Similarity

I think that the letter V is similar than a Scissors

Similarity

I think that the letter A is similar than a high-heels

Similarity

I think that a comb is similar than the fire

Similarity

I think that a clock is similar than a flower

The divine proportion

El entierro del señor Orgaz, populary called El Entierro del conde Orgaz is a large painting painted by El Greco (1541-1614). Is and oil painting, done for parish of Santo Tomé, in Toledo, between 1586 and 1588. The painting is preserved in this place and is considered one of the best works of the author and is one of the most admired.

In this painting we can see that that the lower part of the painting is based on thedivine proportion, whereas the higher part is based the MysticPentagram and the pentagon which fits in it.


Iratxe and Lucía

The Golden Number

Dalí painted in 1949 a painting called Leda atómica. It represent centuries of mathematics and symbolic tradition (especially Pythagoras ‘ideas). It is a drawing based on the golden number, but it is making in a way that is not easy to see. Looking the sketch which Dalí painting on 1947, we can observe that Dalí care about the geometric aspect. Besides, the painting is based in the Pythagoras’ pentagon.




Lucía and Iratxe

The Golden Number

In Montepellier, Spanish postmodern architect Ricardo Bofill, designed "The square of the number Golden". Ricardo Bofill, is one of most important Spanish architects and is highly regarded in the world of the architecture and urbanism. Place du Nombre d’Or or Plaza in Montellier, France was built in 1984. Its structure responds to the geometric principles of harmony, based on the rules of the number of gold. The perimeter of the square, of twelve metres thick, is occupied by houses. The floor of the square distributes the apartments in three semicircles, four corners and a gateway to the square. The semicircles consist of 12X12metres square modules distributed according to the geometry of the decagon. The curvature is close which causes an appearance of individual homes that stand out, whereas, there is a continuous internal façade. The houses of the corners and the door of the square are quite different.
                               
Iratxe and Lucía

The Golden Number

Goya worked on this painting for the Spanish monarchy, in Madrid from the year 1780 until 1783. This picture represents the Royal family, the Kings Charles IV and Maria Luisa are the key figures.
In this painting the symmetry is not present, despite the fact that at first see it may seem. The axis of the composition is the child of red (dressed as this color to stand out that role) and is aligned with the painting that is on its back. The proportion that Goya used makes the right side, with respect to the axis, smaller than the left side. This is due to the Golden Number that is a synonym for harmony.
To give dynamism to the scene, because as you can see in the image everything seems to be straight lines, we can look at studied line that create the heads and the position of the feet of the people in the painting.

Iratxe and Lucía

SImilarity with the knob.

I think that the knob of the door i similar that the exercise weights.

Similarity with the whale

I think that modern submarines are usually whale-shaped.

DIVINE PROPORTION IN TORONTO

The CN Tower in Toronto, the tallest tower and freestanding structure in the world, has contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of Phi!

MARÍA CARRACEDO DE VEGA Y PILAR SUAREZ 3ºB

DIVINE PROPORTION IN TAJ MAHAL

Renaissance artists of the 1500's in the time of Leonardo Da Vinci knew it as the Divine Proportion. In India, it was used in the construction of the Taj Mahal, which was completed in 1648.

MARIA CARRACEDO Y PILAR SUAREZ 3ºB

PHI IN PYRAMIDES

Phi , the Golden Section, has been used by mankind for centuries in architecture
Its use started as early as with the Egyptians in the design of the pyramids. When the basic phi relationships are used to create a right triangle, it forms the dimensions of the great pyramids of Egypt, with the geometry shown below creating an angle of 51.83 degrees, the cosine of which is phi, or 0.618.

MARÍA CARRACEDO Y PILAR SUÁREZ 3ºB

Fibonacci's Rabbits

The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was...

How many pairs will there be in one year?

1. At the end of the first month, they mate, but there is still one only 1 pair.
2. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
3. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
4. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.

The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Can you see how the series is formed and how it continues? If not, look at the answer!

The first 300 Fibonacci numbers are here and some questions for you to answer.

Now can you see why this is the answer to our Rabbits problem? If not, here's why.
Another view of the Rabbit's Family Tree:

Both diagrams above represent the same information. Rabbits have been numbered to enable comparisons and to count them, as follows:

• All the rabbits born in the same month are of the same generation and are on the same level in the tree.
• The rabbits have been uniquely numbered so that in the same generation the new rabbits are numbered in the order of their parent's number. Thus 5, 6 and 7 are the children of 0, 1 and 2 respectively.
• The rabbits labelled with a Fibonacci number are the children of the original rabbit (0) at the top of the tree.
• There are a Fibonacci number of new rabbits in each generation, marked with a dot.
• There are a Fibonacci number of rabbits in total from the top down to any single generation.

Alexandra Brancovean, Candela Megido, Aida Zapico

similarity

I think that a ladder plane is similar to a high heels.

similarity

I think that a toothbrush is similar to a comb.

similarity

I think that a boomerang is similar to the moon.

similarity

I think that a clock is similar to a dish

The Golden Number in nature and architecture.

The Golden Number (also called Phi) is an important number. It is present in nature proportions such as in shells or in pine cones.



Greeks first used this number in buildings because they thought it was the beautiness number so, if the buildings proportions were based on Phi number, the construction would be beautyful as well. Buildings such as in the Partenon.



Since Greeks, Phi number became more used in other countrys in architecture (As in Eiffel thower) but also in paintings as in "A Venus Birth" or in "La Gioconda"


EIFFEL TOWER



THE BIRTH OF A VENUS


LA GIOCONDA


ILLÁN RIESTRA NAVA 3ºA

A special number: Phi

Among all rectangles, there is one which is more beautiful for the people. It´s an special rectangle. If you divide the longest side by the shortest side you obtain 1,6180339... and if you cut a square whose side is equal to the small side of the rectangle we obtain a rectangle similar to the original. This rectangle is used by designers, engineers, painters... to do a lot of things: credit cards snuff packages, buildings, pictures, etc.

Examples:

THE VENUS OF MILO

Venus´s navel divides the segment of the total height as the golden ratio.

SNUFF PACKAGES / CREDIT CARDS

Snuff packages has got the golden proportion and credit cards, too.

DURERO´S SPIRAL

It´s a spiral embedded in golden rectangles.

NOTRE-DAME

The façade of the Notre-Dame has got the golden proportion, because number Phi is related to the divinity.

THE GOLDEN PROPORTION

The positive solution of the ecuation x(x-1)-1=0 is 1,6180339887... This number is called phi, or the Golden Number and it's very very special.

In the environment, lots of things are made related to this number, due to the beauty of the proportion this number makes. Along the history, many cultures have discovered this number and they have tried to reproduce it in the art, so it's very common to see it in paintings, sculptures, buildings,...

There are many examples of this proportion. One of it it's the Keops Pyramid. Phi appears there not once, but many times. For example, the height of one face divided into the half of the side of the base, it's exactly 1,6180339887...

Another example is the famous New York building of United Nations. It's divided into three golden rectangles (which proportion is phi).

The last example is in the Sandro Boticcelli's painting El Nacimiento de Venus. The body of Venus takes exactly the golden proportion, but as well, the total dimensions of the painting forms a golden rectangle.

Pelayo Fernández Arias 3ºA

similarity

I think that a scissors are similar to stork beats.

Diego de Velazquez used the golden section to represent the Meninas, one of his best known works.

He used it to differentiate the bottom, with characters, and the top, with gloom and darkness.

Pilar Suarez de Cepeda y Maria Carracedo

Similarity with the moon

I think that the Cheshire Cat´s smile is similar than the crescent moon.