Materials for Origami

Get your Modeling tools ready...

Having seen what makes Origami,lets see what it takes to make Origami.

First lets start with the basic tool and the only tool(almost).. The paper.
Though readily available, it takes a right kind of paper for different models to bring out its best... There are various kinds of paper that can be used for Origami. The different kinds are listed below... Go on... Grab the right paper you need for your model..

• Origami paper comes in many grades, types, and sizes. They are usually square in shape, though some are circular or rectangular. The most common type is colored on one side and white on the bottom size.
• Duo paper has one color on the top, and another color on the bottom. This type of paper is great for models where both sides of the paper will be visible.
• Foil paper looks like aluminum foil on one side and white on the bottom side. This paper is a little more difficult to fold because, once folded, it will make a crease mark. In other words, there’s no room for mistakes with this type of paper.
• Washi and chiyogami paper: Washi simply means handmade Japanese paper. Washi is more textured and softer than ordinary office paper. There are lots of different kinds of washi made from different plant fiber. Chiyogami is a kind of washi with traditional Japanese imagery imprinted on it.
• Really big paper: The biggest origami paper we found was from Paper Jade (31” x 22”). If you need even bigger paper, try buying a roll of wrapping paper and cutting it to size with a cutting tool.
• Really small paper: are great for making origami models for greeting cards and origami jewelry.
• Circular Origami Paper There are very few sources of circular origami paper because there are relatively few diagrams starting with a circle.However, circular paper is often used in kirigami.
• Animal print origami paper: for kids, it's sometimes nice to use origami paper with animal prints on it. Be warned though: sometimes the animal patterns look great on a flat sheet of paper, but they don't match up properly when folded. Still... kids are imaginative and would appreciate them.

For those of you, who were unable to get the right size of paper get your second tool ready...
The paper cutter...

How to Cut Paper

The simplest way to cut paper is with a pair of scissors. Alternatively, you can use a sharp knife and slice along the inside of a folded edge. This may leave an undesirable jagged edge.

About Paper Cutters

If you are a serious paper folder, you might consider investing in a paper cutter. There are two kinds of paper cutters: the guillotine type and the razor type.

• The guillotine type has a lever which you can press downwards and it will “chop” the paper. These cutters are good, but when they are well used, the lever may become loose. At this point, it is necessary to manually push the lever close to the cutting edge before you chop.
  

• The razor type has a sharp blade which will “slice” paper as you move the blade up and down. After much use, the blade may become dull and you may wish to buy a replacement blade.
  

• A third option is a self-healing cutting mat often used in quilting. These mats are made of a composite material so that they are not damaged by cutting knives. Cutting mats often have 1” and ¼” grid lines, but you still need a ruler and a hobby knife (such as a rotary cutter) to make the cut.

Once, you have these both... you are ready for the journey to the wonderful world of Origami...

Simple Applications of Origami

Mathematics and Origami

Wondering how these both are connected? Well, You can teach Mathematical principles using the techniques of Origami. The most common of this is the demonstration of the Pythagoras theorem, using the simple foldings of origami.. Now-a-days, more and more scientists are integrating origami into studies. Folding and unfolding problems have applications in robotics, hydraulic tube bending, and have connections to protein folding, sheet-metal bending, packaging, and air-bag folding. There are still lot more to know about Origami in the future posts.. So hang on..

Kirigami

Kirigami

Many scrapbookers are familiar with the art of origami -- the decorative Japanese paper folding technique. Less well-known is the art of kirigami, which in translation means "cutting paper." Like origami, kirigami begins with the folding of a thin paper, but ends with the cutting of shapes into the folded edges.

The powerful dot

"Bindi - The Energy behind it"

Exotic women wearing a red dot on their forehead...Have you ever wondered why the women of India wear the little red dot on their forehead? Many people think that this little red dot has something to do with the caste system of India. The truth of the matter is that they have absolutely nothing to do with the caste system of India. They are such a part of India's heritage and culture that we must make mention of their value.

The very positioning of the bindi is significant. The area between the eyebrows is the seat of latent wisdom. This area is known as the "Agna" (6th chakra) meaning "command". It is said to control various levels of concentration attained through meditation. The central point of this area is the "Bindu" wherein all experience is gathered in total concentration. Tantric tradition has it that during meditation, the "kundalini" - the latent energy that lies at the base of the spine is awakened and rises to the point of sahasrara (7th chakra) situated in the head or brain. The central point, the bindhu, becomes therefore a possible outlet for this potent energy. It is believed that the red kumkum lies between the eyebrows to retain energy in the human body.

Now-a-days…There are lots of Indian women, especially young "modern" girls, who don't wear it because it doesn't look "modern" or “western”!!... Here is to all you girls and women. India is known for its culture, and there are many countries and nations which are borrowing the culture from India. Fashion does not always mean western. For those of you whe are shying away to wear bindi just because you don’t think it is modern.. rethink.. You may in fact create a new fashion statement with it. And moreover.. We don't need to impress anyone on anything! Ours is a unique identity with many beautiful features, one being the ever-enchanting bindi. It is something we shouldn't allow to fade away like some old fad!

The fascinating world of Origami

"Origami!!!!!!!!!"

Origami...... It is one of the fascinating things I've always wanted to learn... There maybe many like me out there... So here is for all u ppl.... Let's learn Origami step by step...

First, lets formally look into the world of Origami and know its true meaning... The Art of Origami is one of the cultural treasures of mankind that offers us enormous amounts of joy.

Origami is the ancient Japanese art of paper folding. The Japanese word "ORU" means "to fold" and "KAMI" means "paper".

So that finishes of the formal definition of Origami....

Exploring deeper into it... What exactly makes up this Origami and where lies its Charm?

Well, much of the charm of Origami lies in its simplicity. There lies a square, there are the folds. There are only two types of folds:

1. The mountain folds (which form a ridge)
2. The valley folds (which form a trough)

So, Square + Mountain folds + Valley folds is the recipe for nearly all of Origami

How simple can it get?

Well, It is almost simple once we get to learn it.

More about Origami and some models in the following posts... So hold on...

Sutra 2 - All from 9 and Last from 10

With this method you only ever need multiplication tables up to 5 times 5. It is one of many ancient Indian sutras and this one involves a cross subtraction method which, according to old historical traditions, is responsible for the acceptance of the ´ mark as the sign of multiplication. Here is a very simple example of the method. Can you give a good explanation of WHY it works?

Suppose we want to multiply 9 by 7. We subtract each number from 10 and, using these differences (or deficiencies), write:

9-1

7-3

6 3

The product has two parts, left and right.
To get the right part (or units digit) multiply the deficiencies (1×3)
The left hand digit (tens digit) of the answer can be found in four different ways. Why do they all give the same answer?

1. Subtract 10 from the sum of the two given numbers (9+7=16, 16-10=6)
2. Subtract the sum of the two deficiencies (1+3=4) from 10 and you get 6.
3. Cross subtract (9-3=6)
4. Cross subtract (7-1=6)

This gives the answer 63.

Here are some more examples. Try some of your own.

9-1	8-2	9-1	8-2
6-4	7-3	9-1	5-5
5 4	5 6	8 1	4 0	Note: Here you have to express 5 times 2 as 1 ten and 0 units.

Sutra 1 - By one more than the one before

By one more than the one before

"Ekādhikena Pūrveṇa" is the Sanskrit term for "[by] One more than the previous one". It provides a simple way of calculating values like 1/x9 (e.g: 1/19, 1/29, etc). The sūtra can be used for multiplying as well as dividing algorithms.

Example: let's calculate 1/19. In this case, x = 1 . For the multiplication algorithm (working from right to left), the method is to start by denoting the dividend, 1, as the first (rightmost) digit of the result. Then multiply that digit by 2 (i.e.: x + 1 ), and denote that next digit to its left. If the result of this multiplication was greater than 10, denote (value – 10) and keep the "1" as "carry over" which you'll add to the next digit directly after multiplying.

The preposition "by" means the operations this formula concerns are either multiplication or division. [In case of addition/subtraction preposition "to" or "from" is used.] Thus this formula is used for either multiplication or division. It turns out that it is applicable in both operations.

Note: This sūtra can also be applied to multiplication of numbers with the same first digit and the sum of their last unit digits is 10.

An interesting sub-application of this formula is in computing squares of numbers ending in five. Examples:

35×35 = ((3×3)+3),25 = 12,25 and 125×125 = ((12×12)+12),25 = 156,25

or by the sūtra, multiply "by one more than the previous one."

35×35 = ((3×4),25 = 12,25 and 125×125 = ((12×13),25 = 156,25

The latter portion is multiplied by itself (5 by 5) and the previous portion is square of first digit or first two digit (3×3) or (12×12) and adding the same digit in that figure (3or12) resulting in the answer 1225.

(Proof) This is a simple application of (a + b)² = a² + 2ab + b² when a = 10c and b = 5, i.e.

It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Examples:

37 × 33 = (3 × 4),7 × 3 = 12,21

29 × 21 = (2 × 3),9 × 1 = 6,09

This uses (a + b)(a − b) = a² − b² twice combined with the previous result to produce:

(10c + 5 + d)(10c + 5 − d) = (10c + 5)² − d² = 100c(c + 1) + 25 − d² = 100c(c + 1) + (5 + d)(5 − d).

We illustrate this sūtra by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods.

Method 1: example: using multiplication to calculate 1/19

For 1/19, since 19 is not divisible by 2 or 5, the fractional result is a purely circulating decimal. (If the denominator contains only factors 2 and 5, the result is a purely non-circulating decimal, else it is a mixture of the two: a short non-circulating sequence of digits, followed by an endless repetition.) Each factor of 2 or 5 or 10 in the denominator gives one fixed decimal digit.

So we start with the last digit of the result, being the dividend:

1

Multiply this by "one more", that is, 2 (this is the "key" digit from 'Ekādhikena')

21

Multiplying 2 by 2, followed by multiplying 4 by 2

421 → 8421

Now, multiplying 8 by 2, sixteen

68421

1 ← carry

multiplying 6 by 2 is 12 plus 1 carry gives 13

368421

1 ← carry

Continuing

7368421 → 47368421 → 947368421

1

Now we have 9 digits of the answer. There are a total of 18 digits (= denominator − numerator) in the answer computed by complementing the lower half (with its complement from nine):

052631578

947368421

Thus the result is 1/19 = 0.052631578,947368421 repeating.

1
21
421
8421
68421 (carry 1) – we got 16, so we keep 6 and carry 1
368421 (carry 1) – we get 6*2 + carry 1 = 13, so we keep 3 and carry one

do this to eighteen digits (19–1. If you picked up 1/29,
you'll have to do it till 28 digits). You'll get the following
1/19 = 052631578947368421
     10100111101011000

Run this on your favorite calculator and check the result!

Method 2: example: using division to calculate 1/19

The earlier process can also be done using division instead of multiplication. We start again with 1 (dividend of "1/x9"), dividing by 2 (" x + 1 "). We divide 1 by 2, answer is 0 with remainder 1

result .0

Next 10 divided by 2 is five

.05

Next 5 divided by 2 is 2 with remainder 1

.052

next 12 (remainder,2) divided by 2 is 6

.0526

and so on.

Other fractions can sometimes be converted into the format of "d/x9"; as another example, consider 1/7, this is the same as 7/49 which has 9 as the last digit of the denominator. The previous digit is 4, by one more is 5. So we multiply (or divide) by 5, that is:

…7 → 57 → 857 → 2857 → 42857 → 142857 → .142,857 (stop after 7 − 1 digits)

Carry overs - 3 2 4 1 2

Next step into Vedic Mathematics...

Having known about Vedic Mathematics how about getting to know some of the basics of it... So here they are... Don't worry if u do not make a head or tail of them... We'll look into the details one by one in the later posts...

Below is a list of the sūtras, translated from Sanskrit into English: "By one more than the previous one" "All from 9 and the last from 10" "Vertically and crosswise (multiplications)" "Transpose and apply" "Transpose and adjust (the coefficient)" "If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero" By the Parāvartya rule "If one is in ratio, the other one is zero." "By addition and by subtraction." By the completion or non-completion (of the square, the cube, the fourth power, etc.) Differential calculus By the deficiency Specific and general The remainders by the last digit "The ultimate (binomial) and twice the penultimate (binomial) (equals zero)," "Only the last terms," By one less than the one before The product of the sum All the multipliers Subsūtras or corollaries "Proportionately" The remainder remains constant "The first by the first and the last by the last" For 7 the multiplicand is 143 By osculation Lessen by the deficiency "Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square (of the deficiency)" "By one more than the previous one" "Last totaling ten" The sum of the products "By (alternative) elimination and retention (of the highest and lowest powers)" By mere observation The product of the sum is the sum of the products On the flag

Vedic Mathematics - Number rules the universe

Hi...

Afraid of Mathematics??? or Want to master it?? Try Vedic Mathematics - get rid of the fear and master the subject... It is a really cool concept consisting of a list of 16 basic sutras, or aphorisms. The 16 sutras are cryptic in the beginning, but practise unleashes their true power...

You need to see Vedic Mathematics in action to appreciate it fully the many special aspects and features. The main points are:

1) The system rediscovered by Bharati Krsna is based on sixteen formulae (or Sutras) and some sub-formulae (sub-Sutras). These Sutras are given in word form: for example Vertically and Crosswise and By One More than the One Before. These Sutras can be related to natural mental functions such as completing a whole, noticing analogies, generalisation and so on.

2) Not only does the system give many striking general and special methods, previously unknown to modern mathematics, but it is far more coherent and integrated as a system.

3) Vedic Mathematics is a system of mental mathematics (though it can also be written down).

Many of the Vedic methods are new, simple and striking. They are also beautifully interrelated so that division, for example, can be seen as an easy reversal of the simple multiplication method (similarly with squaring and square roots).

This is in complete contrast to the modern system. Because the Vedic methods are so different to the conventional methods, and also to gain familiarity with the Vedic system, it is best to practice the techniques as you go along.

Different Colours of Friendship

Hi everyone...

This is my first blog entry. Today happens to be Friendship day... So wishing everyone Happy Friendship day first... I thought of spending my time with friends today, but had to put off the idea...and I don't regret it. I had a different experience today...

A few days back I volunteered myself to teach some under-privileged students and today was my first day with them. I did not know what to expect, but when I saw them I was moved. I was welcomed by the head of the NGO there and he took me the actual study place. There were about 10-15 people in a small room, both children and grown-ups. They welcomed with a very enthusiastic "Good Afternoon Ma'am". Then one by one they introduced themselves. Some of the names I remember are Vignesh, Raja, Preeti, Selvi, Naveen, Selvaraghavan, Chandru... Then I was briefed about the undertakings of the NGO. The grown ups had a different tale to tell. They were all drop-outs who left studying due to lack of interest. Now, they had realized their mistake and they want to rectify themselves. There were queries about how to speak English fluently, how to avoid spelling mistakes and the like. This is one part of the story...

After few minutes of my arrival, I was offered fruit drink. After some hesitation (due to good manners taught by our parents), I finally accepted the drink. The head of the NGO had been working for about 25 years in the place and made some tremendous improvements and rehabilitation there. He was in good rapport with the people around there. When he was offered the fruit drink, he did not accept it and gave it to a child. What touched me most was that, he did not drink it all by himself, instead he shared it(about half a glass of fruit-drink) with all his friends(the entire class), and then had just a small pint to himself. I was embarrassed. I saw the true meaning of Friendship there...

On my way back I reflected upon my experience. Friendship as most of us know is hanging out with friends, taking pictures together and most importantly helping them through thick and thin. Joy for us is when we receive those birthday gifts, have birthday parties...But today I saw the joy of the entire class in sharing those tiny and not so important pleasures of life. Though they can not afford to live a normal life, they live their life to the fullest. Hats off to them...

With this memorable experience I am signing off with this cute Greeting card