop-out Prosperity", you'll see that the negative building block is not used on its own in the model; instead, it is used in conjunction with the Building Block to create a "well" structure. One example of such a structure is the "口" radical in the Pop-out Prosperity model; This post will show you how to convert a negative building block into that structure.

Firstly, you have to create a negative building block.



For details on how to fold a negative buidling block, refer to my last post.

I used a 15 x 15 grid for this model instead of the 9 x 9 one used in my last post, because I needed more space to fold the "well structure" than the negative building block itself. This gives a little insight on how paper is sucked up two-dimensionally while we try to build "upwards"... I call it "The Law of Conservation of Paper" - In an isolated model, the amount of paper present is always constant. ^_^

Anyway, for the next step, treat the model at the current step as flat paper (i.e. disregard the presence of the little hole in the center of the model). This step seems to be crucial in the superimposing of certain sub-models in this form of origami. Form a 1 x 3 x 3 building block with the hole at its center.

Before we continue, I feel that we should set down a standard way of referring to the dimensions of a building block so it is easier to refer to.

A building block with dimensions x x y x z has height x, length y and breadth z.
(For problems in the direction of y and z, I will clarify in a future post.)

A view of the model in the current stage:



And you're done! My, that was fast, wasn't it? Let's take a closer look at the "well structure" in the middle:





Now, you can see that the center part of the model corresponds to the "口" radical in the Pop-out Prosperity model.

The superimposing of sub-models does give you interesting results; the important thing is to know which sub-models to use and how to merge them to form a new model.

Now for a view of the underside of the model:



Compare this to the flip-sides of the Pop-out Prosperity model and the Negative Building Block; curious folders may also want to fold a 1 x 3 x 3 building block on a separate piece of paper and compare its reverse side to the picture above.

We're done with the model, but there's one more technique to show you that will help in folding this form of origami. How do we measure how much space the model takes up? Remember that what makes this form of origami unique is that the paper around the model can be extended without bound without affecting the model (because the model itself "pops out" of the paper and does not require edges and corners) and the extended portion can be used to fit in more models so long as the models do not interfere with one another. Hence, it is important for a folder to measure the amount of space his or her model takes up so he or she knows whether another model can be fitted in, or what grid size he or she should use. The space the model takes up is measured in terms of the two-dimensional area on the paper which the model takes up, as opposed to the three-dimensional notation of a building block.

Because of the sucking up of paper inside the model, it is rather impossible to gauge the number of squares it takes up by counting from the inside. However, we can use another approach; counting from the outside! If you've folded the model already, measure the distance from any edge of the paper to one side of the model in terms of the number of squares (in this case, 4) . Do the same for the opposite side (4 again) , and add the distances together (4 + 4 = 8) . subtract that total distance from the grid size (in this case, 15, because a 15 x 15 grid was used) to get the number of squares the model takes up in that dimension (15 - 8 = 7). Repeat for the other dimension (7 again). Thus, in this case, the dimensions of the model is 7 x 7.

Theoretically, a 7 x 7 grid can be used to fold this model; yes, it can be done, all the features of the model will be inside, but the edges of the model will not be locked vertically, and the thickness of the paper will force it to open up a little, resulting in the model not looking very nice. The edges of the model depend on the flat paper surrounding it for locking, so it is best to give a bit of leeway, like a 10 x 10 grid or more ( a 9 x 9 grid would not give enough locking for stiffer paper) .

Ahhh... a long post! I hope that you have enjoyed this post, and thanks for the support!

The next post will be really cool, I'm smoothing out the details for it now, it won't be long!
I'll be cross if you don't come back for the next post! ^_^


Origami as Pure as Snow
shonen